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sagemath/sagemath-pari2.7.patch
pcpa fa9204b9a9 Update to sagemath 6.2
2014-05-27 10:47:12 -03:00

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From f26a0a0136b0067e12b05c207e0939ba5654a4ee Mon Sep 17 00:00:00 2001
From: Jeroen Demeyer <jdemeyer@cage.ugent.be>
Date: Mon, 05 May 2014 08:27:34 +0000
Subject: Upgrade to PARI-2.7.1
diff --git a/src/doc/de/tutorial/interfaces.rst b/src/doc/de/tutorial/interfaces.rst
index 9ace22d..9f79b8f 100644
--- a/src/doc/de/tutorial/interfaces.rst
+++ b/src/doc/de/tutorial/interfaces.rst
@@ -135,7 +135,7 @@ Dinge mit ihr berechnen.
sage: e.elltors()
[1, [], []]
sage: e.ellglobalred()
- [10351, [1, -1, 0, -1], 1]
+ [10351, [1, -1, 0, -1], 1, [11, 1; 941, 1], [[1, 5, 0, 1], [1, 5, 0, 1]]]
sage: f = e.ellchangecurve([1,-1,0,-1])
sage: f[:5]
[1, -1, 0, 4, 3]
diff --git a/src/doc/de/tutorial/tour_advanced.rst b/src/doc/de/tutorial/tour_advanced.rst
index b5fff8e..9308ac7 100644
--- a/src/doc/de/tutorial/tour_advanced.rst
+++ b/src/doc/de/tutorial/tour_advanced.rst
@@ -359,12 +359,12 @@ Nun berechnen wir mehrere Invarianten von ``G``:
sage: G.gens()
(Dirichlet character modulo 20 of conductor 4 mapping 11 |--> -1, 17 |--> 1,
- Dirichlet character modulo 20 of conductor 5 mapping 11 |--> 1, 17 |--> -i)
+ Dirichlet character modulo 20 of conductor 5 mapping 11 |--> 1, 17 |--> i)
sage: G.unit_gens()
(11, 17)
sage: G.zeta()
- -i
+ i
sage: G.zeta_order()
4
diff --git a/src/doc/en/bordeaux_2008/nf_galois_groups.rst b/src/doc/en/bordeaux_2008/nf_galois_groups.rst
index c67867b..4061d96 100644
--- a/src/doc/en/bordeaux_2008/nf_galois_groups.rst
+++ b/src/doc/en/bordeaux_2008/nf_galois_groups.rst
@@ -311,7 +311,7 @@ ideal classes containing :math:`(5,\sqrt{-30})` and
sage: category(C)
Category of groups
sage: C.gens()
- (Fractional ideal class (5, a), Fractional ideal class (3, a))
+ (Fractional ideal class (2, a), Fractional ideal class (3, a))
Arithmetic in the class group
@@ -328,17 +328,17 @@ means "the product of the 0th and 1st generators of the class group
sage: K.<a> = QuadraticField(-30)
sage: C = K.class_group()
sage: C.0
- Fractional ideal class (5, a)
+ Fractional ideal class (2, a)
sage: C.0.ideal()
- Fractional ideal (5, a)
+ Fractional ideal (2, a)
sage: I = C.0 * C.1
sage: I
- Fractional ideal class (2, a)
+ Fractional ideal class (5, a)
Next we find that the class of the fractional ideal
:math:`(2,\sqrt{-30}+4/3)` is equal to the ideal class
-:math:`I`.
+:math:`C.0`.
.. link
@@ -348,7 +348,7 @@ Next we find that the class of the fractional ideal
sage: J = C(A)
sage: J
Fractional ideal class (2/3, 1/3*a)
- sage: J == I
+ sage: J == C.0
True
diff --git a/src/doc/en/tutorial/interfaces.rst b/src/doc/en/tutorial/interfaces.rst
index b1dc175..0d3c598 100644
--- a/src/doc/en/tutorial/interfaces.rst
+++ b/src/doc/en/tutorial/interfaces.rst
@@ -132,7 +132,7 @@ things about it.
sage: e.elltors()
[1, [], []]
sage: e.ellglobalred()
- [10351, [1, -1, 0, -1], 1]
+ [10351, [1, -1, 0, -1], 1, [11, 1; 941, 1], [[1, 5, 0, 1], [1, 5, 0, 1]]]
sage: f = e.ellchangecurve([1,-1,0,-1])
sage: f[:5]
[1, -1, 0, 4, 3]
diff --git a/src/doc/en/tutorial/tour_advanced.rst b/src/doc/en/tutorial/tour_advanced.rst
index 5069d4b..32717e4 100644
--- a/src/doc/en/tutorial/tour_advanced.rst
+++ b/src/doc/en/tutorial/tour_advanced.rst
@@ -357,12 +357,12 @@ We next compute several invariants of ``G``:
sage: G.gens()
(Dirichlet character modulo 20 of conductor 4 mapping 11 |--> -1, 17 |--> 1,
- Dirichlet character modulo 20 of conductor 5 mapping 11 |--> 1, 17 |--> -i)
+ Dirichlet character modulo 20 of conductor 5 mapping 11 |--> 1, 17 |--> i)
sage: G.unit_gens()
(11, 17)
sage: G.zeta()
- -i
+ i
sage: G.zeta_order()
4
diff --git a/src/doc/fr/tutorial/interfaces.rst b/src/doc/fr/tutorial/interfaces.rst
index 147fd49..e420350 100644
--- a/src/doc/fr/tutorial/interfaces.rst
+++ b/src/doc/fr/tutorial/interfaces.rst
@@ -133,7 +133,7 @@ calculs avec.
sage: e.elltors()
[1, [], []]
sage: e.ellglobalred()
- [10351, [1, -1, 0, -1], 1]
+ [10351, [1, -1, 0, -1], 1, [11, 1; 941, 1], [[1, 5, 0, 1], [1, 5, 0, 1]]]
sage: f = e.ellchangecurve([1,-1,0,-1])
sage: f[:5]
[1, -1, 0, 4, 3]
diff --git a/src/doc/fr/tutorial/tour_advanced.rst b/src/doc/fr/tutorial/tour_advanced.rst
index fbaa3ac..92e300d 100644
--- a/src/doc/fr/tutorial/tour_advanced.rst
+++ b/src/doc/fr/tutorial/tour_advanced.rst
@@ -357,12 +357,12 @@ Nous calculons ensuite différents invariants de ``G``:
sage: G.gens()
(Dirichlet character modulo 20 of conductor 4 mapping 11 |--> -1, 17 |--> 1,
- Dirichlet character modulo 20 of conductor 5 mapping 11 |--> 1, 17 |--> -i)
+ Dirichlet character modulo 20 of conductor 5 mapping 11 |--> 1, 17 |--> i)
sage: G.unit_gens()
(11, 17)
sage: G.zeta()
- -i
+ i
sage: G.zeta_order()
4
diff --git a/src/doc/ru/tutorial/interfaces.rst b/src/doc/ru/tutorial/interfaces.rst
index 8baa52c..497707b 100644
--- a/src/doc/ru/tutorial/interfaces.rst
+++ b/src/doc/ru/tutorial/interfaces.rst
@@ -128,7 +128,7 @@ Sage использует С-библиотеку PARI, чтобы поддер<D0B5>
sage: e.elltors()
[1, [], []]
sage: e.ellglobalred()
- [10351, [1, -1, 0, -1], 1]
+ [10351, [1, -1, 0, -1], 1, [11, 1; 941, 1], [[1, 5, 0, 1], [1, 5, 0, 1]]]
sage: f = e.ellchangecurve([1,-1,0,-1])
sage: f[:5]
[1, -1, 0, 4, 3]
diff --git a/src/doc/ru/tutorial/tour_advanced.rst b/src/doc/ru/tutorial/tour_advanced.rst
index d9ab2c5..b7a64a7 100644
--- a/src/doc/ru/tutorial/tour_advanced.rst
+++ b/src/doc/ru/tutorial/tour_advanced.rst
@@ -322,12 +322,12 @@ Sage может вычислить тороидальный идеал непл<D0BF>
sage: G.gens()
(Dirichlet character modulo 20 of conductor 4 mapping 11 |--> -1, 17 |--> 1,
- Dirichlet character modulo 20 of conductor 5 mapping 11 |--> 1, 17 |--> -i)
+ Dirichlet character modulo 20 of conductor 5 mapping 11 |--> 1, 17 |--> i)
sage: G.unit_gens()
(11, 17)
sage: G.zeta()
- -i
+ i
sage: G.zeta_order()
4
diff --git a/src/ext/pari/dokchitser/computel.gp b/src/ext/pari/dokchitser/computel.gp
index f7f5d66..9768874 100644
--- a/src/ext/pari/dokchitser/computel.gp
+++ b/src/ext/pari/dokchitser/computel.gp
@@ -169,7 +169,7 @@ errprint(x)=if(type(x)=="t_COMPLEX",x=abs(x));
{
gammaseries(z0,terms,
- Avec,Bvec,Qvec,n,z,err,res,c0,c1,c2,c3,sinser,reflect,digits,srprec,negint)=
+ Avec,Bvec,Qvec,n,z,err,res,c0,c1,c2,c3,sinser,reflect,digits_,srprec,negint)=
srprec=default(seriesprecision);
if (z0==real(round(z0)),z0=real(round(z0))); \\ you don't want to know
negint=type(z0)=="t_INT" && z0<=0; \\ z0 is a pole
@@ -181,17 +181,17 @@ gammaseries(z0,terms,
if (z0==1, res=gamma(1+x),
if (z0==2, res=gamma(1+x)*(1+x),
\\ otherwise use Luke's rational approximations for psi(x)
- digits=default(realprecision); \\ save working precision
- default(realprecision,digits+3); \\ and work with 3 digits more
+ digits_=default(realprecision); \\ save working precision
+ default(realprecision,digits_+3); \\ and work with 3 digits more
reflect=real(z0)<0.5; \\ left of 1/2 use reflection formula
if (reflect,z0=1-z0);
- z=subst(Ser(precision(1.*z0,digits+3)+X),X,x);
+ z=subst(Ser(precision(1.*z0,digits_+3)+X),X,x);
\\ work with z0+x as a variable gives power series in X as an answer
Avec=[1,(z+6)/2,(z^2+82*z+96)/6,(z^3+387*z^2+2906*z+1920)/12];
Bvec=[1,4,8*z+28,14*z^2+204*z+310];
Qvec=[0,0,0,Avec[4]/Bvec[4]];
n=4;
- until(err<0.1^(digits+1.5), \\ Luke's recursions for psi(x)
+ until(err<0.1^(digits_+1.5), \\ Luke's recursions for psi(x)
c1=(2*n-1)*(3*(n-1)*z+7*n^2-9*n-6);
c2=-(2*n-3)*(z-n-1)*(3*(n-1)*z-7*n^2+19*n-4);
c3=(2*n-1)*(n-3)*(z-n)*(z-n-1)*(z+n-4);
@@ -208,7 +208,7 @@ gammaseries(z0,terms,
if (negint,sinser[1]=0); \\ taking slight care at integers<0
res=subst(Pi/res/Ser(sinser),x,-x);
);
- default(realprecision,digits);
+ default(realprecision,digits_);
)))));
default(seriesprecision,srprec);
res;
@@ -231,10 +231,10 @@ fullgamma(ss) = if(ss!=lastFGs,lastFGs=ss;\
{
fullgammaseries(ss,extraterms,
- digits,GSD)=
- digits=default(realprecision);
+ digits_,GSD)=
+ digits_=default(realprecision);
if (lastFGSs!=ss || lastFGSterms!=extraterms,
- GSD=sum(j=1,numpoles,(abs((ss+poles[j])/2-round(real((ss+poles[j])/2)))<10^(2-digits)) * PoleOrders[j] )+extraterms;
+ GSD=sum(j=1,numpoles,(abs((ss+poles[j])/2-round(real((ss+poles[j])/2)))<10^(2-digits_)) * PoleOrders[j] )+extraterms;
lastFGSs=ss;
lastFGSterms=extraterms;
lastFGSval=subst(prod(j=1,length(gammaV),gammaseries((ss+gammaV[j])/2,GSD)),x,S/2);
diff --git a/src/ext/pari/simon/ell.gp b/src/ext/pari/simon/ell.gp
index 0d130f4..acd807c 100644
--- a/src/ext/pari/simon/ell.gp
+++ b/src/ext/pari/simon/ell.gp
@@ -84,6 +84,11 @@
*/
+
+nf_scalar_or_multable_to_alg(nf, z) = {
+ if (type(z) == "t_MAT", nfbasistoalg(nf, z[,1]), z);
+}
+
{
\\
\\ Usual global variables
@@ -505,7 +510,7 @@ if( DEBUGLEVEL_ell >= 5, print(" end of nfissquaremodp"));
if( DEBUGLEVEL_ell >= 5, print(" end of nfissquaremodp"));
return(0));
if( valap,
- zlog = ideallog(nf,a*(nfbasistoalg(nf,p[5])/p.p)^valap,zinit)
+ zlog = ideallog(nf,a*(nf_scalar_or_multable_to_alg(nf,p[5])/p.p)^valap,zinit)
,
zlog = ideallog(nf,a,zinit));
for( i = 1, #zinit[2][2],
@@ -533,7 +538,7 @@ if( DEBUGLEVEL_ell >= 5, print(" end of nfissquaremodpq"));
if( DEBUGLEVEL_ell >= 5, print(" end of nfissquaremodpq"));
return(0));
zinit = idealstar(nf,idealpow(nf,p,q-vala),2);
- zlog = ideallog(nf,a*nfbasistoalg(nf,p[5]/2)^vala,zinit);
+ zlog = ideallog(nf,a*nf_scalar_or_multable_to_alg(nf,p[5]/2)^vala,zinit);
for( i = 1, #zinit[2][2],
if( !(zinit[2][2][i]%2) && (zlog[i]%2),
if( DEBUGLEVEL_ell >= 5, print(" end of nfissquaremodpq"));
@@ -556,7 +561,7 @@ if( DEBUGLEVEL_ell >= 5, print(" end of nfsqrtmodpq"));
return(0));
if( f%2, error("nfsqrtmodpq: a is not a square, odd valuation"));
a = nfalgtobasis(nf,a);
- if( f, aaa = nfeltpow(nf,nfeltdiv(nf,a,p[5]/p.p),f), aaa = a);
+ if( f, aaa = nfeltpow(nf,nfeltdiv(nf,a,nf_scalar_or_multable_to_alg(nf,p[5]/p.p)),f), aaa = a);
p_hnf = idealhnf(nf,p);
p_ini = nfmodprinit(nf,p);
if( DEBUGLEVEL_ell >= 5, print(" p_hnf = ",p_hnf));
@@ -680,7 +685,7 @@ if( DEBUGLEVEL_ell >= 5, print("fin de nflemma7"));
if( q > 2*v,
if( DEBUGLEVEL_ell >= 5, print("fin de nflemma7"));
return(-1));
- if( nfissquaremodpq(nf,gx*nfbasistoalg(nf,p[5]/2)^lambda,p,q),
+ if( nfissquaremodpq(nf,gx*nf_scalar_or_multable_to_alg(nf,p[5]/2)^lambda,p,q),
if( DEBUGLEVEL_ell >= 5, print("fin de nflemma7"));
return(1))
,
@@ -694,7 +699,7 @@ if( DEBUGLEVEL_ell >= 5, print("fin de nflemma7"));
if( q > 2*v,
if( DEBUGLEVEL_ell >= 5, print("fin de nflemma7"));
return(-1));
- if( nfissquaremodpq(nf,gx*nfbasistoalg(nf,p[5]/2)^lambda,p,q),
+ if( nfissquaremodpq(nf,gx*nf_scalar_or_multable_to_alg(nf,p[5]/2)^lambda,p,q),
if( DEBUGLEVEL_ell >= 5, print("fin de nflemma7"));
return(0))
);
@@ -772,7 +777,7 @@ if( DEBUGLEVEL_ell >= 4, print(" end of nfqp_solublebig"));
cont = idealval(nf,polcoeff(pol,0),p);
for( i = 1, deg,
if( cont, cont = min(cont,idealval(nf,polcoeff(pol,i),p))));
- if( cont, pi = nfbasistoalg(nf,p[5]/p.p));
+ if( cont, pi = nf_scalar_or_multable_to_alg(nf,p[5]/p.p));
if( cont > 1, pol *= pi^(2*(cont\2)));
\\ On essaye des valeurs de x au hasard
@@ -984,7 +989,7 @@ if( DEBUGLEVEL_ell >= 2, print(" Algorithm of 2-descent via isogenies"));
if( DEBUGLEVEL_ell >= 3, print(" starting bnfell2descent_viaisog"));
if( variable(bnf.pol) != 'y,
error("bnfell2descent_viaisog: the variable of the number field must be y"));
- ell = ellinit(Mod(lift(ell),bnf.pol),1);
+ ell = ellinit(Mod(lift(ell),bnf.pol));
if( ell.disc == 0,
error("bnfell2descent_viaisog: singular curve !!"));
@@ -1231,7 +1236,7 @@ if( DEBUGLEVEL_ell >= 4, print(" bbbnf.clgp = ",bbbnf.clgp));
SL = idealfactor(bbbnf,SL1)[,1]~;
sunL = bnfsunit(bbbnf,SL);
fondsunL = concat(bbbnf.futu,vector(#sunL[1],i,nfbasistoalg(bbbnf,sunL[1][i])));
- normfondsunL = norm(rnfeltabstorel( rrrnf,fondsunL));
+ normfondsunL = vector(#fondsunL, i, norm(rnfeltabstorel(rrrnf,fondsunL[i])));
SK = idealfactor(bnf,idealnorm(bbbnf,SL1))[,1]~;
sunK = bnfsunit(bnf,SK);
fondsunK = concat(bnf.futu,vector(#sunK[1],i,nfbasistoalg(bnf,sunK[1][i])));
@@ -1500,7 +1505,7 @@ if( DEBUGLEVEL_ell >= 4, print(" starting bnfell2descent_gen"));
nf = bnf.nf;
unnf = Mod(1,nf.pol);
ellnf = ell*unnf;
- if( #ellnf <= 5, ellnf = ellinit(ellnf,1));
+ if( #ellnf <= 5, ellnf = ellinit(ellnf));
A = ellnf.a2; if( DEBUGLEVEL_ell >= 2, print(" A = ",A));
B = ellnf.a4; if( DEBUGLEVEL_ell >= 2, print(" B = ",B));
@@ -1887,7 +1892,8 @@ if( DEBUGLEVEL_ell >= 4, print(" end of bnfell2descent_gen"));
local(urst,urst1,den,factden,eqtheta,rnfeq,bbnf,ext,rang,f);
if( DEBUGLEVEL_ell >= 3, print(" starting bnfellrank"));
- if( #ell <= 5, ell = ellinit(ell,1));
+ if( #ell < 5, ell = ellinit(ell));
+ ell = vector(5, i, ell[i]);
\\ removes the coefficients a1 and a3
urst = [1,0,0,0];
diff --git a/src/ext/pari/simon/ellQ.gp b/src/ext/pari/simon/ellQ.gp
index c114534..6861066 100644
--- a/src/ext/pari/simon/ellQ.gp
+++ b/src/ext/pari/simon/ellQ.gp
@@ -117,7 +117,7 @@
Courbes de la forme : k*y^2 = x^3+A*x^2+B*x+C
sans 2-torsion, A,B,C entiers.
gp > bnf = bnfinit(x^3+A*x^2+B*x+C);
- gp > ell = ellinit([0,A,0,B,C],1);
+ gp > ell = ellinit([0,A,0,B,C]);
gp > rank = ell2descent_gen(ell,bnf,k);
Courbes avec #E[2](Q) >= 2 :
@@ -833,7 +833,7 @@ if( DEBUGLEVEL_ell >= 4, print(" end of LS2localimage"));
\\ returns all the points Q on ell such that 2Q = P.
my(pol2,ratroots,half,x2,y2,P2);
- if(#ell < 13, ell=ellinit(ell,1));
+ if(#ell < 13, ell=ellinit(ell));
pol2 = Pol([4,ell.b2,2*ell.b4,ell.b6]); \\ 2-division polynomial
@@ -880,7 +880,7 @@ if( DEBUGLEVEL_ell >= 3, print(" E[2] = ",tors2));
my(torseven,P2);
if( DEBUGLEVEL_ell >= 4, print(" computing the 2^n-torsion"));
- if(#ell < 13, ell=ellinit(ell,1));
+ if(#ell < 13, ell=ellinit(ell));
torseven = elltors2(ell);
while( torseven[1] != 1,
@@ -976,7 +976,7 @@ if( DEBUGLEVEL_ell >= 5, print(" ell=",ell));
d = #listgen;
if( d == 0, return([]));
- if( #ell < 13, ell = ellinit(ell,1));
+ if( #ell < 13, ell = ellinit(ell));
if( K != 1,
if( ell.a1 != 0 || ell.a3 != 0, error(" ellredgen: a1*a3 != 0"));
@@ -1323,7 +1323,7 @@ my(A,B,C,polrel,polprime,ttheta,badprimes,S,LS2,selmer,rootapprox,p,pp,locimage,
if( DEBUGLEVEL_ell >= 4, print(" starting ell2descent_gen"));
- if( #ell < 13, ell = ellinit(ell,1));
+ if( #ell < 13, ell = ellinit(ell));
if( ell.a1 != 0 || ell.a3 != 0,
error(" ell2descent_gen: the curve is not of the form [0,a,0,b,c]"));
@@ -1579,7 +1579,7 @@ if( DEBUGLEVEL_ell >= 4, print(" end of ell2descent_gen"));
my(urst,urst1,den,eqell,tors2,bnf,rang,time1);
if( DEBUGLEVEL_ell >= 3, print(" starting ellrank"));
- if( #ell < 13, ell = ellinit(ell,1));
+ if( #ell < 13, ell = ellinit(ell));
\\ kill the coefficients a1 and a3
urst = [1,0,0,0];
@@ -1915,7 +1915,7 @@ if( DEBUGLEVEL_ell >= 4, print(" end of ellcount"));
my(P,Pfact,tors,listpointstriv,KS2prod,KS2gen,listpoints,pointgen,n1,n2,certain,apinit,bpinit,np1,np2,listpoints2,aux1,aux2,certainp,rang,strange);
if( DEBUGLEVEL_ell >= 2, print(" Algorithm of 2-descent via isogenies"));
- if( #ell < 13, ell = ellinit(ell,1));
+ if( #ell < 13, ell = ellinit(ell));
if( ell.disc == 0,
error(" ell2descent_viaisog: singular curve !!"));
diff --git a/src/sage/calculus/calculus.py b/src/sage/calculus/calculus.py
index bb6660a..b0f24c0 100644
--- a/src/sage/calculus/calculus.py
+++ b/src/sage/calculus/calculus.py
@@ -732,13 +732,13 @@ def nintegral(ex, x, a, b,
to high precision::
sage: gp.eval('intnum(x=17,42,exp(-x^2)*log(x))')
- '2.565728500561051482917356396 E-127' # 32-bit
- '2.5657285005610514829173563961304785900 E-127' # 64-bit
+ '2.565728500561051482917356396 E-127' # 32-bit
+ '2.5657285005610514829173563961304785900 E-127' # 64-bit
sage: old_prec = gp.set_real_precision(50)
sage: gp.eval('intnum(x=17,42,exp(-x^2)*log(x))')
'2.5657285005610514829173563961304785900147709554020 E-127'
sage: gp.set_real_precision(old_prec)
- 50
+ 57
Note that the input function above is a string in PARI syntax.
"""
diff --git a/src/sage/functions/exp_integral.py b/src/sage/functions/exp_integral.py
index 182e80c..69f0e0d 100644
--- a/src/sage/functions/exp_integral.py
+++ b/src/sage/functions/exp_integral.py
@@ -1493,10 +1493,10 @@ def exponential_integral_1(x, n=0):
sage: exponential_integral_1(2)
0.0489005107080611
- sage: exponential_integral_1(2,4) # abs tol 1e-18
+ sage: exponential_integral_1(2, 4) # abs tol 1e-18
[0.0489005107080611, 0.00377935240984891, 0.000360082452162659, 0.0000376656228439245]
- sage: exponential_integral_1(40,5)
- [1.03677326145166e-19, 2.22854325868847e-37, 6.33732515501151e-55, 2.02336191509997e-72, 6.88522610630764e-90]
+ sage: exponential_integral_1(40, 5)
+ [0.000000000000000, 2.22854325868847e-37, 6.33732515501151e-55, 2.02336191509997e-72, 6.88522610630764e-90]
sage: exponential_integral_1(0)
+Infinity
sage: r = exponential_integral_1(RealField(150)(1))
@@ -1569,7 +1569,7 @@ def exponential_integral_1(x, n=0):
if n <= 0:
# Add extra bits to the input.
# (experimentally verified -- Jeroen Demeyer)
- inprec = prec + math.ceil(math.log(2*prec))
+ inprec = prec + 5 + math.ceil(math.log(prec))
x = RealField(inprec)(x)._pari_()
return R(x.eint1())
else:
diff --git a/src/sage/groups/generic.py b/src/sage/groups/generic.py
index ff20df8..cde865e 100644
--- a/src/sage/groups/generic.py
+++ b/src/sage/groups/generic.py
@@ -420,8 +420,7 @@ def bsgs(a, b, bounds, operation='*', identity=None, inverse=None, op=None):
sage: F.<a> = GF(37^5)
sage: E = EllipticCurve(F, [1,1])
sage: P = E.lift_x(a); P
- (a : 28*a^4 + 15*a^3 + 14*a^2 + 7 : 1) # 32-bit
- (a : 9*a^4 + 22*a^3 + 23*a^2 + 30 : 1) # 64-bit
+ (a : 28*a^4 + 15*a^3 + 14*a^2 + 7 : 1)
This will return a multiple of the order of P::
@@ -853,8 +852,8 @@ def discrete_log_lambda(a, base, bounds, operation='*', hash_function=hash):
sage: F.<a> = GF(37^5)
sage: E = EllipticCurve(F, [1,1])
sage: P = E.lift_x(a); P
- (a : 9*a^4 + 22*a^3 + 23*a^2 + 30 : 1) # 32-bit
- (a : 28*a^4 + 15*a^3 + 14*a^2 + 7 : 1) # 64-bit
+ (a : 28*a^4 + 15*a^3 + 14*a^2 + 7 : 1) # 32-bit
+ (a : 9*a^4 + 22*a^3 + 23*a^2 + 30 : 1) # 64-bit
This will return a multiple of the order of P::
diff --git a/src/sage/interfaces/gp.py b/src/sage/interfaces/gp.py
index 767c668..6f13f3c 100644
--- a/src/sage/interfaces/gp.py
+++ b/src/sage/interfaces/gp.py
@@ -24,7 +24,7 @@ PARI interpreter)::
sage: E = gp.ellinit([1,2,3,4,5])
sage: E.ellglobalred()
- [10351, [1, -1, 0, -1], 1]
+ [10351, [1, -1, 0, -1], 1, [11, 1; 941, 1], [[1, 5, 0, 1], [1, 5, 0, 1]]]
sage: E.ellan(20)
[1, 1, 0, -1, -3, 0, -1, -3, -3, -3, -1, 0, 1, -1, 0, -1, 5, -3, 4, 3]
@@ -113,7 +113,7 @@ Test error recovery::
PARI/GP ERROR:
*** at top-level: sage[...]=1/0
*** ^--
- *** _/_: division by zero
+ *** _/_: impossible inverse in gdiv: 0.
AUTHORS:
@@ -322,9 +322,16 @@ class Gp(Expect):
get_real_precision = get_precision
- def set_precision(self, prec=None):
+ def set_precision(self, prec):
"""
- Sets the PARI precision (in decimal digits) for real computations, and returns the old value.
+ Sets the PARI precision (in decimal digits) for real
+ computations, and returns the old value.
+
+ .. NOTE::
+
+ PARI/GP rounds up precisions to the nearest machine word,
+ so the result of :meth:`get_precision` is not always the
+ same as the last value inputted to :meth:`set_precision`.
EXAMPLES::
@@ -332,9 +339,9 @@ class Gp(Expect):
28 # 32-bit
38 # 64-bit
sage: gp.get_precision()
- 53
+ 57
sage: gp.set_precision(old_prec)
- 53
+ 57
sage: gp.get_precision()
28 # 32-bit
38 # 64-bit
@@ -436,25 +443,23 @@ class Gp(Expect):
return m - t
return m
- def set_default(self, var=None, value=None):
+ def set_default(self, var, value):
"""
Set a PARI gp configuration variable, and return the old value.
INPUT:
- - ``var`` (string, default None) -- the name of a PARI gp
+ - ``var`` (string) -- the name of a PARI gp
configuration variable. (See ``gp.default()`` for a list.)
- ``value`` -- the value to set the variable to.
EXAMPLES::
- sage: old_prec = gp.set_default('realprecision',100); old_prec
- 28 # 32-bit
- 38 # 64-bit
+ sage: old_prec = gp.set_default('realprecision', 110)
sage: gp.get_default('realprecision')
- 100
- sage: gp.set_default('realprecision',old_prec)
- 100
+ 115
+ sage: gp.set_default('realprecision', old_prec)
+ 115
sage: gp.get_default('realprecision')
28 # 32-bit
38 # 64-bit
@@ -463,13 +468,13 @@ class Gp(Expect):
self._eval_line('default(%s,%s)'%(var,value))
return old
- def get_default(self, var=None):
+ def get_default(self, var):
"""
Return the current value of a PARI gp configuration variable.
INPUT:
- - ``var`` (string, default None) -- the name of a PARI gp
+ - ``var`` (string) -- the name of a PARI gp
configuration variable. (See ``gp.default()`` for a list.)
OUTPUT:
@@ -808,13 +813,16 @@ class GpElement(ExpectElement):
sage: E = gp('ellinit([1,2,3,4,5])')
sage: loads(dumps(E)) == E
+ True
+ sage: x = gp.Pi()/3
+ sage: loads(dumps(x)) == x
False
- sage: loads(E.dumps())
- [1, 2, 3, 4, 5, 9, 11, 29, 35, -183, -3429, -10351, 6128487/10351, [-1.618909932267371342378000940, -0.3155450338663143288109995302 - 2.092547096911958607981689447*I, -0.3155450338663143288109995302 + 2.092547096911958607981689447*I]~, 2.780740013766729771063197627, 1.390370006883364885531598814 - 1.068749776356193066159263548*I, 3.109648242324380328550149122 + 1.009741959000000000000000000 E-28*I, 1.554824121162190164275074561 + 1.064374745210273756943885994*I, 2.971915267817909670771647951] # 32-bit
- [1, 2, 3, 4, 5, 9, 11, 29, 35, -183, -3429, -10351, 6128487/10351, [-1.6189099322673713423780009396072169751, -0.31554503386631432881099953019639151248 - 2.0925470969119586079816894466366945829*I, -0.31554503386631432881099953019639151248 + 2.0925470969119586079816894466366945829*I]~, 2.7807400137667297710631976271813584994, 1.3903700068833648855315988135906792497 - 1.0687497763561930661592635474375038788*I, 3.1096482423243803285501491221965830079 + 2.3509887016445750160000000000000000000 E-38*I, 1.5548241211621901642750745610982915040 + 1.0643747452102737569438859937299427442*I, 2.9719152678179096707716479509361896060] # 64-bit
- sage: E
- [1, 2, 3, 4, 5, 9, 11, 29, 35, -183, -3429, -10351, 6128487/10351, [-1.618909932267371342378000940, -0.3155450338663143288109995302 - 2.092547096911958607981689447*I, -0.3155450338663143288109995302 + 2.092547096911958607981689447*I]~, 2.780740013766729771063197627, 1.390370006883364885531598814 - 1.068749776356193066159263548*I, 3.109648242324380328550149122 + 1.009741959 E-28*I, 1.554824121162190164275074561 + 1.064374745210273756943885994*I, 2.971915267817909670771647951] # 32-bit
- [1, 2, 3, 4, 5, 9, 11, 29, 35, -183, -3429, -10351, 6128487/10351, [-1.6189099322673713423780009396072169751, -0.31554503386631432881099953019639151248 - 2.0925470969119586079816894466366945829*I, -0.31554503386631432881099953019639151248 + 2.0925470969119586079816894466366945829*I]~, 2.7807400137667297710631976271813584994, 1.3903700068833648855315988135906792497 - 1.0687497763561930661592635474375038788*I, 3.1096482423243803285501491221965830079 + 2.350988701644575016 E-38*I, 1.5548241211621901642750745610982915040 + 1.0643747452102737569438859937299427442*I, 2.9719152678179096707716479509361896060] # 64-bit
+ sage: x
+ 1.047197551196597746154214461 # 32-bit
+ 1.0471975511965977461542144610931676281 # 64-bit
+ sage: loads(dumps(x))
+ 1.047197551196597746154214461 # 32-bit
+ 1.0471975511965977461542144610931676281 # 64-bit
The two elliptic curves look the same, but internally the floating
point numbers are slightly different.
diff --git a/src/sage/lfunctions/dokchitser.py b/src/sage/lfunctions/dokchitser.py
index da6ae49..12e991f 100644
--- a/src/sage/lfunctions/dokchitser.py
+++ b/src/sage/lfunctions/dokchitser.py
@@ -108,7 +108,7 @@ class Dokchitser(SageObject):
sage: L.taylor_series(1,4)
0.000000000000000 + 0.305999773834052*z + 0.186547797268162*z^2 - 0.136791463097188*z^3 + O(z^4)
sage: L.check_functional_equation()
- 6.11218974800000e-18 # 32-bit
+ 6.11218974700000e-18 # 32-bit
6.04442711160669e-18 # 64-bit
RANK 2 ELLIPTIC CURVE:
@@ -125,8 +125,8 @@ class Dokchitser(SageObject):
sage: L.derivative(1,E.rank())
1.51863300057685
sage: L.taylor_series(1,4)
- 2.90759778535572e-20 + (-1.64772676916085e-20)*z + 0.759316500288427*z^2 - 0.430302337583362*z^3 + O(z^4) # 32-bit
- -3.11623283109075e-21 + (1.76595961125962e-21)*z + 0.759316500288427*z^2 - 0.430302337583362*z^3 + O(z^4) # 64-bit
+ 2.90760251490292e-20 + (-1.64772944938078e-20)*z + 0.759316500288427*z^2 - 0.430302337583362*z^3 + O(z^4) # 32-bit
+ -3.11661104824958e-21 + (1.76617394576638e-21)*z + 0.759316500288427*z^2 - 0.430302337583362*z^3 + O(z^4) # 64-bit
RAMANUJAN DELTA L-FUNCTION:
@@ -218,7 +218,9 @@ class Dokchitser(SageObject):
except AttributeError:
logfile = None
# For debugging
- #logfile = os.path.join(DOT_SAGE, 'dokchitser.log')
+ import os
+ from sage.env import DOT_SAGE
+ logfile = os.path.join(DOT_SAGE, 'dokchitser.log')
g = sage.interfaces.gp.Gp(script_subdirectory='dokchitser', logfile=logfile)
g.read('computel.gp')
self.__gp = g
@@ -484,7 +486,7 @@ class Dokchitser(SageObject):
sage: E = EllipticCurve('389a')
sage: L = E.lseries().dokchitser(200)
sage: L.taylor_series(1,3)
- 6.2240188634103774348273446965620801288836328651973234573133e-73 + (-3.527132447498646306292650465494647003849868770...e-73)*z + 0.75931650028842677023019260789472201907809751649492435158581*z^2 + O(z^3)
+ -9.094...e-82 + (5.1538...e-82)*z + 0.75931650028842677023019260789472201907809751649492435158581*z^2 + O(z^3)
"""
self.__check_init()
a = self.__CC(a)
diff --git a/src/sage/libs/pari/decl.pxi b/src/sage/libs/pari/decl.pxi
index 41a8e1a..baa03d5 100644
--- a/src/sage/libs/pari/decl.pxi
+++ b/src/sage/libs/pari/decl.pxi
@@ -16,16 +16,14 @@ AUTHORS:
- Jeroen Demeyer (2010-08-15): big clean up (#9898)
+ - Jeroen Demeyer (2014-02-09): upgrade to PARI 2.7 (#15767)
+
"""
include 'sage/ext/cdefs.pxi'
-cdef extern from 'setjmp.h':
- struct __jmp_buf_tag:
- pass
- ctypedef __jmp_buf_tag jmp_buf
- int setjmp (jmp_buf __env)
- int longjmp (jmp_buf __env, int val)
+cdef extern from '<stdarg.h>':
+ ctypedef void* va_list
ctypedef unsigned long ulong
@@ -35,6 +33,46 @@ cdef extern from 'pari/paricfg.h':
cdef extern from 'pari/pari.h':
ctypedef long* GEN
+ ctypedef char* byteptr
+
+ # Various structures that we don't use in Sage but which need to be
+ # declared, otherwise Cython complains.
+ struct bb_group:
+ pass
+ struct bb_field:
+ pass
+ struct bb_algebra:
+ pass
+ struct qfr_data:
+ pass
+ struct nfmaxord_t:
+ pass
+ struct forcomposite_t:
+ pass
+ struct forpart_t:
+ pass
+ struct forprime_t:
+ pass
+ struct forvec_t:
+ pass
+ struct entree:
+ pass
+ struct gp_context:
+ pass
+ struct pariFILE:
+ pass
+ struct pari_mt:
+ pass
+ struct pari_thread:
+ pass
+ struct pari_timer:
+ pass
+ struct GENbin:
+ pass
+ struct hashentry:
+ pass
+ struct hashtable:
+ pass
# PARI types: these are actually an enum type, but that doesn't
# matter for Cython.
@@ -49,13 +87,19 @@ cdef extern from 'pari/pari.h':
# parierr.h
- int syntaxer, bugparier, alarmer, openfiler, talker, flagerr, \
- impl, archer, notfuncer, precer, typeer, consister, user, \
- errpile, overflower, matinv1, mattype1, arither1, primer1, \
- invmoder, constpoler, notpoler, redpoler, zeropoler, operi, \
- operf, gdiver, memer, negexper, sqrter5, noer
+ int e_SYNTAX, e_BUG, \
+ e_ALARM, e_FILE, \
+ e_MISC, e_FLAG, e_IMPL, e_ARCH, e_PACKAGE, e_NOTFUNC, \
+ e_PREC, e_TYPE, e_DIM, e_VAR, e_PRIORITY, e_USER, \
+ e_STACK, e_OVERFLOW, e_DOMAIN, e_COMPONENT, \
+ e_MAXPRIME, \
+ e_CONSTPOL, e_IRREDPOL, e_COPRIME, e_PRIME, e_MODULUS, e_ROOTS0, \
+ e_OP, e_TYPE2, e_INV, \
+ e_MEM, \
+ e_SQRTN, \
+ e_NONE
- int warner, warnprec, warnfile, warnmem
+ int warner, warnprec, warnfile, warnmem, warnuser
# parigen.h
@@ -93,20 +137,20 @@ cdef extern from 'pari/pari.h':
# paricast.h
- long mael2(GEN,long,long)
- long mael3(GEN,long,long,long)
- long mael4(GEN,long,long,long,long)
- long mael5(GEN,long,long,long,long,long)
- long mael(GEN,long,long)
- GEN gmael1(GEN,long)
- GEN gmael2(GEN,long,long)
- GEN gmael3(GEN,long,long,long)
- GEN gmael4(GEN,long,long,long,long)
- GEN gmael5(GEN,long,long,long,long,long)
- GEN gmael(GEN,long,long)
- GEN gel(GEN,long)
- GEN gcoeff(GEN,long,long)
- long coeff(GEN,long,long)
+ long mael2(GEN, long, long)
+ long mael3(GEN, long, long, long)
+ long mael4(GEN, long, long, long, long)
+ long mael5(GEN, long, long, long, long, long)
+ long mael(GEN, long, long)
+ GEN gmael1(GEN, long)
+ GEN gmael2(GEN, long, long)
+ GEN gmael3(GEN, long, long, long)
+ GEN gmael4(GEN, long, long, long, long)
+ GEN gmael5(GEN, long, long, long, long, long)
+ GEN gmael(GEN, long, long)
+ GEN gel(GEN, long)
+ GEN gcoeff(GEN, long, long)
+ long coeff(GEN, long, long)
# paricom.h
@@ -131,11 +175,14 @@ cdef extern from 'pari/pari.h':
ulong Fl_add(ulong a, ulong b, ulong p)
long Fl_center(ulong u, ulong p, ulong ps2)
ulong Fl_div(ulong a, ulong b, ulong p)
+ ulong Fl_double(ulong a, ulong p)
ulong Fl_mul(ulong a, ulong b, ulong p)
ulong Fl_neg(ulong x, ulong p)
ulong Fl_sqr(ulong a, ulong p)
ulong Fl_sub(ulong a, ulong b, ulong p)
+ ulong Fl_triple(ulong a, ulong p)
GEN absi(GEN x)
+ GEN absi_shallow(GEN x)
GEN absr(GEN x)
int absrnz_equal1(GEN x)
int absrnz_equal2n(GEN x)
@@ -165,11 +212,13 @@ cdef extern from 'pari/pari.h':
void affui(ulong s, GEN x)
void affur(ulong s, GEN x)
GEN cgetg(long x, long y)
+ GEN cgetg_block(long x, long y)
GEN cgetg_copy(GEN x, long *plx)
GEN cgeti(long x)
GEN cgetineg(long x)
GEN cgetipos(long x)
GEN cgetr(long x)
+ GEN cgetr_block(long prec)
int cmpir(GEN x, GEN y)
int cmpis(GEN x, long y)
int cmpiu(GEN x, ulong y)
@@ -215,19 +264,23 @@ cdef extern from 'pari/pari.h':
int equalui(ulong x, GEN y)
long evalexpo(long x)
long evallg(long x)
+ long evalprecp(long x)
long evalvalp(long x)
long expi(GEN x)
long expu(ulong x)
void fixlg(GEN z, long ly)
GEN fractor(GEN x, long prec)
GEN icopy(GEN x)
+ GEN icopyspec(GEN x, long nx)
GEN icopy_avma(GEN x, pari_sp av)
+ ulong int_bit(GEN x, long n)
GEN itor(GEN x, long prec)
long itos(GEN x)
long itos_or_0(GEN x)
ulong itou(GEN x)
ulong itou_or_0(GEN x)
GEN leafcopy(GEN x)
+ GEN leafcopy_avma(GEN x, pari_sp av)
double maxdd(double x, double y)
long maxss(long x, long y)
long maxuu(ulong x, ulong y)
@@ -248,6 +301,7 @@ cdef extern from 'pari/pari.h':
GEN modss(long x, long y)
void modssz(long s, long y, GEN z)
GEN mpabs(GEN x)
+ GEN mpabs_shallow(GEN x)
GEN mpadd(GEN x, GEN y)
void mpaddz(GEN x, GEN y, GEN z)
void mpaff(GEN x, GEN y)
@@ -262,7 +316,7 @@ cdef extern from 'pari/pari.h':
GEN mpneg(GEN x)
int mpodd(GEN x)
GEN mpround(GEN x)
- GEN mpshift(GEN x,long s)
+ GEN mpshift(GEN x, long s)
GEN mpsqr(GEN x)
GEN mpsub(GEN x, GEN y)
void mpsubz(GEN x, GEN y, GEN z)
@@ -289,6 +343,7 @@ cdef extern from 'pari/pari.h':
GEN rdivsi(long x, GEN y, long prec)
GEN rdivss(long x, long y, long prec)
GEN real2n(long n, long prec)
+ GEN real_m2n(long n, long prec)
GEN real_0(long prec)
GEN real_0_bit(long bitprec)
GEN real_1(long prec)
@@ -305,15 +360,20 @@ cdef extern from 'pari/pari.h':
long sdivsi(long x, GEN y)
long sdivsi_rem(long x, GEN y, long *rem)
long sdivss_rem(long x, long y, long *rem)
+ ulong udiviu_rem(GEN n, ulong d, ulong *r)
+ ulong udivuu_rem(ulong x, ulong y, ulong *r)
void setabssign(GEN x)
void shift_left(GEN z2, GEN z1, long min, long M, ulong f, ulong sh)
void shift_right(GEN z2, GEN z1, long min, long M, ulong f, ulong sh)
ulong shiftl(ulong x, ulong y)
ulong shiftlr(ulong x, ulong y)
GEN shiftr(GEN x, long n)
+ void shiftr_inplace(GEN z, long d)
long smodis(GEN x, long y)
long smodss(long x, long y)
void stackdummy(pari_sp av, pari_sp ltop)
+ char *stack_malloc(size_t N)
+ char *stack_calloc(size_t N)
GEN stoi(long x)
GEN stor(long x, long prec)
GEN subii(GEN x, GEN y)
@@ -338,7 +398,7 @@ cdef extern from 'pari/pari.h':
void togglesign_safe(GEN *px)
void affectsign(GEN x, GEN y)
void affectsign_safe(GEN x, GEN *py)
- GEN truedivii(GEN a,GEN b)
+ GEN truedivii(GEN a, GEN b)
GEN truedivis(GEN a, long b)
GEN truedivsi(long a, GEN b)
ulong udivui_rem(ulong x, GEN y, ulong *rem)
@@ -351,28 +411,51 @@ cdef extern from 'pari/pari.h':
GEN uutoineg(ulong x, ulong y)
long vali(GEN x)
+ # OBSOLETE
+
+ GEN bernvec(long nomb)
+
# F2x.c
+ GEN F2c_to_Flc(GEN x)
GEN F2c_to_ZC(GEN x)
+ GEN F2c_to_mod(GEN x)
+ GEN F2m_rowslice(GEN x, long a, long b)
+ GEN F2m_to_Flm(GEN z)
GEN F2m_to_ZM(GEN z)
+ GEN F2m_to_mod(GEN z)
void F2v_add_inplace(GEN x, GEN y)
+ ulong F2v_dotproduct(GEN x, GEN y)
+ GEN F2v_slice(GEN x, long a, long b)
+ GEN F2x_F2xq_eval(GEN Q, GEN x, GEN T)
+ GEN F2x_F2xqV_eval(GEN P, GEN V, GEN T)
GEN F2x_1_add(GEN y)
GEN F2x_add(GEN x, GEN y)
+ GEN F2x_deflate(GEN x0, long d)
long F2x_degree(GEN x)
GEN F2x_deriv(GEN x)
GEN F2x_divrem(GEN x, GEN y, GEN *pr)
+ void F2x_even_odd(GEN p, GEN *pe, GEN *po)
GEN F2x_extgcd(GEN a, GEN b, GEN *ptu, GEN *ptv)
GEN F2x_gcd(GEN a, GEN b)
+ GEN F2x_halfgcd(GEN a, GEN b)
+ int F2x_issquare(GEN a)
GEN F2x_mul(GEN x, GEN y)
GEN F2x_rem(GEN x, GEN y)
+ GEN F2x_shift(GEN y, long d)
GEN F2x_sqr(GEN x)
+ GEN F2x_sqrt(GEN x)
GEN F2x_to_F2v(GEN x, long n)
GEN F2x_to_Flx(GEN x)
GEN F2x_to_ZX(GEN x)
+ long F2x_valrem(GEN x, GEN *Z)
GEN F2xC_to_ZXC(GEN x)
GEN F2xV_to_F2m(GEN v, long n)
+ GEN F2xq_Artin_Schreier(GEN a, GEN T)
+ GEN FlxqXQV_autsum(GEN aut, long n, GEN S, GEN T, ulong p)
+ GEN F2xq_autpow(GEN x, long n, GEN T)
GEN F2xq_conjvec(GEN x, GEN T)
- GEN F2xq_div(GEN x,GEN y,GEN T)
+ GEN F2xq_div(GEN x, GEN y, GEN T)
GEN F2xq_inv(GEN x, GEN T)
GEN F2xq_invsafe(GEN x, GEN T)
GEN F2xq_log(GEN a, GEN g, GEN ord, GEN T)
@@ -380,46 +463,86 @@ cdef extern from 'pari/pari.h':
GEN F2xq_mul(GEN x, GEN y, GEN pol)
GEN F2xq_order(GEN a, GEN ord, GEN T)
GEN F2xq_pow(GEN x, GEN n, GEN pol)
+ GEN F2xq_powu(GEN x, ulong n, GEN pol)
GEN F2xq_powers(GEN x, long l, GEN T)
- GEN F2xq_sqr(GEN x,GEN pol)
+ GEN F2xq_sqr(GEN x, GEN pol)
GEN F2xq_sqrt(GEN a, GEN T)
+ GEN F2xq_sqrt_fast(GEN c, GEN sqx, GEN T)
GEN F2xq_sqrtn(GEN a, GEN n, GEN T, GEN *zeta)
ulong F2xq_trace(GEN x, GEN T)
GEN Flm_to_F2m(GEN x)
GEN Flv_to_F2v(GEN x)
GEN Flx_to_F2x(GEN x)
- GEN Z_to_F2x(GEN x, long sv)
+ GEN Rg_to_F2xq(GEN x, GEN T)
+ GEN RgM_to_F2m(GEN x)
+ GEN RgV_to_F2v(GEN x)
+ GEN RgX_to_F2x(GEN x)
+ GEN Z_to_F2x(GEN x, long v)
GEN ZM_to_F2m(GEN x)
GEN ZV_to_F2v(GEN x)
GEN ZX_to_F2x(GEN x)
+ GEN ZXT_to_FlxT(GEN z, ulong p)
GEN ZXX_to_F2xX(GEN B, long v)
GEN gener_F2xq(GEN T, GEN *po)
+ bb_field *get_F2xq_field(void **E, GEN T)
GEN random_F2x(long d, long vs)
+ # F2xqE.c
+
+ GEN F2xq_ellcard(GEN a2, GEN a6, GEN T)
+ GEN F2xq_ellgens(GEN a2, GEN a6, GEN ch, GEN D, GEN m, GEN T)
+ GEN F2xq_ellgroup(GEN a2, GEN a6, GEN N, GEN T, GEN *pt_m)
+ GEN F2xqE_add(GEN P, GEN Q, GEN a2, GEN T)
+ GEN F2xqE_changepoint(GEN x, GEN ch, GEN T)
+ GEN F2xqE_changepointinv(GEN x, GEN ch, GEN T)
+ GEN F2xqE_dbl(GEN P, GEN a2, GEN T)
+ GEN F2xqE_log(GEN a, GEN b, GEN o, GEN a2, GEN T)
+ GEN F2xqE_mul(GEN P, GEN n, GEN a2, GEN T)
+ GEN F2xqE_neg(GEN P, GEN a2, GEN T)
+ GEN F2xqE_order(GEN z, GEN o, GEN a2, GEN T)
+ GEN F2xqE_sub(GEN P, GEN Q, GEN a2, GEN T)
+ GEN F2xqE_tatepairing(GEN t, GEN s, GEN m, GEN a2, GEN T)
+ GEN F2xqE_weilpairing(GEN t, GEN s, GEN m, GEN a2, GEN T)
+ bb_group * get_F2xqE_group(void **E, GEN a2, GEN a6, GEN T)
+ GEN RgE_to_F2xqE(GEN x, GEN T)
+ GEN random_F2xqE(GEN a2, GEN a6, GEN T)
+
# Flx.c
GEN Fl_to_Flx(ulong x, long sv)
+ GEN Flc_to_ZC(GEN z)
GEN Flm_to_FlxV(GEN x, long sv)
- GEN Flm_to_FlxX(GEN x, long v,long w)
+ GEN Flm_to_FlxX(GEN x, long v, long w)
GEN Flm_to_ZM(GEN z)
GEN Flv_to_Flx(GEN x, long vs)
GEN Flv_to_ZV(GEN z)
GEN Flv_polint(GEN xa, GEN ya, ulong p, long vs)
GEN Flv_roots_to_pol(GEN a, ulong p, long vs)
+ GEN Fly_to_FlxY(GEN B, long v)
+ GEN Flx_Fl_add(GEN y, ulong x, ulong p)
GEN Flx_Fl_mul(GEN y, ulong x, ulong p)
- GEN Flx_to_Flv(GEN x, long N)
- GEN Flx_to_ZX(GEN z)
- GEN Flx_to_ZX_inplace(GEN z)
+ GEN Flx_Fl_mul_to_monic(GEN y, ulong x, ulong p)
+ GEN Flx_Flxq_eval(GEN f, GEN x, GEN T, ulong p)
+ GEN Flx_FlxqV_eval(GEN f, GEN x, GEN T, ulong p)
GEN Flx_add(GEN x, GEN y, ulong p)
+ GEN Flx_deflate(GEN x0, long d)
GEN Flx_deriv(GEN z, ulong p)
+ GEN Flx_double(GEN y, ulong p)
GEN Flx_div_by_X_x(GEN a, ulong x, ulong p, ulong *rem)
GEN Flx_divrem(GEN x, GEN y, ulong p, GEN *pr)
+ int Flx_equal(GEN V, GEN W)
ulong Flx_eval(GEN x, ulong y, ulong p)
GEN Flx_extgcd(GEN a, GEN b, ulong p, GEN *ptu, GEN *ptv)
ulong Flx_extresultant(GEN a, GEN b, ulong p, GEN *ptU, GEN *ptV)
GEN Flx_gcd(GEN a, GEN b, ulong p)
- GEN Flx_gcd_i(GEN a, GEN b, ulong p)
+ GEN Flx_get_red(GEN T, ulong p)
+ GEN Flx_halfgcd(GEN a, GEN b, ulong p)
+ GEN Flx_inflate(GEN x0, long d)
+ GEN Flx_invBarrett(GEN T, ulong p)
int Flx_is_squarefree(GEN z, ulong p)
+ int Flx_is_smooth(GEN g, long r, ulong p)
+ GEN Flx_mod_Xn1(GEN T, ulong n, ulong p)
+ GEN Flx_mod_Xnm1(GEN T, ulong n, ulong p)
GEN Flx_mul(GEN x, GEN y, ulong p)
GEN Flx_neg(GEN x, ulong p)
GEN Flx_neg_inplace(GEN x, ulong p)
@@ -431,380 +554,1409 @@ cdef extern from 'pari/pari.h':
GEN Flx_renormalize(GEN x, long l)
ulong Flx_resultant(GEN a, GEN b, ulong p)
GEN Flx_shift(GEN a, long n)
+ GEN Flx_splitting(GEN p, long k)
GEN Flx_sqr(GEN x, ulong p)
GEN Flx_sub(GEN x, GEN y, ulong p)
+ GEN Flx_to_Flv(GEN x, long N)
+ GEN Flx_to_FlxX(GEN z, long v)
+ GEN Flx_to_ZX(GEN z)
+ GEN Flx_to_ZX_inplace(GEN z)
+ GEN Flx_triple(GEN y, ulong p)
+ long Flx_val(GEN x)
+ long Flx_valrem(GEN x, GEN *Z)
+ GEN FlxC_to_ZXC(GEN x)
+ GEN FlxM_Flx_add_shallow(GEN x, GEN y, ulong p)
GEN FlxM_to_ZXM(GEN z)
+ GEN FlxT_red(GEN z, ulong p)
+ GEN FlxV_to_ZXV(GEN x)
+ GEN FlxV_Flc_mul(GEN V, GEN W, ulong p)
+ GEN FlxV_red(GEN z, ulong p)
GEN FlxV_to_Flm(GEN v, long n)
+ GEN FlxX_Fl_mul(GEN x, ulong y, ulong p)
+ GEN FlxX_Flx_add(GEN y, GEN x, ulong p)
+ GEN FlxX_Flx_mul(GEN x, GEN y, ulong p)
GEN FlxX_add(GEN P, GEN Q, ulong p)
+ GEN FlxX_double(GEN x, ulong p)
+ GEN FlxX_neg(GEN x, ulong p)
+ GEN FlxX_sub(GEN P, GEN Q, ulong p)
+ GEN FlxX_swap(GEN x, long n, long ws)
+ GEN FlxX_renormalize(GEN x, long lx)
GEN FlxX_shift(GEN a, long n)
GEN FlxX_to_Flm(GEN v, long n)
GEN FlxX_to_ZXX(GEN B)
- GEN FlxYqQ_pow(GEN x, GEN n, GEN S, GEN T, ulong p)
- GEN Flxq_inv(GEN x,GEN T,ulong p)
+ GEN FlxX_triple(GEN x, ulong p)
+ GEN FlxY_Flxq_evalx(GEN P, GEN x, GEN T, ulong p)
+ GEN FlxY_Flx_div(GEN x, GEN y, ulong p)
+ GEN FlxY_evalx(GEN Q, ulong x, ulong p)
+ GEN FlxYqq_pow(GEN x, GEN n, GEN S, GEN T, ulong p)
+ GEN Flxq_autpow(GEN x, ulong n, GEN T, ulong p)
+ GEN Flxq_autsum(GEN x, ulong n, GEN T, ulong p)
+ GEN Flxq_charpoly(GEN x, GEN T, ulong p)
+ GEN Flxq_conjvec(GEN x, GEN T, ulong p)
+ GEN Flxq_div(GEN x, GEN y, GEN T, ulong p)
+ GEN Flxq_inv(GEN x, GEN T, ulong p)
GEN Flxq_invsafe(GEN x, GEN T, ulong p)
- GEN Flxq_mul(GEN y,GEN x,GEN T,ulong p)
+ int Flxq_issquare(GEN x, GEN T, ulong p)
+ int Flxq_is2npower(GEN x, long n, GEN T, ulong p)
+ GEN Flxq_log(GEN a, GEN g, GEN ord, GEN T, ulong p)
+ GEN Flxq_lroot(GEN a, GEN T, long p)
+ GEN Flxq_lroot_fast(GEN a, GEN sqx, GEN T, long p)
+ GEN Flxq_matrix_pow(GEN y, long n, long m, GEN P, ulong l)
+ GEN Flxq_minpoly(GEN x, GEN T, ulong p)
+ GEN Flxq_mul(GEN x, GEN y, GEN T, ulong p)
+ ulong Flxq_norm(GEN x, GEN T, ulong p)
+ GEN Flxq_order(GEN a, GEN ord, GEN T, ulong p)
GEN Flxq_pow(GEN x, GEN n, GEN T, ulong p)
+ GEN Flxq_powu(GEN x, ulong n, GEN T, ulong p)
GEN Flxq_powers(GEN x, long l, GEN T, ulong p)
- GEN Flxq_sqr(GEN y,GEN T,ulong p)
- GEN FlxqX_normalize(GEN z, GEN T, ulong p)
+ GEN Flxq_sqr(GEN y, GEN T, ulong p)
+ GEN Flxq_sqrt(GEN a, GEN T, ulong p)
+ GEN Flxq_sqrtn(GEN a, GEN n, GEN T, ulong p, GEN *zetan)
+ ulong Flxq_trace(GEN x, GEN T, ulong p)
+ GEN FlxqV_dotproduct(GEN x, GEN y, GEN T, ulong p)
+ GEN FlxqV_roots_to_pol(GEN V, GEN T, ulong p, long v)
+ GEN FlxqX_FlxqXQ_eval(GEN Q, GEN x, GEN S, GEN T, ulong p)
+ GEN FlxqX_FlxqXQV_eval(GEN P, GEN V, GEN S, GEN T, ulong p)
GEN FlxqX_Flxq_mul(GEN P, GEN U, GEN T, ulong p)
- GEN FlxqX_red(GEN z, GEN T, ulong p)
+ GEN FlxqX_Flxq_mul_to_monic(GEN P, GEN U, GEN T, ulong p)
+ GEN FlxqX_divrem(GEN x, GEN y, GEN T, ulong p, GEN *pr)
+ GEN FlxqX_extgcd(GEN a, GEN b, GEN T, ulong p, GEN *ptu, GEN *ptv)
+ GEN FlxqX_gcd(GEN P, GEN Q, GEN T, ulong p)
+ GEN FlxqX_invBarrett(GEN T, GEN Q, ulong p)
GEN FlxqX_mul(GEN x, GEN y, GEN T, ulong p)
+ GEN FlxqX_normalize(GEN z, GEN T, ulong p)
+ GEN FlxqX_pow(GEN V, long n, GEN T, ulong p)
+ GEN FlxqX_red(GEN z, GEN T, ulong p)
+ GEN FlxqX_rem_Barrett(GEN x, GEN mg, GEN T, GEN Q, ulong p)
GEN FlxqX_safegcd(GEN P, GEN Q, GEN T, ulong p)
GEN FlxqX_sqr(GEN x, GEN T, ulong p)
- GEN FlxqX_divrem(GEN x, GEN y, GEN T, ulong p, GEN *pr)
+ GEN FlxqXQ_div(GEN x, GEN y, GEN S, GEN T, ulong p)
+ GEN FlxqXQ_inv(GEN x, GEN S, GEN T, ulong p)
+ GEN FlxqXQ_invsafe(GEN x, GEN S, GEN T, ulong p)
+ GEN FlxqXQ_matrix_pow(GEN x, long n, long m, GEN S, GEN T, ulong p)
+ GEN FlxqXQ_mul(GEN x, GEN y, GEN S, GEN T, ulong p)
GEN FlxqXQ_pow(GEN x, GEN n, GEN S, GEN T, ulong p)
+ GEN FlxqXQ_powers(GEN x, long n, GEN S, GEN T, ulong p)
+ GEN FlxqXQ_sqr(GEN x, GEN S, GEN T, ulong p)
+ GEN FlxqXQV_autpow(GEN x, long n, GEN S, GEN T, ulong p)
+ GEN FlxqXV_prod(GEN V, GEN T, ulong p)
+ GEN Kronecker_to_FlxqX(GEN z, GEN T, ulong p)
+ ulong Rg_to_F2(GEN x)
+ ulong Rg_to_Fl(GEN x, ulong p)
+ GEN Rg_to_Flxq(GEN x, GEN T, ulong p)
+ GEN RgX_to_Flx(GEN x, ulong p)
GEN Z_to_Flx(GEN x, ulong p, long v)
- GEN ZM_to_Flm(GEN x, ulong p)
- GEN ZV_to_Flv(GEN x, ulong p)
GEN ZX_to_Flx(GEN x, ulong p)
GEN ZXV_to_FlxV(GEN v, ulong p)
GEN ZXX_to_FlxX(GEN B, ulong p, long v)
- GEN polx_Flx(long sv)
- GEN zero_Flx(long sv)
+ GEN ZXXV_to_FlxXV(GEN V, ulong p, long v)
+ GEN gener_Flxq(GEN T, ulong p, GEN *o)
+ long get_Flx_degree(GEN T)
+ GEN get_Flx_mod(GEN T)
+ long get_Flx_var(GEN T)
+ bb_field *get_Flxq_field(void **E, GEN T, ulong p)
+ GEN pol1_FlxX(long v, long sv)
+ GEN random_Flx(long d1, long v, ulong p)
+ GEN zxX_to_Kronecker(GEN P, GEN Q)
+
+ # FlxqE.c
+
+ GEN Flxq_ellcard(GEN a4, GEN a6, GEN T, ulong p)
+ GEN Flxq_ellgens(GEN a4, GEN a6, GEN ch, GEN D, GEN m, GEN T, ulong p)
+ GEN Flxq_ellgroup(GEN a4, GEN a6, GEN N, GEN T, ulong p, GEN *pt_m)
+ GEN Flxq_ellj(GEN a4, GEN a6, GEN T, ulong p)
+ GEN FlxqE_add(GEN P, GEN Q, GEN a4, GEN T, ulong p)
+ GEN FlxqE_changepoint(GEN x, GEN ch, GEN T, ulong p)
+ GEN FlxqE_changepointinv(GEN x, GEN ch, GEN T, ulong p)
+ GEN FlxqE_dbl(GEN P, GEN a4, GEN T, ulong p)
+ GEN FlxqE_log(GEN a, GEN b, GEN o, GEN a4, GEN T, ulong p)
+ GEN FlxqE_mul(GEN P, GEN n, GEN a4, GEN T, ulong p)
+ GEN FlxqE_neg(GEN P, GEN T, ulong p)
+ GEN FlxqE_order(GEN z, GEN o, GEN a4, GEN T, ulong p)
+ GEN FlxqE_sub(GEN P, GEN Q, GEN a4, GEN T, ulong p)
+ GEN FlxqE_tatepairing(GEN t, GEN s, GEN m, GEN a4, GEN T, ulong p)
+ GEN FlxqE_weilpairing(GEN t, GEN s, GEN m, GEN a4, GEN T, ulong p)
+ bb_group * get_FlxqE_group(void **E, GEN a4, GEN a6, GEN T, ulong p)
+ GEN RgE_to_FlxqE(GEN x, GEN T, ulong p)
+ GEN random_FlxqE(GEN a4, GEN a6, GEN T, ulong p)
+
+ # FpE.c
+
+ long Fl_elltrace(ulong a4, ulong a6, ulong p)
+ GEN Fle_add(GEN P, GEN Q, ulong a4, ulong p)
+ GEN Fle_dbl(GEN P, ulong a4, ulong p)
+ GEN Fle_mul(GEN P, GEN n, ulong a4, ulong p)
+ GEN Fle_mulu(GEN P, ulong n, ulong a4, ulong p)
+ GEN Fle_order(GEN z, GEN o, ulong a4, ulong p)
+ GEN Fle_sub(GEN P, GEN Q, ulong a4, ulong p)
+ GEN Fp_ellcard(GEN a4, GEN a6, GEN p)
+ GEN Fp_elldivpol(GEN a4, GEN a6, long n, GEN p)
+ GEN Fp_ellgens(GEN a4, GEN a6, GEN ch, GEN D, GEN m, GEN p)
+ GEN Fp_ellgroup(GEN a4, GEN a6, GEN N, GEN p, GEN *pt_m)
+ GEN Fp_ellj(GEN a4, GEN a6, GEN p)
+ GEN Fp_ffellcard(GEN a4, GEN a6, GEN q, long n, GEN p)
+ GEN FpE_add(GEN P, GEN Q, GEN a4, GEN p)
+ GEN FpE_changepoint(GEN x, GEN ch, GEN p)
+ GEN FpE_changepointinv(GEN x, GEN ch, GEN p)
+ GEN FpE_dbl(GEN P, GEN a4, GEN p)
+ GEN FpE_log(GEN a, GEN b, GEN o, GEN a4, GEN p)
+ GEN FpE_mul(GEN P, GEN n, GEN a4, GEN p)
+ GEN FpE_neg(GEN P, GEN p)
+ GEN FpE_order(GEN z, GEN o, GEN a4, GEN p)
+ GEN FpE_sub(GEN P, GEN Q, GEN a4, GEN p)
+ GEN FpE_to_mod(GEN P, GEN p)
+ GEN FpE_tatepairing(GEN t, GEN s, GEN m, GEN a4, GEN p)
+ GEN FpE_weilpairing(GEN t, GEN s, GEN m, GEN a4, GEN p)
+ GEN FpXQ_ellcard(GEN a4, GEN a6, GEN T, GEN p)
+ GEN FpXQ_elldivpol(GEN a4, GEN a6, long n, GEN T, GEN p)
+ GEN FpXQ_ellgens(GEN a4, GEN a6, GEN ch, GEN D, GEN m, GEN T, GEN p)
+ GEN FpXQ_ellgroup(GEN a4, GEN a6, GEN N, GEN T, GEN p, GEN *pt_m)
+ GEN FpXQ_ellj(GEN a4, GEN a6, GEN T, GEN p)
+ GEN FpXQE_add(GEN P, GEN Q, GEN a4, GEN T, GEN p)
+ GEN FpXQE_changepoint(GEN x, GEN ch, GEN T, GEN p)
+ GEN FpXQE_changepointinv(GEN x, GEN ch, GEN T, GEN p)
+ GEN FpXQE_dbl(GEN P, GEN a4, GEN T, GEN p)
+ GEN FpXQE_log(GEN a, GEN b, GEN o, GEN a4, GEN T, GEN p)
+ GEN FpXQE_mul(GEN P, GEN n, GEN a4, GEN T, GEN p)
+ GEN FpXQE_neg(GEN P, GEN T, GEN p)
+ GEN FpXQE_order(GEN z, GEN o, GEN a4, GEN T, GEN p)
+ GEN FpXQE_sub(GEN P, GEN Q, GEN a4, GEN T, GEN p)
+ GEN FpXQE_tatepairing(GEN t, GEN s, GEN m, GEN a4, GEN T, GEN p)
+ GEN FpXQE_weilpairing(GEN t, GEN s, GEN m, GEN a4, GEN T, GEN p)
+ GEN Fq_elldivpolmod(GEN a4, GEN a6, long n, GEN h, GEN T, GEN p)
+ GEN RgE_to_FpE(GEN x, GEN p)
+ GEN RgE_to_FpXQE(GEN x, GEN T, GEN p)
+ bb_group * get_FpE_group(void **E, GEN a4, GEN a6, GEN p)
+ bb_group * get_FpXQE_group(void **E, GEN a4, GEN a6, GEN T, GEN p)
+ GEN elltrace_extension(GEN t, long n, GEN p)
+ GEN random_Fle(ulong a4, ulong a6, ulong p)
+ GEN random_FpE(GEN a4, GEN a6, GEN p)
+ GEN random_FpXQE(GEN a4, GEN a6, GEN T, GEN p)
+
+ # FpX.c
+
+ int Fp_issquare(GEN x, GEN p)
+ GEN Fp_FpX_sub(GEN x, GEN y, GEN p)
+ GEN Fp_FpXQ_log(GEN a, GEN g, GEN ord, GEN T, GEN p)
+ GEN FpV_inv(GEN x, GEN p)
+ GEN FpV_roots_to_pol(GEN V, GEN p, long v)
+ GEN FpX_Fp_add(GEN x, GEN y, GEN p)
+ GEN FpX_Fp_add_shallow(GEN y, GEN x, GEN p)
+ GEN FpX_Fp_mul(GEN x, GEN y, GEN p)
+ GEN FpX_Fp_mul_to_monic(GEN y, GEN x, GEN p)
+ GEN FpX_Fp_mulspec(GEN y, GEN x, GEN p, long ly)
+ GEN FpX_Fp_sub(GEN x, GEN y, GEN p)
+ GEN FpX_Fp_sub_shallow(GEN y, GEN x, GEN p)
+ GEN FpX_FpXQ_eval(GEN f, GEN x, GEN T, GEN p)
+ GEN FpX_FpXQV_eval(GEN f, GEN x, GEN T, GEN p)
+ GEN FpX_add(GEN x, GEN y, GEN p)
+ GEN FpX_center(GEN x, GEN p, GEN pov2)
+ GEN FpX_chinese_coprime(GEN x, GEN y, GEN Tx, GEN Ty, GEN Tz, GEN p)
+ GEN FpX_deriv(GEN x, GEN p)
+ GEN FpX_disc(GEN x, GEN p)
+ GEN FpX_div_by_X_x(GEN a, GEN x, GEN p, GEN *r)
+ GEN FpX_divrem(GEN x, GEN y, GEN p, GEN *pr)
+ GEN FpX_eval(GEN x, GEN y, GEN p)
+ GEN FpX_extgcd(GEN x, GEN y, GEN p, GEN *ptu, GEN *ptv)
+ GEN FpX_gcd(GEN x, GEN y, GEN p)
+ GEN FpX_get_red(GEN T, GEN p)
+ GEN FpX_halfgcd(GEN x, GEN y, GEN p)
+ GEN FpX_invBarrett(GEN T, GEN p)
+ int FpX_is_squarefree(GEN f, GEN p)
+ GEN FpX_mul(GEN x, GEN y, GEN p)
+ GEN FpX_mulspec(GEN a, GEN b, GEN p, long na, long nb)
+ GEN FpX_mulu(GEN x, ulong y, GEN p)
+ GEN FpX_neg(GEN x, GEN p)
+ GEN FpX_normalize(GEN z, GEN p)
+ GEN FpX_red(GEN z, GEN p)
+ GEN FpX_rem(GEN x, GEN y, GEN p)
+ GEN FpX_rescale(GEN P, GEN h, GEN p)
+ GEN FpX_resultant(GEN a, GEN b, GEN p)
+ GEN FpX_sqr(GEN x, GEN p)
+ GEN FpX_sub(GEN x, GEN y, GEN p)
+ long FpX_valrem(GEN x0, GEN t, GEN p, GEN *py)
+ GEN FpXQ_autpow(GEN x, ulong n, GEN T, GEN p)
+ GEN FpXQ_autpowers(GEN aut, long f, GEN T, GEN p)
+ GEN FpXQ_autsum(GEN x, ulong n, GEN T, GEN p)
+ GEN FpXQ_charpoly(GEN x, GEN T, GEN p)
+ GEN FpXQ_conjvec(GEN x, GEN T, GEN p)
+ GEN FpXQ_div(GEN x, GEN y, GEN T, GEN p)
+ GEN FpXQ_inv(GEN x, GEN T, GEN p)
+ GEN FpXQ_invsafe(GEN x, GEN T, GEN p)
+ int FpXQ_issquare(GEN x, GEN T, GEN p)
+ GEN FpXQ_log(GEN a, GEN g, GEN ord, GEN T, GEN p)
+ GEN FpXQ_matrix_pow(GEN y, long n, long m, GEN P, GEN l)
+ GEN FpXQ_minpoly(GEN x, GEN T, GEN p)
+ GEN FpXQ_mul(GEN y, GEN x, GEN T, GEN p)
+ GEN FpXQ_norm(GEN x, GEN T, GEN p)
+ GEN FpXQ_order(GEN a, GEN ord, GEN T, GEN p)
+ GEN FpXQ_pow(GEN x, GEN n, GEN T, GEN p)
+ GEN FpXQ_powu(GEN x, ulong n, GEN T, GEN p)
+ GEN FpXQ_powers(GEN x, long l, GEN T, GEN p)
+ GEN FpXQ_red(GEN x, GEN T, GEN p)
+ GEN FpXQ_sqr(GEN y, GEN T, GEN p)
+ GEN FpXQ_sqrt(GEN a, GEN T, GEN p)
+ GEN FpXQ_sqrtn(GEN a, GEN n, GEN T, GEN p, GEN *zetan)
+ GEN FpXQ_trace(GEN x, GEN T, GEN p)
+ GEN FpXQC_to_mod(GEN z, GEN T, GEN p)
+ GEN FpXT_red(GEN z, GEN p)
+ GEN FpXV_prod(GEN V, GEN p)
+ GEN FpXV_red(GEN z, GEN p)
+ int Fq_issquare(GEN x, GEN T, GEN p)
+ GEN FqV_inv(GEN x, GEN T, GEN p)
+ GEN Z_to_FpX(GEN a, GEN p, long v)
+ GEN gener_FpXQ(GEN T, GEN p, GEN *o)
+ GEN gener_FpXQ_local(GEN T, GEN p, GEN L)
+ long get_FpX_degree(GEN T)
+ GEN get_FpX_mod(GEN T)
+ long get_FpX_var(GEN T)
+ bb_group *get_FpXQ_star(void **E, GEN T, GEN p)
+ GEN random_FpX(long d, long v, GEN p)
- # alglin1.c
+ # FpX_factor.c
+ GEN F2x_factor(GEN f)
+ int F2x_is_irred(GEN f)
+ void F2xV_to_FlxV_inplace(GEN v)
+ void F2xV_to_ZXV_inplace(GEN v)
+ int Flx_is_irred(GEN f, ulong p)
+ GEN Flx_degfact(GEN f, ulong p)
+ GEN Flx_factor(GEN f, ulong p)
+ long Flx_nbfact(GEN z, ulong p)
+ GEN Flx_nbfact_by_degree(GEN z, long *nb, ulong p)
+ long Flx_nbroots(GEN f, ulong p)
+ ulong Flx_oneroot(GEN f, ulong p)
+ GEN Flx_roots(GEN f, ulong p)
+ GEN FlxqX_Frobenius(GEN S, GEN T, ulong p)
+ GEN FlxqXQ_halfFrobenius(GEN a, GEN S, GEN T, ulong p)
+ long FlxqX_nbroots(GEN f, GEN T, ulong p)
+ void FlxV_to_ZXV_inplace(GEN v)
+ GEN FpX_degfact(GEN f, GEN p)
+ int FpX_is_irred(GEN f, GEN p)
+ int FpX_is_totally_split(GEN f, GEN p)
+ GEN FpX_factor(GEN f, GEN p)
+ GEN FpX_factorff(GEN P, GEN T, GEN p)
+ long FpX_nbfact(GEN f, GEN p)
+ long FpX_nbroots(GEN f, GEN p)
+ GEN FpX_oneroot(GEN f, GEN p)
+ GEN FpX_roots(GEN f, GEN p)
+ GEN FpX_rootsff(GEN P, GEN T, GEN p)
+ GEN FpXQX_Frobenius(GEN S, GEN T, GEN p)
+ long FpXQX_nbfact(GEN u, GEN T, GEN p)
+ long FpXQX_nbroots(GEN f, GEN T, GEN p)
+ GEN FpXQXQ_halfFrobenius(GEN a, GEN S, GEN T, GEN p)
+ GEN FqX_deriv(GEN f, GEN T, GEN p)
+ GEN FqX_factor(GEN x, GEN T, GEN p)
+ long FqX_is_squarefree(GEN P, GEN T, GEN p)
+ long FqX_nbfact(GEN u, GEN T, GEN p)
+ long FqX_nbroots(GEN f, GEN T, GEN p)
+ GEN FqX_roots(GEN f, GEN T, GEN p)
+ GEN factcantor(GEN x, GEN p)
+ GEN factorff(GEN f, GEN p, GEN a)
+ GEN factormod0(GEN f, GEN p, long flag)
+ GEN polrootsff(GEN f, GEN p, GEN T)
+ GEN rootmod0(GEN f, GEN p, long flag)
+
+ # FpXX.c
+
+ GEN FpXQX_FpXQ_mul(GEN P, GEN U, GEN T, GEN p)
+ GEN FpXQX_FpXQXQV_eval(GEN P, GEN V, GEN S, GEN T, GEN p)
+ GEN FpXQX_FpXQXQ_eval(GEN P, GEN x, GEN S, GEN T, GEN p)
+ GEN FpXQX_divrem(GEN x, GEN y, GEN T, GEN p, GEN *pr)
+ GEN FpXQX_divrem_Barrett(GEN x, GEN B, GEN S, GEN T, GEN p, GEN *pr)
+ GEN FpXQX_extgcd(GEN x, GEN y, GEN T, GEN p, GEN *ptu, GEN *ptv)
+ GEN FpXQX_gcd(GEN P, GEN Q, GEN T, GEN p)
+ GEN FpXQX_invBarrett(GEN S, GEN T, GEN p)
+ GEN FpXQX_mul(GEN x, GEN y, GEN T, GEN p)
+ GEN FpXQX_red(GEN z, GEN T, GEN p)
+ GEN FpXQX_rem(GEN x, GEN S, GEN T, GEN p)
+ GEN FpXQX_rem_Barrett(GEN x, GEN mg, GEN S, GEN T, GEN p)
+ GEN FpXQX_sqr(GEN x, GEN T, GEN p)
+ GEN FpXQXQ_div(GEN x, GEN y, GEN S, GEN T, GEN p)
+ GEN FpXQXQ_inv(GEN x, GEN S, GEN T, GEN p)
+ GEN FpXQXQ_invsafe(GEN x, GEN S, GEN T, GEN p)
+ GEN FpXQXQ_matrix_pow(GEN y, long n, long m, GEN S, GEN T, GEN p)
+ GEN FpXQXQ_mul(GEN x, GEN y, GEN S, GEN T, GEN p)
+ GEN FpXQXQ_pow(GEN x, GEN n, GEN S, GEN T, GEN p)
+ GEN FpXQXQ_powers(GEN x, long n, GEN S, GEN T, GEN p)
+ GEN FpXQXQ_sqr(GEN x, GEN S, GEN T, GEN p)
+ GEN FpXQXQV_autpow(GEN aut, long n, GEN S, GEN T, GEN p)
+ GEN FpXQXQV_autsum(GEN aut, long n, GEN S, GEN T, GEN p)
+ GEN FpXQXV_prod(GEN V, GEN Tp, GEN p)
+ GEN FpXX_Fp_mul(GEN x, GEN y, GEN p)
+ GEN FpXX_FpX_mul(GEN x, GEN y, GEN p)
+ GEN FpXX_add(GEN x, GEN y, GEN p)
+ GEN FpXX_mulu(GEN P, ulong u, GEN p)
+ GEN FpXX_neg(GEN x, GEN p)
+ GEN FpXX_red(GEN z, GEN p)
+ GEN FpXX_sub(GEN x, GEN y, GEN p)
+ GEN FpXY_FpXQ_evalx(GEN P, GEN x, GEN T, GEN p)
+ GEN FpXY_eval(GEN Q, GEN y, GEN x, GEN p)
+ GEN FpXY_evalx(GEN Q, GEN x, GEN p)
+ GEN FpXY_evaly(GEN Q, GEN y, GEN p, long vy)
+ GEN FpXYQQ_pow(GEN x, GEN n, GEN S, GEN T, GEN p)
+ GEN Kronecker_to_FpXQX(GEN z, GEN pol, GEN p)
+ GEN Kronecker_to_ZXX(GEN z, long N, long v)
+ GEN ZXX_mul_Kronecker(GEN x, GEN y, long n)
+
+ # FpV.c
+
+ GEN F2m_F2c_mul(GEN x, GEN y)
+ GEN F2m_mul(GEN x, GEN y)
+ GEN F2m_powu(GEN x, ulong n)
+ GEN Flc_Fl_div(GEN x, ulong y, ulong p)
+ void Flc_Fl_div_inplace(GEN x, ulong y, ulong p)
+ GEN Flc_Fl_mul(GEN x, ulong y, ulong p)
+ void Flc_Fl_mul_inplace(GEN x, ulong y, ulong p)
+ void Flc_Fl_mul_part_inplace(GEN x, ulong y, ulong p, long l)
+ GEN Flc_to_mod(GEN z, ulong pp)
+ GEN Flm_Fl_add(GEN x, ulong y, ulong p)
+ GEN Flm_Fl_mul(GEN y, ulong x, ulong p)
+ void Flm_Fl_mul_inplace(GEN y, ulong x, ulong p)
+ GEN Flm_Flc_mul(GEN x, GEN y, ulong p)
+ GEN Flm_center(GEN z, ulong p, ulong ps2)
+ GEN Flm_mul(GEN x, GEN y, ulong p)
+ GEN Flm_neg(GEN y, ulong p)
+ GEN Flm_powu(GEN x, ulong n, ulong p)
+ GEN Flm_to_mod(GEN z, ulong pp)
+ GEN Flm_transpose(GEN x)
+ GEN Flv_add(GEN x, GEN y, ulong p)
+ void Flv_add_inplace(GEN x, GEN y, ulong p)
+ ulong Flv_dotproduct(GEN x, GEN y, ulong p)
+ GEN Flv_center(GEN z, ulong p, ulong ps2)
+ GEN Flv_sub(GEN x, GEN y, ulong p)
+ void Flv_sub_inplace(GEN x, GEN y, ulong p)
+ ulong Flv_sum(GEN x, ulong p)
+ GEN Fp_to_mod(GEN z, GEN p)
+ GEN FpC_FpV_mul(GEN x, GEN y, GEN p)
+ GEN FpC_Fp_mul(GEN x, GEN y, GEN p)
+ GEN FpC_center(GEN z, GEN p, GEN pov2)
+ GEN FpC_red(GEN z, GEN p)
+ GEN FpC_to_mod(GEN z, GEN p)
+ GEN FpM_FpC_mul(GEN x, GEN y, GEN p)
+ GEN FpM_FpC_mul_FpX(GEN x, GEN y, GEN p, long v)
+ GEN FpM_center(GEN z, GEN p, GEN pov2)
+ GEN FpM_mul(GEN x, GEN y, GEN p)
+ GEN FpM_powu(GEN x, ulong n, GEN p)
+ GEN FpM_red(GEN z, GEN p)
+ GEN FpM_to_mod(GEN z, GEN p)
+ GEN FpMs_FpC_mul(GEN M, GEN B, GEN p)
+ GEN FpMs_FpCs_solve(GEN M, GEN B, long nbrow, GEN p)
+ GEN FpMs_FpCs_solve_safe(GEN M, GEN A, long nbrow, GEN p)
+ GEN FpMs_leftkernel_elt(GEN M, long nbrow, GEN p)
+ GEN FpC_add(GEN x, GEN y, GEN p)
+ GEN FpC_sub(GEN x, GEN y, GEN p)
+ GEN FpV_FpMs_mul(GEN B, GEN M, GEN p)
+ GEN FpV_add(GEN x, GEN y, GEN p)
+ GEN FpV_sub(GEN x, GEN y, GEN p)
+ GEN FpV_dotproduct(GEN x, GEN y, GEN p)
+ GEN FpV_dotsquare(GEN x, GEN p)
+ GEN FpV_red(GEN z, GEN p)
+ GEN FpV_to_mod(GEN z, GEN p)
+ GEN FpVV_to_mod(GEN z, GEN p)
+ GEN FpX_to_mod(GEN z, GEN p)
+ GEN ZV_zMs_mul(GEN B, GEN M)
+ GEN ZpMs_ZpCs_solve(GEN M, GEN B, long nbrow, GEN p, long e)
+ GEN gen_FpM_Wiedemann(void *E, GEN (*f)(void*, GEN), GEN B, GEN p)
+ GEN gen_ZpM_Dixon(void *E, GEN (*f)(void*, GEN), GEN B, GEN p, long e)
+ GEN gen_matid(long n, void *E, bb_field *S)
+ GEN matid_F2m(long n)
+ GEN matid_Flm(long n)
+ GEN matid_F2xqM(long n, GEN T)
+ GEN matid_FlxqM(long n, GEN T, ulong p)
+ GEN scalar_Flm(long s, long n)
+ GEN zCs_to_ZC(GEN C, long nbrow)
+ GEN zMs_to_ZM(GEN M, long nbrow)
+ GEN zMs_ZC_mul(GEN M, GEN B)
+
+ # Hensel.c
+
+ GEN Zp_sqrtlift(GEN b, GEN a, GEN p, long e)
+ GEN Zp_sqrtnlift(GEN b, GEN n, GEN a, GEN p, long e)
+ GEN ZpX_liftfact(GEN pol, GEN Q, GEN T, GEN p, long e, GEN pe)
+ GEN ZpX_liftroot(GEN f, GEN a, GEN p, long e)
+ GEN ZpX_liftroots(GEN f, GEN S, GEN q, long e)
+ GEN ZpXQ_inv(GEN a, GEN T, GEN p, long e)
+ GEN ZpXQ_invlift(GEN b, GEN a, GEN T, GEN p, long e)
+ GEN ZpXQ_log(GEN a, GEN T, GEN p, long N)
+ GEN ZpXQ_sqrtnlift(GEN b, GEN n, GEN a, GEN T, GEN p, long e)
+ GEN ZpXQX_liftroot(GEN f, GEN a, GEN T, GEN p, long e)
+ GEN ZpXQX_liftroot_vald(GEN f, GEN a, long v, GEN T, GEN p, long e)
+ GEN gen_ZpX_Dixon(GEN F, GEN V, GEN q, GEN p, long N, void *E,
+ GEN lin(void *E, GEN F, GEN d, GEN q),
+ GEN invl(void *E, GEN d))
+ GEN gen_ZpX_Newton(GEN x, GEN p, long n, void *E,
+ GEN eval(void *E, GEN f, GEN q),
+ GEN invd(void *E, GEN V, GEN v, GEN q, long M))
+ GEN polhensellift(GEN pol, GEN fct, GEN p, long exp)
+ ulong quadratic_prec_mask(long n)
+
+ # QX_factor.c
+
+ GEN QX_factor(GEN x)
+ GEN ZX_factor(GEN x)
+ long ZX_is_irred(GEN x)
+ GEN ZX_squff(GEN f, GEN *ex)
+ GEN polcyclofactors(GEN f)
+ long poliscyclo(GEN f)
+ long poliscycloprod(GEN f)
+
+ # RgV.c
+
+ GEN RgC_Rg_add(GEN x, GEN y)
+ GEN RgC_Rg_div(GEN x, GEN y)
+ GEN RgC_Rg_mul(GEN x, GEN y)
+ GEN RgC_RgM_mul(GEN x, GEN y)
+ GEN RgC_RgV_mul(GEN x, GEN y)
+ GEN RgC_add(GEN x, GEN y)
+ GEN RgC_neg(GEN x)
+ GEN RgC_sub(GEN x, GEN y)
+ GEN RgM_Rg_add(GEN x, GEN y)
+ GEN RgM_Rg_add_shallow(GEN x, GEN y)
+ GEN RgM_Rg_div(GEN x, GEN y)
+ GEN RgM_Rg_mul(GEN x, GEN y)
+ GEN RgM_Rg_sub(GEN x, GEN y)
+ GEN RgM_Rg_sub_shallow(GEN x, GEN y)
+ GEN RgM_RgC_mul(GEN x, GEN y)
+ GEN RgM_RgV_mul(GEN x, GEN y)
+ GEN RgM_add(GEN x, GEN y)
+ GEN RgM_det_triangular(GEN x)
+ int RgM_is_ZM(GEN x)
+ int RgM_isdiagonal(GEN x)
+ int RgM_isidentity(GEN x)
+ int RgM_isscalar(GEN x, GEN s)
+ GEN RgM_mul(GEN x, GEN y)
+ GEN RgM_multosym(GEN x, GEN y)
+ GEN RgM_neg(GEN x)
+ GEN RgM_powers(GEN x, long l)
+ GEN RgM_sqr(GEN x)
+ GEN RgM_sub(GEN x, GEN y)
+ GEN RgM_transmul(GEN x, GEN y)
+ GEN RgM_transmultosym(GEN x, GEN y)
+ GEN RgM_zc_mul(GEN x, GEN y)
+ GEN RgM_zm_mul(GEN x, GEN y)
+ GEN RgMrow_RgC_mul(GEN x, GEN y, long i)
+ GEN RgV_RgM_mul(GEN x, GEN y)
+ GEN RgV_RgC_mul(GEN x, GEN y)
+ GEN RgV_Rg_mul(GEN x, GEN y)
+ GEN RgV_add(GEN x, GEN y)
+ GEN RgV_dotproduct(GEN x, GEN y)
+ GEN RgV_dotsquare(GEN x)
+ int RgV_is_ZMV(GEN V)
+ long RgV_isin(GEN v, GEN x)
+ GEN RgV_neg(GEN x)
+ GEN RgV_sub(GEN x, GEN y)
+ GEN RgV_sum(GEN v)
+ GEN RgV_sumpart(GEN v, long n)
+ GEN RgV_sumpart2(GEN v, long m, long n)
+ GEN RgV_zc_mul(GEN x, GEN y)
+ GEN RgV_zm_mul(GEN x, GEN y)
+ GEN RgX_RgM_eval(GEN x, GEN y)
+ GEN RgX_RgMV_eval(GEN x, GEN y)
+ int isdiagonal(GEN x)
+ GEN matid(long n)
+ GEN scalarcol(GEN x, long n)
+ GEN scalarcol_shallow(GEN x, long n)
+ GEN scalarmat(GEN x, long n)
+ GEN scalarmat_shallow(GEN x, long n)
+ GEN scalarmat_s(long x, long n)
+
+ # RgX.c
+
+ GEN Kronecker_to_mod(GEN z, GEN pol)
+ GEN QX_ZXQV_eval(GEN P, GEN V, GEN dV)
+ GEN QXQ_powers(GEN a, long n, GEN T)
+ GEN QXQX_to_mod_shallow(GEN z, GEN T)
+ GEN QXQV_to_mod(GEN V, GEN T)
+ GEN QXQXV_to_mod(GEN V, GEN T)
+ GEN QXV_QXQ_eval(GEN v, GEN a, GEN T)
+ GEN QXX_QXQ_eval(GEN v, GEN a, GEN T)
+ GEN Rg_to_RgV(GEN x, long N)
+ GEN RgM_to_RgXV(GEN x, long v)
+ GEN RgM_to_RgXX(GEN x, long v, long w)
+ GEN RgV_to_RgX(GEN x, long v)
+ GEN RgV_to_RgX_reverse(GEN x, long v)
+ GEN RgXQC_red(GEN P, GEN T)
+ GEN RgXQV_red(GEN P, GEN T)
+ GEN RgXQX_RgXQ_mul(GEN x, GEN y, GEN T)
+ GEN RgXQX_divrem(GEN x, GEN y, GEN T, GEN *r)
+ GEN RgXQX_mul(GEN x, GEN y, GEN T)
+ GEN RgXQX_pseudodivrem(GEN x, GEN y, GEN T, GEN *ptr)
+ GEN RgXQX_pseudorem(GEN x, GEN y, GEN T)
+ GEN RgXQX_red(GEN P, GEN T)
+ GEN RgXQX_sqr(GEN x, GEN T)
+ GEN RgXQX_translate(GEN P, GEN c, GEN T)
+ GEN RgXQ_matrix_pow(GEN y, long n, long m, GEN P)
+ GEN RgXQ_norm(GEN x, GEN T)
+ GEN RgXQ_pow(GEN x, GEN n, GEN T)
+ GEN RgXQ_powu(GEN x, ulong n, GEN T)
+ GEN RgXQ_powers(GEN x, long l, GEN T)
+ GEN RgXV_to_RgM(GEN v, long n)
+ GEN RgXV_unscale(GEN v, GEN h)
+ GEN RgXX_to_RgM(GEN v, long n)
+ GEN RgXY_swap(GEN x, long n, long w)
+ GEN RgXY_swapspec(GEN x, long n, long w, long nx)
+ GEN RgX_RgXQ_eval(GEN f, GEN x, GEN T)
+ GEN RgX_RgXQV_eval(GEN P, GEN V, GEN T)
+ GEN RgX_Rg_add(GEN y, GEN x)
+ GEN RgX_Rg_add_shallow(GEN y, GEN x)
+ GEN RgX_Rg_div(GEN y, GEN x)
+ GEN RgX_Rg_divexact(GEN x, GEN y)
+ GEN RgX_Rg_mul(GEN y, GEN x)
+ GEN RgX_Rg_sub(GEN y, GEN x)
+ GEN RgX_add(GEN x, GEN y)
+ GEN RgX_blocks(GEN P, long n, long m)
+ GEN RgX_deflate(GEN x0, long d)
+ GEN RgX_deriv(GEN x)
+ GEN RgX_div_by_X_x(GEN a, GEN x, GEN *r)
+ GEN RgX_divrem(GEN x, GEN y, GEN *r)
+ GEN RgX_divs(GEN y, long x)
+ long RgX_equal(GEN x, GEN y)
+ void RgX_even_odd(GEN p, GEN *pe, GEN *po)
+ GEN RgX_get_0(GEN x)
+ GEN RgX_get_1(GEN x)
+ GEN RgX_inflate(GEN x0, long d)
+ GEN RgX_modXn_shallow(GEN a, long n)
+ GEN RgX_modXn_eval(GEN Q, GEN x, long n)
+ GEN RgX_mul(GEN x, GEN y)
+ GEN RgX_mul_normalized(GEN A, long a, GEN B, long b)
+ GEN RgX_mulXn(GEN x, long d)
+ GEN RgX_mullow(GEN f, GEN g, long n)
+ GEN RgX_muls(GEN y, long x)
+ GEN RgX_mulspec(GEN a, GEN b, long na, long nb)
+ GEN RgX_neg(GEN x)
+ GEN RgX_pseudodivrem(GEN x, GEN y, GEN *ptr)
+ GEN RgX_pseudorem(GEN x, GEN y)
+ GEN RgX_recip(GEN x)
+ GEN RgX_recip_shallow(GEN x)
+ GEN RgX_renormalize_lg(GEN x, long lx)
+ GEN RgX_rescale(GEN P, GEN h)
+ GEN RgX_rotate_shallow(GEN P, long k, long p)
+ GEN RgX_shift(GEN a, long n)
+ GEN RgX_shift_shallow(GEN x, long n)
+ GEN RgX_splitting(GEN p, long k)
+ GEN RgX_sqr(GEN x)
+ GEN RgX_sqrlow(GEN f, long n)
+ GEN RgX_sqrspec(GEN a, long na)
+ GEN RgX_sub(GEN x, GEN y)
+ GEN RgX_to_RgV(GEN x, long N)
+ GEN RgX_translate(GEN P, GEN c)
+ GEN RgX_unscale(GEN P, GEN h)
+ GEN Rg_RgX_sub(GEN x, GEN y)
+ GEN ZX_translate(GEN P, GEN c)
+ GEN ZX_unscale(GEN P, GEN h)
+ GEN ZX_unscale_div(GEN P, GEN h)
+ int ZXQX_dvd(GEN x, GEN y, GEN T)
+ long brent_kung_optpow(long d, long n, long m)
+ GEN gen_bkeval(GEN Q, long d, GEN x, int use_sqr, void *E,
+ bb_algebra *ff, GEN cmul(void *E, GEN P, long a, GEN x))
+ GEN gen_bkeval_powers(GEN P, long d, GEN V, void *E,
+ bb_algebra *ff, GEN cmul(void *E, GEN P, long a, GEN x))
+
+ # ZV.c
+
+ void Flc_lincomb1_inplace(GEN X, GEN Y, ulong v, ulong q)
+ void RgM_check_ZM(GEN A, const char *s)
+ void RgV_check_ZV(GEN A, const char *s)
+ GEN ZC_ZV_mul(GEN x, GEN y)
+ GEN ZC_Z_add(GEN x, GEN y)
+ GEN ZC_Z_divexact(GEN X, GEN c)
+ GEN ZC_Z_mul(GEN X, GEN c)
+ GEN ZC_Z_sub(GEN x, GEN y)
+ GEN ZC_add(GEN x, GEN y)
+ GEN ZC_copy(GEN x)
+ GEN ZC_hnfremdiv(GEN x, GEN y, GEN *Q)
+ GEN ZC_lincomb(GEN u, GEN v, GEN X, GEN Y)
+ void ZC_lincomb1_inplace(GEN X, GEN Y, GEN v)
+ GEN ZC_neg(GEN M)
+ GEN ZC_reducemodlll(GEN x, GEN y)
+ GEN ZC_reducemodmatrix(GEN v, GEN y)
+ GEN ZC_sub(GEN x, GEN y)
+ GEN ZC_z_mul(GEN X, long c)
+ GEN ZM_ZC_mul(GEN x, GEN y)
+ GEN ZM_Z_divexact(GEN X, GEN c)
+ GEN ZM_Z_mul(GEN X, GEN c)
+ GEN ZM_add(GEN x, GEN y)
+ GEN ZM_copy(GEN x)
+ GEN ZM_det_triangular(GEN mat)
+ int ZM_equal(GEN A, GEN B)
+ GEN ZM_hnfdivrem(GEN x, GEN y, GEN *Q)
+ int ZM_ishnf(GEN x)
+ int ZM_isidentity(GEN x)
+ long ZM_max_lg(GEN x)
+ GEN ZM_mul(GEN x, GEN y)
+ GEN ZM_multosym(GEN x, GEN y)
+ GEN ZM_neg(GEN x)
+ GEN ZM_nm_mul(GEN x, GEN y)
+ GEN ZM_pow(GEN x, GEN n)
+ GEN ZM_powu(GEN x, ulong n)
+ GEN ZM_reducemodlll(GEN x, GEN y)
+ GEN ZM_reducemodmatrix(GEN v, GEN y)
+ GEN ZM_sub(GEN x, GEN y)
+ GEN ZM_supnorm(GEN x)
+ GEN ZM_to_Flm(GEN x, ulong p)
+ GEN ZM_to_zm(GEN z)
+ GEN ZM_transmultosym(GEN x, GEN y)
+ GEN ZMV_to_zmV(GEN z)
+ void ZM_togglesign(GEN M)
+ GEN ZM_zc_mul(GEN x, GEN y)
+ GEN ZM_zm_mul(GEN x, GEN y)
+ GEN ZMrow_ZC_mul(GEN x, GEN y, long i)
+ GEN ZV_ZM_mul(GEN x, GEN y)
+ int ZV_abscmp(GEN x, GEN y)
+ int ZV_cmp(GEN x, GEN y)
+ GEN ZV_content(GEN x)
+ GEN ZV_dotproduct(GEN x, GEN y)
+ GEN ZV_dotsquare(GEN x)
+ int ZV_equal(GEN V, GEN W)
+ int ZV_equal0(GEN V)
+ long ZV_max_lg(GEN x)
+ void ZV_neg_inplace(GEN M)
+ GEN ZV_prod(GEN v)
+ GEN ZV_sum(GEN v)
+ GEN ZV_to_Flv(GEN x, ulong p)
+ GEN ZV_to_nv(GEN z)
+ void ZV_togglesign(GEN M)
+ GEN gram_matrix(GEN M)
+ GEN nm_Z_mul(GEN X, GEN c)
+ GEN zm_mul(GEN x, GEN y)
+ GEN zm_to_Flm(GEN z, ulong p)
+ GEN zm_to_ZM(GEN z)
+ GEN zm_zc_mul(GEN x, GEN y)
+ GEN zmV_to_ZMV(GEN z)
+ long zv_content(GEN x)
+ long zv_dotproduct(GEN x, GEN y)
+ int zv_equal(GEN V, GEN W)
+ int zv_equal0(GEN V)
+ GEN zv_neg(GEN x)
+ GEN zv_neg_inplace(GEN M)
+ long zv_prod(GEN v)
+ GEN zv_prod_Z(GEN v)
+ long zv_sum(GEN v)
+ GEN zv_to_Flv(GEN z, ulong p)
+ GEN zv_z_mul(GEN v, long n)
+ int zvV_equal(GEN V, GEN W)
+
+ # ZX.c
+
+ void RgX_check_QX(GEN x, const char *s)
+ void RgX_check_ZX(GEN x, const char *s)
+ void RgX_check_ZXX(GEN x, const char *s)
+ GEN Z_ZX_sub(GEN x, GEN y)
+ GEN ZX_Z_add(GEN y, GEN x)
+ GEN ZX_Z_add_shallow(GEN y, GEN x)
+ GEN ZX_Z_divexact(GEN y, GEN x)
+ GEN ZX_Z_mul(GEN y, GEN x)
+ GEN ZX_Z_sub(GEN y, GEN x)
+ GEN ZX_add(GEN x, GEN y)
+ GEN ZX_copy(GEN x)
+ GEN ZX_deriv(GEN x)
+ int ZX_equal(GEN V, GEN W)
+ GEN ZX_eval1(GEN x)
+ long ZX_max_lg(GEN x)
+ GEN ZX_mod_Xnm1(GEN T, ulong n)
+ GEN ZX_mul(GEN x, GEN y)
+ GEN ZX_mulspec(GEN a, GEN b, long na, long nb)
+ GEN ZX_mulu(GEN y, ulong x)
+ GEN ZX_neg(GEN x)
+ GEN ZX_rem(GEN x, GEN y)
+ GEN ZX_remi2n(GEN y, long n)
+ GEN ZX_rescale(GEN P, GEN h)
+ GEN ZX_rescale_lt(GEN P)
+ GEN ZX_shifti(GEN x, long n)
+ GEN ZX_sqr(GEN x)
+ GEN ZX_sqrspec(GEN a, long na)
+ GEN ZX_sub(GEN x, GEN y)
+ long ZX_val(GEN x)
+ long ZX_valrem(GEN x, GEN *Z)
+ GEN ZXT_remi2n(GEN z, long n)
+ GEN ZXV_Z_mul(GEN y, GEN x)
+ GEN ZXV_dotproduct(GEN V, GEN W)
+ int ZXV_equal(GEN V, GEN W)
+ GEN ZXV_remi2n(GEN x, long n)
+ GEN ZXX_Z_divexact(GEN y, GEN x)
+ long ZXX_max_lg(GEN x)
+ GEN ZXX_renormalize(GEN x, long lx)
+ GEN ZXX_to_Kronecker(GEN P, long n)
+ GEN ZXX_to_Kronecker_spec(GEN P, long lP, long n)
+ GEN scalar_ZX(GEN x, long v)
+ GEN scalar_ZX_shallow(GEN x, long v)
+ GEN zx_to_ZX(GEN z)
+
+ # alglin1.c
+
+ GEN F2m_F2c_gauss(GEN a, GEN b)
+ GEN F2m_F2c_invimage(GEN A, GEN y)
+ GEN F2m_deplin(GEN x)
+ ulong F2m_det(GEN x)
+ ulong F2m_det_sp(GEN x)
+ GEN F2m_gauss(GEN a, GEN b)
+ GEN F2m_image(GEN x)
+ GEN F2m_indexrank(GEN x)
+ GEN F2m_inv(GEN x)
+ GEN F2m_invimage(GEN A, GEN B)
+ GEN F2m_ker(GEN x)
+ GEN F2m_ker_sp(GEN x, long deplin)
+ long F2m_rank(GEN x)
+ GEN F2m_suppl(GEN x)
+ GEN F2xqM_F2xqC_mul(GEN a, GEN b, GEN T)
+ GEN F2xqM_det(GEN a, GEN T)
+ GEN F2xqM_ker(GEN x, GEN T)
+ GEN F2xqM_image(GEN x, GEN T)
+ GEN F2xqM_inv(GEN a, GEN T)
+ GEN F2xqM_mul(GEN a, GEN b, GEN T)
+ long F2xqM_rank(GEN x, GEN T)
+ GEN Flm_Flc_gauss(GEN a, GEN b, ulong p)
+ GEN Flm_Flc_invimage(GEN mat, GEN y, ulong p)
GEN Flm_deplin(GEN x, ulong p)
+ ulong Flm_det(GEN x, ulong p)
+ ulong Flm_det_sp(GEN x, ulong p)
+ GEN Flm_gauss(GEN a, GEN b, ulong p)
+ GEN Flm_image(GEN x, ulong p)
+ GEN Flm_invimage(GEN m, GEN v, ulong p)
GEN Flm_indexrank(GEN x, ulong p)
GEN Flm_inv(GEN x, ulong p)
GEN Flm_ker(GEN x, ulong p)
GEN Flm_ker_sp(GEN x, ulong p, long deplin)
- GEN Flm_mul(GEN x, GEN y, ulong p)
+ long Flm_rank(GEN x, ulong p)
+ GEN Flm_suppl(GEN x, ulong p)
+ GEN FlxqM_FlxqC_gauss(GEN a, GEN b, GEN T, ulong p)
+ GEN FlxqM_FlxqC_mul(GEN a, GEN b, GEN T, ulong p)
+ GEN FlxqM_det(GEN a, GEN T, ulong p)
+ GEN FlxqM_gauss(GEN a, GEN b, GEN T, ulong p)
GEN FlxqM_ker(GEN x, GEN T, ulong p)
- GEN FpC_FpV_mul(GEN x, GEN y, GEN p)
+ GEN FlxqM_image(GEN x, GEN T, ulong p)
+ GEN FlxqM_inv(GEN x, GEN T, ulong p)
+ GEN FlxqM_mul(GEN a, GEN b, GEN T, ulong p)
+ long FlxqM_rank(GEN x, GEN T, ulong p)
+ GEN FpM_FpC_gauss(GEN a, GEN b, GEN p)
+ GEN FpM_FpC_invimage(GEN m, GEN v, GEN p)
GEN FpM_deplin(GEN x, GEN p)
+ GEN FpM_det(GEN x, GEN p)
+ GEN FpM_gauss(GEN a, GEN b, GEN p)
GEN FpM_image(GEN x, GEN p)
+ GEN FpM_indexrank(GEN x, GEN p)
GEN FpM_intersect(GEN x, GEN y, GEN p)
GEN FpM_inv(GEN x, GEN p)
GEN FpM_invimage(GEN m, GEN v, GEN p)
GEN FpM_ker(GEN x, GEN p)
- GEN FpM_mul(GEN x, GEN y, GEN p)
long FpM_rank(GEN x, GEN p)
- GEN FpM_indexrank(GEN x, GEN p)
GEN FpM_suppl(GEN x, GEN p)
+ GEN FqM_FqC_gauss(GEN a, GEN b, GEN T, GEN p)
+ GEN FqM_FqC_mul(GEN a, GEN b, GEN T, GEN p)
+ GEN FqM_deplin(GEN x, GEN T, GEN p)
+ GEN FqM_det(GEN x, GEN T, GEN p)
GEN FqM_gauss(GEN a, GEN b, GEN T, GEN p)
GEN FqM_ker(GEN x, GEN T, GEN p)
+ GEN FqM_image(GEN x, GEN T, GEN p)
+ GEN FqM_inv(GEN x, GEN T, GEN p)
+ GEN FqM_mul(GEN a, GEN b, GEN T, GEN p)
+ long FqM_rank(GEN a, GEN T, GEN p)
GEN FqM_suppl(GEN x, GEN T, GEN p)
GEN QM_inv(GEN M, GEN dM)
+ GEN RgM_Fp_init(GEN a, GEN p, ulong *pp)
+ GEN RgM_RgC_invimage(GEN A, GEN B)
+ GEN RgM_diagonal(GEN m)
+ GEN RgM_diagonal_shallow(GEN m)
+ GEN RgM_Hadamard(GEN a)
+ GEN RgM_inv_upper(GEN a)
+ GEN RgM_invimage(GEN A, GEN B)
+ GEN RgM_solve(GEN a, GEN b)
+ GEN RgM_solve_realimag(GEN x, GEN y)
+ void RgMs_structelim(GEN M, long N, GEN A, GEN *p_col, GEN *p_lin)
+ GEN ZM_det(GEN a)
+ GEN ZM_detmult(GEN A)
+ GEN ZM_gauss(GEN a, GEN b)
+ GEN ZM_imagecompl(GEN x)
+ GEN ZM_indeximage(GEN x)
GEN ZM_inv(GEN M, GEN dM)
- GEN concat(GEN x, GEN y)
+ long ZM_rank(GEN x)
+ GEN ZlM_gauss(GEN a, GEN b, ulong p, long e, GEN C)
+ GEN closemodinvertible(GEN x, GEN y)
GEN deplin(GEN x)
GEN det(GEN a)
- GEN det0(GEN a,long flag)
+ GEN det0(GEN a, long flag)
GEN det2(GEN a)
GEN detint(GEN x)
- GEN diagonal(GEN x)
GEN eigen(GEN x, long prec)
- GEN shallowextract(GEN x, GEN l)
- GEN extract0(GEN x, GEN l1, GEN l2)
GEN gauss(GEN a, GEN b)
GEN gaussmodulo(GEN M, GEN D, GEN Y)
GEN gaussmodulo2(GEN M, GEN D, GEN Y)
- GEN scalarmat_s(long x, long n)
- GEN gtomat(GEN x)
- GEN gtrans(GEN x)
- int hnfdivide(GEN A, GEN B)
- GEN matid(long n)
+ GEN gen_Gauss(GEN a, GEN b, void *E, bb_field *ff)
+ GEN gen_Gauss_pivot(GEN x, long *rr, void *E, bb_field *ff)
+ GEN gen_det(GEN a, void *E, bb_field *ff)
+ GEN gen_ker(GEN x, long deplin, void *E, bb_field *ff)
+ GEN gen_matcolmul(GEN a, GEN b, void *E, bb_field *ff)
+ GEN gen_matmul(GEN a, GEN b, void *E, bb_field *ff)
GEN image(GEN x)
GEN image2(GEN x)
GEN imagecompl(GEN x)
GEN indexrank(GEN x)
GEN inverseimage(GEN mat, GEN y)
- long isdiagonal(GEN x)
GEN ker(GEN x)
GEN keri(GEN x)
- GEN matimage0(GEN x,long flag)
+ GEN mateigen(GEN x, long flag, long prec)
+ GEN matimage0(GEN x, long flag)
GEN matker0(GEN x, long flag)
- GEN matmuldiagonal(GEN x, GEN d)
- GEN matmultodiagonal(GEN x, GEN y)
- GEN matsolvemod0(GEN M, GEN D, GEN Y,long flag)
+ GEN matsolvemod0(GEN M, GEN D, GEN Y, long flag)
long rank(GEN x)
- GEN indexrank(GEN x)
- # we rename sum to pari_sum to avoid conflicts with
- # python's sum function
- GEN pari_sum "sum"(GEN v, long a, long b)
+ GEN reducemodinvertible(GEN x, GEN y)
+ GEN reducemodlll(GEN x, GEN y)
+ GEN split_realimag(GEN x, long r1, long r2)
GEN suppl(GEN x)
- GEN vconcat(GEN A, GEN B)
# alglin2.c
- GEN ZM_to_zm(GEN z)
+ GEN FpM_charpoly(GEN x, GEN p)
+ GEN FpM_hess(GEN x, GEN p)
+ GEN Flm_charpoly(GEN x, long p)
+ GEN Flm_hess(GEN x, ulong p)
+ GEN QM_minors_coprime(GEN x, GEN pp)
+ GEN QM_ImZ_hnf(GEN x)
+ GEN QM_ImQ_hnf(GEN x)
+ GEN gnorml1_fake(GEN x)
+ GEN ZM_charpoly(GEN x)
GEN adj(GEN x)
- GEN caract(GEN x, int v)
+ GEN adjsafe(GEN x)
+ GEN caract(GEN x, long v)
GEN caradj(GEN x, long v, GEN *py)
+ GEN carberkowitz(GEN x, long v)
GEN carhess(GEN x, long v)
- GEN charpoly0(GEN x, int v,long flag)
- GEN conjvec(GEN x,long prec)
- GEN gconj(GEN x)
+ GEN charpoly(GEN x, long v)
+ GEN charpoly0(GEN x, long v, long flag)
GEN gnorm(GEN x)
- GEN gnorml1(GEN x,long prec)
+ GEN gnorml1(GEN x, long prec)
+ GEN gnormlp(GEN x, GEN p, long prec)
GEN gnorml2(GEN x)
+ GEN gsupnorm(GEN x, long prec)
+ void gsupnorm_aux(GEN x, GEN *m, GEN *msq, long prec)
GEN gtrace(GEN x)
GEN hess(GEN x)
- GEN hnf(GEN x)
- GEN hnfall(GEN x)
- GEN hnflll(GEN x)
- GEN hnfmod(GEN x, GEN detmat)
- GEN hnfmodid(GEN x,GEN p)
- GEN hnfperm(GEN x)
GEN intersect(GEN x, GEN y)
GEN jacobi(GEN a, long prec)
- GEN matfrobenius(GEN M, long flag, long v)
- GEN matrixqz(GEN x, GEN pp)
+ GEN matadjoint0(GEN x, long flag)
+ GEN matcompanion(GEN x)
GEN matrixqz0(GEN x, GEN pp)
- GEN qfsign(GEN a)
- GEN smith(GEN x)
- GEN smithall(GEN x)
- GEN smithclean(GEN z)
+ GEN minpoly(GEN x, long v)
GEN qfgaussred(GEN a)
- GEN zm_to_ZM(GEN z)
- GEN zx_to_ZX(GEN z)
+ GEN qfgaussred_positive(GEN a)
+ GEN qfsign(GEN a)
+
+ # alglin3.c
+
+ GEN apply0(GEN f, GEN A)
+ GEN diagonal(GEN x)
+ GEN diagonal_shallow(GEN x)
+ GEN extract0(GEN x, GEN l1, GEN l2)
+ GEN genapply(void *E, GEN (*f)(void *E, GEN x), GEN A)
+ GEN genindexselect(void *E, long (*f)(void *E, GEN x), GEN A)
+ GEN genselect(void *E, long (*f)(void *E, GEN x), GEN A)
+ GEN gtomat(GEN x)
+ GEN gtrans(GEN x)
+ GEN matmuldiagonal(GEN x, GEN d)
+ GEN matmultodiagonal(GEN x, GEN y)
+ GEN matslice0(GEN A, long x1, long x2, long y1, long y2)
+ GEN parapply(GEN V, GEN C)
+ GEN parselect(GEN C, GEN D, long flag)
+ GEN select0(GEN A, GEN f, long flag)
+ GEN shallowextract(GEN x, GEN L)
+ GEN shallowtrans(GEN x)
+ GEN vecapply(void *E, GEN (*f)(void* E, GEN x), GEN x)
+ GEN veccatapply(void *E, GEN (*f)(void* E, GEN x), GEN x)
+ GEN veccatselapply(void *Epred, long (*pred)(void* E, GEN x), void *Efun,
+ GEN (*fun)(void* E, GEN x), GEN A)
+ GEN vecrange(GEN a, GEN b)
+ GEN vecrangess(long a, long b)
+ GEN vecselapply(void *Epred, long (*pred)(void* E, GEN x), void *Efun,
+ GEN (*fun)(void* E, GEN x), GEN A)
+ GEN vecselect(void *E, long (*f)(void* E, GEN x), GEN A)
+ GEN vecslice0(GEN A, long y1, long y2)
+ GEN vecsum(GEN v)
# anal.c
- void addhelp(char *e, char *s)
+ void addhelp(const char *e, char *s)
+ void alias0(const char *s, const char *old)
+ GEN compile_str(const char *s)
+ GEN chartoGENstr(char c)
long delete_var()
- long fetch_user_var(char *s)
+ entree* fetch_named_var(const char *s)
+ long fetch_user_var(const char *s)
long fetch_var()
- GEN gp_read_str(char *s)
- void kill0(char *e)
- void name_var(long n, char *s)
+ GEN fetch_var_value(long vx, GEN t)
+ GEN gp_read_str(const char *t)
+ entree* install(void *f, const char *name, const char *code)
+ entree* is_entry(const char *s)
+ void kill0(const char *e)
+ long manage_var(long n, entree *ep)
+ void pari_var_init()
+ long pari_var_next()
+ long pari_var_next_temp()
+ void pari_var_create(entree *ep)
+ void name_var(long n, const char *s)
GEN readseq(char *t)
- GEN strtoGENstr(char *s)
+ GEN* safegel(GEN x, long l)
+ long* safeel(GEN x, long l)
+ GEN* safelistel(GEN x, long l)
+ GEN* safegcoeff(GEN x, long a, long b)
+ GEN strntoGENstr(const char *s, long n0)
+ GEN strtoGENstr(const char *s)
+ GEN strtoi(const char *s)
+ GEN strtor(const char *s, long prec)
GEN type0(GEN x)
+ # aprcl.c
+
+ long isprimeAPRCL(GEN N)
+
+ # Qfb.c
+
+ GEN Qfb0(GEN x, GEN y, GEN z, GEN d, long prec)
+ void check_quaddisc(GEN x, long *s, long *r, const char *f)
+ void check_quaddisc_imag(GEN x, long *r, const char *f)
+ void check_quaddisc_real(GEN x, long *r, const char *f)
+ long cornacchia(GEN d, GEN p, GEN *px, GEN *py)
+ long cornacchia2(GEN d, GEN p, GEN *px, GEN *py)
+ GEN nucomp(GEN x, GEN y, GEN l)
+ GEN nudupl(GEN x, GEN l)
+ GEN nupow(GEN x, GEN n)
+ GEN primeform(GEN x, GEN p, long prec)
+ GEN primeform_u(GEN x, ulong p)
+ GEN qfbcompraw(GEN x, GEN y)
+ GEN qfbpowraw(GEN x, long n)
+ GEN qfbred0(GEN x, long flag, GEN D, GEN isqrtD, GEN sqrtD)
+ GEN qfbsolve(GEN Q, GEN n)
+ GEN qfi(GEN x, GEN y, GEN z)
+ GEN qfi_1(GEN x)
+ GEN qficomp(GEN x, GEN y)
+ GEN qficompraw(GEN x, GEN y)
+ GEN qfipowraw(GEN x, long n)
+ GEN qfisolvep(GEN Q, GEN p)
+ GEN qfisqr(GEN x)
+ GEN qfisqrraw(GEN x)
+ GEN qfr(GEN x, GEN y, GEN z, GEN d)
+ GEN qfr3_comp(GEN x, GEN y, qfr_data *S)
+ GEN qfr3_pow(GEN x, GEN n, qfr_data *S)
+ GEN qfr3_red(GEN x, qfr_data *S)
+ GEN qfr3_rho(GEN x, qfr_data *S)
+ GEN qfr3_to_qfr(GEN x, GEN z)
+ GEN qfr5_comp(GEN x, GEN y, qfr_data *S)
+ GEN qfr5_dist(GEN e, GEN d, long prec)
+ GEN qfr5_pow(GEN x, GEN n, qfr_data *S)
+ GEN qfr5_red(GEN x, qfr_data *S)
+ GEN qfr5_rho(GEN x, qfr_data *S)
+ GEN qfr5_to_qfr(GEN x, GEN d0)
+ GEN qfr_1(GEN x)
+ void qfr_data_init(GEN D, long prec, qfr_data *S)
+ GEN qfr_to_qfr5(GEN x, long prec)
+ GEN qfrcomp(GEN x, GEN y)
+ GEN qfrcompraw(GEN x, GEN y)
+ GEN qfrpow(GEN x, GEN n)
+ GEN qfrpowraw(GEN x, long n)
+ GEN qfrsolvep(GEN Q, GEN p)
+ GEN qfrsqr(GEN x)
+ GEN qfrsqrraw(GEN x)
+ GEN quadgen(GEN x)
+ GEN quadpoly(GEN x)
+ GEN quadpoly0(GEN x, long v)
+ GEN redimag(GEN x)
+ GEN redreal(GEN x)
+ GEN redrealnod(GEN x, GEN isqrtD)
+ GEN rhoreal(GEN x)
+ GEN rhorealnod(GEN x, GEN isqrtD)
+
# arith1.c
- GEN bestappr0(GEN x, GEN a, GEN b)
+ ulong Fl_order(ulong a, ulong o, ulong p)
+ ulong Fl_powu(ulong x, ulong n, ulong p)
+ ulong Fl_sqrt(ulong a, ulong p)
+ GEN Fp_factored_order(GEN a, GEN o, GEN p)
+ int Fp_ispower(GEN x, GEN K, GEN p)
+ GEN Fp_log(GEN a, GEN g, GEN ord, GEN p)
+ GEN Fp_order(GEN a, GEN o, GEN p)
+ GEN Fp_pow(GEN a, GEN n, GEN m)
+ GEN Fp_pows(GEN A, long k, GEN N)
+ GEN Fp_powu(GEN x, ulong k, GEN p)
+ GEN Fp_sqrt(GEN a, GEN p)
+ GEN Fp_sqrtn(GEN a, GEN n, GEN p, GEN *zetan)
+ GEN Z_chinese(GEN a, GEN b, GEN A, GEN B)
+ GEN Z_chinese_all(GEN a, GEN b, GEN A, GEN B, GEN *pC)
+ GEN Z_chinese_coprime(GEN a, GEN b, GEN A, GEN B, GEN C)
+ GEN Z_chinese_post(GEN a, GEN b, GEN C, GEN U, GEN d)
+ void Z_chinese_pre(GEN A, GEN B, GEN *pC, GEN *pU, GEN *pd)
+ GEN Z_factor_listP(GEN N, GEN L)
+ long Z_isanypower(GEN x, GEN *y)
+ long Z_isfundamental(GEN x)
+ long Z_ispow2(GEN x)
+ long Z_ispowerall(GEN x, ulong k, GEN *pt)
+ long Z_issquareall(GEN x, GEN *pt)
+ long Zp_issquare(GEN a, GEN p)
GEN bestappr(GEN x, GEN k)
- long cgcd(long a,long b)
- void check_quaddisc(GEN x, long *s, long *r, char *f)
+ GEN bestapprPade(GEN x, long B)
+ long cgcd(long a, long b)
GEN chinese(GEN x, GEN y)
- GEN classno2(GEN x)
+ GEN chinese1(GEN x)
+ GEN chinese1_coprime_Z(GEN x)
GEN classno(GEN x)
- long clcm(long a,long b)
+ GEN classno2(GEN x)
+ long clcm(long a, long b)
GEN contfrac0(GEN x, GEN b, long flag)
+ GEN contfracpnqn(GEN x, long n)
GEN fibo(long n)
GEN gboundcf(GEN x, long k)
- GEN gissquareall(GEN x, GEN *pt)
- GEN gissquare(GEN x)
- GEN gcf2(GEN b, GEN x)
GEN gcf(GEN x)
- GEN quadunit(GEN x)
+ GEN gcf2(GEN b, GEN x)
+ bb_field *get_Fp_field(void **E, GEN p)
+ ulong pgener_Fl(ulong p)
+ ulong pgener_Fl_local(ulong p, GEN L)
+ GEN pgener_Fp(GEN p)
+ GEN pgener_Fp_local(GEN p, GEN L)
+ ulong pgener_Zl(ulong p)
+ GEN pgener_Zp(GEN p)
long gisanypower(GEN x, GEN *pty)
- GEN gisprime(GEN x, long flag)
- GEN gispseudoprime(GEN x, long flag)
- GEN gkronecker(GEN x, GEN y)
- GEN gnextprime(GEN n)
- GEN gprecprime(GEN n)
- GEN quadregulator(GEN x, long prec)
+ GEN gissquare(GEN x)
+ GEN gissquareall(GEN x, GEN *pt)
GEN hclassno(GEN x)
- long hilbert0 "hilbert"(GEN x, GEN y, GEN p)
- long Z_isfundamental(GEN x)
+ long hilbert(GEN x, GEN y, GEN p)
+ long hilbertii(GEN x, GEN y, GEN p)
+ long isfundamental(GEN x)
+ long ispolygonal(GEN x, GEN S, GEN *N)
long ispower(GEN x, GEN k, GEN *pty)
- long isprimeAPRCL(GEN N)
- long isprime(GEN x)
- long ispseudoprime(GEN x, long flag)
+ long isprimepower(GEN x, GEN *pty)
+ long issquare(GEN x)
+ long issquareall(GEN x, GEN *pt)
long krois(GEN x, long y)
+ long kroiu(GEN x, ulong y)
long kronecker(GEN x, GEN y)
long krosi(long s, GEN x)
long kross(long x, long y)
long krouu(ulong x, ulong y)
GEN lcmii(GEN a, GEN b)
+ long logint(GEN B, GEN y, GEN *ptq)
+ long logint0(GEN B, GEN y, GEN *ptq)
GEN mpfact(long n)
- GEN mpfactr(long n, long prec)
- GEN Fp_pow(GEN a, GEN n, GEN m)
- GEN Fp_sqrt(GEN a, GEN p)
- GEN Fp_sqrtn(GEN a, GEN n, GEN p, GEN *zetan)
- GEN nucomp(GEN x, GEN y, GEN l)
- GEN nudupl(GEN x, GEN l)
- GEN nupow(GEN x, GEN n)
+ GEN mulu_interval(ulong a, ulong b)
+ GEN odd_prime_divisors(GEN q)
GEN order(GEN x)
GEN pnqn(GEN x)
- GEN primeform(GEN x, GEN p, long prec)
- GEN Qfb0(GEN x, GEN y, GEN z, GEN d, long prec)
- GEN qfbclassno0(GEN x,long flag)
- GEN qfbred0(GEN x, long flag, GEN D, GEN isqrtD, GEN sqrtD)
- GEN qfbsolve(GEN Q, GEN n)
- GEN qfi(GEN x, GEN y, GEN z)
- GEN qfr(GEN x, GEN y, GEN z, GEN d)
+ GEN qfbclassno0(GEN x, long flag)
GEN quaddisc(GEN x)
- GEN redimag(GEN x)
- GEN redreal(GEN x)
- GEN redrealnod(GEN x, GEN isqrtD)
- GEN rhoreal(GEN x)
- GEN rhorealnod(GEN x, GEN isqrtD)
- ulong Fl_sqrt(ulong a, ulong p)
- GEN znprimroot0(GEN m)
+ GEN quadregulator(GEN x, long prec)
+ GEN quadunit(GEN x)
+ ulong rootsof1_Fl(ulong n, ulong p)
+ GEN rootsof1_Fp(GEN n, GEN p)
+ GEN rootsof1u_Fp(ulong n, GEN p)
+ GEN sqrtint(GEN a)
+ ulong ugcd(ulong a, ulong b)
+ long uisprimepower(ulong n, ulong *p)
+ long uissquare(ulong A)
+ long uissquareall(ulong A, ulong *sqrtA)
+ long unegisfundamental(ulong x)
+ long uposisfundamental(ulong x)
+ GEN znlog(GEN x, GEN g, GEN o)
+ GEN znorder(GEN x, GEN o)
+ GEN znprimroot(GEN m)
GEN znstar(GEN x)
# arith2.c
- GEN addprimes(GEN primes)
- long bigomega(GEN n)
- GEN binaire(GEN x)
- long bittest(GEN x, long n)
- GEN boundfact(GEN n, long lim)
- GEN core(GEN n)
+ GEN Z_smoothen(GEN N, GEN L, GEN *pP, GEN *pe)
+ GEN boundfact(GEN n, ulong lim)
+ GEN check_arith_pos(GEN n, char *f)
+ GEN check_arith_non0(GEN n, char *f)
+ GEN check_arith_all(GEN n, char *f)
+ GEN clean_Z_factor(GEN f)
GEN corepartial(GEN n, long l)
- GEN core0(GEN n,long flag)
+ GEN core0(GEN n, long flag)
GEN core2(GEN n)
GEN core2partial(GEN n, long l)
GEN coredisc(GEN n)
- GEN coredisc0(GEN n,long flag)
+ GEN coredisc0(GEN n, long flag)
GEN coredisc2(GEN n)
- GEN Z_factor(GEN n)
+ GEN digits(GEN N, GEN B)
GEN divisors(GEN n)
- GEN factorint(GEN n, long flag)
- GEN gbigomega(GEN n)
- GEN gbitand(GEN x, GEN y)
- GEN gbitneg(GEN x, long n)
- GEN gbitnegimply(GEN x, GEN y)
- GEN gbitor(GEN x, GEN y)
- GEN gbittest(GEN x, GEN n)
- GEN gbitxor(GEN x, GEN y)
- GEN gissquarefree(GEN x)
- GEN gmoebius(GEN n)
- GEN gnumbdiv(GEN n)
- GEN gomega(GEN n)
- GEN gsumdiv(GEN n)
- GEN gsumdivk(GEN n,long k)
- char* initprimes(ulong maxnum)
- long issquarefree(GEN x)
+ GEN divisorsu(ulong n)
+ GEN factor_pn_1(GEN p, ulong n)
+ GEN factor_pn_1_limit(GEN p, long n, ulong lim)
+ GEN factoru_pow(ulong n)
+ byteptr initprimes(ulong maxnum, long *lenp, ulong *lastp)
+ void initprimetable(ulong maxnum)
+ ulong init_primepointer_geq(ulong a, byteptr *pd)
+ ulong init_primepointer_gt(ulong a, byteptr *pd)
+ ulong init_primepointer_leq(ulong a, byteptr *pd)
+ ulong init_primepointer_lt(ulong a, byteptr *pd)
+ int is_Z_factor(GEN f)
+ int is_Z_factornon0(GEN f)
+ int is_Z_factorpos(GEN f)
ulong maxprime()
void maxprime_check(ulong c)
- GEN numbdiv(GEN n)
- long omega(GEN n)
- GEN geulerphi(GEN n)
- GEN prime(long n)
- GEN primepi(GEN x)
- GEN primes(long n)
- GEN removeprimes(GEN primes)
- GEN sumdiv(GEN n)
- GEN sumdivk(GEN n,long k)
+ GEN sumdigits(GEN n)
+ ulong sumdigitsu(ulong n)
+
+ # DedekZeta.c
+
+ GEN glambdak(GEN nfz, GEN s, long prec)
+ GEN gzetak(GEN nfz, GEN s, long prec)
+ GEN gzetakall(GEN nfz, GEN s, long flag, long prec)
+ GEN initzeta(GEN pol, long prec)
+ GEN dirzetak(GEN nf, GEN b)
# base1.c
- GEN bnfnewprec(GEN nf, long prec)
- GEN bnrnewprec(GEN bnr, long prec)
+ GEN FpX_FpC_nfpoleval(GEN nf, GEN pol, GEN a, GEN p)
+ GEN embed_T2(GEN x, long r1)
+ GEN embednorm_T2(GEN x, long r1)
+ GEN embed_norm(GEN x, long r1)
+ void check_ZKmodule(GEN x, char *s)
void checkbid(GEN bid)
GEN checkbnf(GEN bnf)
void checkbnr(GEN bnr)
void checkbnrgen(GEN bnr)
+ void checkabgrp(GEN v)
+ void checksqmat(GEN x, long N)
GEN checknf(GEN nf)
GEN checknfelt_mod(GEN nf, GEN x, char *s)
+ void checkprid(GEN bid)
void checkrnf(GEN rnf)
+ GEN factoredpolred(GEN x, GEN fa)
+ GEN factoredpolred2(GEN x, GEN fa)
GEN galoisapply(GEN nf, GEN aut, GEN x)
- GEN polgalois(GEN x, long prec)
GEN get_bnf(GEN x, long *t)
GEN get_bnfpol(GEN x, GEN *bnf, GEN *nf)
GEN get_nf(GEN x, long *t)
GEN get_nfpol(GEN x, GEN *nf)
- GEN glambdak(GEN nfz, GEN s, long prec)
- GEN gsmith(GEN x)
- GEN gsmithall(GEN x)
- GEN gzetak(GEN nfz, GEN s, long prec)
- GEN gzetakall(GEN nfz, GEN s, long flag, long prec)
- GEN mathnf0(GEN x,long flag)
- GEN matsnf0(GEN x,long flag)
+ GEN get_prid(GEN x)
+ GEN idealfrobenius(GEN nf, GEN gal, GEN pr)
+ GEN idealramgroups(GEN nf, GEN gal, GEN pr)
+ GEN nf_get_allroots(GEN nf)
+ long nf_get_prec(GEN x)
+ GEN nfcertify(GEN x)
+ GEN nfgaloismatrix(GEN nf, GEN s)
+ GEN nfinit(GEN x, long prec)
GEN nfinit0(GEN x, long flag, long prec)
+ GEN nfinitall(GEN x, long flag, long prec)
+ GEN nfinitred(GEN x, long prec)
+ GEN nfinitred2(GEN x, long prec)
+ GEN nfisincl(GEN a, GEN b)
+ GEN nfisisom(GEN a, GEN b)
GEN nfnewprec(GEN nf, long prec)
- GEN rootsof1(GEN x)
+ GEN nfnewprec_shallow(GEN nf, long prec)
+ GEN nfpoleval(GEN nf, GEN pol, GEN a)
+ long nftyp(GEN x)
+ GEN polredord(GEN x)
+ GEN polgalois(GEN x, long prec)
+ GEN polred(GEN x)
+ GEN polred0(GEN x, long flag, GEN p)
+ GEN polred2(GEN x)
+ GEN polredabs(GEN x)
+ GEN polredabs0(GEN x, long flag)
+ GEN polredabs2(GEN x)
+ GEN polredabsall(GEN x, long flun)
+ GEN polredbest(GEN x, long flag)
+ GEN rnfpolredabs(GEN nf, GEN pol, long flag)
+ GEN rnfpolredbest(GEN nf, GEN relpol, long flag)
+ GEN smallpolred(GEN x)
+ GEN smallpolred2(GEN x)
GEN tschirnhaus(GEN x)
+ GEN ZX_Q_normalize(GEN pol, GEN *ptlc)
+ GEN ZX_Z_normalize(GEN pol, GEN *ptk)
+ GEN ZX_to_monic(GEN pol, GEN *lead)
+ GEN ZX_primitive_to_monic(GEN pol, GEN *lead)
# base2.c
- GEN base(GEN x, GEN *y)
- GEN base2(GEN x, GEN *y)
+ GEN Fq_to_nf(GEN x, GEN modpr)
+ GEN FqM_to_nfM(GEN z, GEN modpr)
+ GEN FqV_to_nfV(GEN z, GEN modpr)
+ GEN FqX_to_nfX(GEN x, GEN modpr)
+ GEN Rg_nffix(const char *f, GEN T, GEN c, int lift)
+ GEN RgV_nffix(const char *f, GEN T, GEN P, int lift)
+ GEN RgX_nffix(const char *s, GEN nf, GEN x, int lift)
+ long ZpX_disc_val(GEN f, GEN p)
+ GEN ZpX_gcd(GEN f1, GEN f2, GEN p, GEN pm)
+ GEN ZpX_reduced_resultant(GEN x, GEN y, GEN p, GEN pm)
+ GEN ZpX_reduced_resultant_fast(GEN f, GEN g, GEN p, long M)
+ long ZpX_resultant_val(GEN f, GEN g, GEN p, long M)
void checkmodpr(GEN modpr)
- GEN compositum(GEN pol1, GEN pol2)
- GEN compositum2(GEN pol1, GEN pol2)
- GEN discf(GEN x)
- long idealval(GEN nf,GEN ix,GEN vp)
- GEN idealprodprime(GEN nf, GEN L)
+ GEN ZX_compositum_disjoint(GEN A, GEN B)
+ GEN compositum(GEN P, GEN Q)
+ GEN compositum2(GEN P, GEN Q)
+ GEN nfdisc(GEN x)
GEN indexpartial(GEN P, GEN DP)
- GEN nfbasis(GEN x, GEN *y,long flag,GEN p)
- GEN nfbasis0(GEN x,long flag,GEN p)
- GEN nfdisc0(GEN x,long flag, GEN p)
+ GEN modpr_genFq(GEN modpr)
+ GEN nf_to_Fq_init(GEN nf, GEN *pr, GEN *T, GEN *p)
+ GEN nf_to_Fq(GEN nf, GEN x, GEN modpr)
+ GEN nfM_to_FqM(GEN z, GEN nf, GEN modpr)
+ GEN nfV_to_FqV(GEN z, GEN nf, GEN modpr)
+ GEN nfX_to_FqX(GEN x, GEN nf, GEN modpr)
+ GEN nfbasis(GEN x, GEN *y, GEN p)
+ GEN nfbasis0(GEN x, long flag, GEN p)
+ GEN nfdisc0(GEN x, long flag, GEN p)
+ void nfmaxord(nfmaxord_t *S, GEN T, long flag)
+ GEN nfmodprinit(GEN nf, GEN pr)
GEN nfreducemodpr(GEN nf, GEN x, GEN modpr)
- GEN polcompositum0(GEN pol1, GEN pol2,long flag)
- GEN idealprimedec(GEN nf,GEN p)
+ GEN polcompositum0(GEN P, GEN Q, long flag)
+ GEN idealprimedec(GEN nf, GEN p)
GEN rnfbasis(GEN bnf, GEN order)
+ GEN rnfdedekind(GEN nf, GEN T, GEN pr, long flag)
GEN rnfdet(GEN nf, GEN order)
GEN rnfdiscf(GEN nf, GEN pol)
- GEN rnfequation(GEN nf, GEN pol2)
- GEN rnfequation0(GEN nf, GEN pol2, long flall)
+ GEN rnfequation(GEN nf, GEN pol)
+ GEN rnfequation0(GEN nf, GEN pol, long flall)
GEN rnfequation2(GEN nf, GEN pol)
+ GEN nf_rnfeq(GEN nf, GEN relpol)
+ GEN nf_rnfeqsimple(GEN nf, GEN relpol)
+ GEN rnfequationall(GEN A, GEN B, long *pk, GEN *pLPRS)
GEN rnfhnfbasis(GEN bnf, GEN order)
long rnfisfree(GEN bnf, GEN order)
- GEN rnflllgram(GEN nf, GEN pol, GEN order,long prec)
+ GEN rnflllgram(GEN nf, GEN pol, GEN order, long prec)
GEN rnfpolred(GEN nf, GEN pol, long prec)
- GEN rnfpolredabs(GEN nf, GEN pol, long flag)
GEN rnfpseudobasis(GEN nf, GEN pol)
GEN rnfsimplifybasis(GEN bnf, GEN order)
+ GEN rnfsteinitz(GEN nf, GEN order)
+ long factorial_lval(ulong n, ulong p)
+ GEN zk_to_Fq_init(GEN nf, GEN *pr, GEN *T, GEN *p)
+ GEN zk_to_Fq(GEN x, GEN modpr)
+ GEN zkmodprinit(GEN nf, GEN pr)
# base3.c
+ GEN Idealstar(GEN nf, GEN x, long flun)
+ GEN RgC_to_nfC(GEN nf, GEN x)
+ GEN RgM_to_nfM(GEN nf, GEN x)
+ GEN RgX_to_nfX(GEN nf, GEN pol)
GEN algtobasis(GEN nf, GEN x)
GEN basistoalg(GEN nf, GEN x)
- long nfval(GEN nf, GEN x, GEN vp)
- GEN ideallist(GEN nf,long bound)
- GEN ideallist0(GEN nf,long bound, long flag)
+ GEN ideallist(GEN nf, long bound)
+ GEN ideallist0(GEN nf, long bound, long flag)
GEN ideallistarch(GEN nf, GEN list, GEN arch)
- GEN idealstar0(GEN nf, GEN x,long flag)
+ GEN idealprincipalunits(GEN nf, GEN pr, long e)
+ GEN idealstar0(GEN nf, GEN x, long flag)
+ GEN indices_to_vec01(GEN archp, long r)
+ GEN matalgtobasis(GEN nf, GEN x)
+ GEN matbasistoalg(GEN nf, GEN x)
+ GEN nf_to_scalar_or_alg(GEN nf, GEN x)
+ GEN nf_to_scalar_or_basis(GEN nf, GEN x)
+ GEN nfadd(GEN nf, GEN x, GEN y)
+ GEN nfarchstar(GEN nf, GEN x, GEN arch)
+ GEN nfdiv(GEN nf, GEN x, GEN y)
GEN nfdiveuc(GEN nf, GEN a, GEN b)
GEN nfdivrem(GEN nf, GEN a, GEN b)
+ GEN nfinv(GEN nf, GEN x)
+ GEN nfinvmodideal(GEN nf, GEN x, GEN ideal)
GEN nfmod(GEN nf, GEN a, GEN b)
- GEN reducemodinvertible(GEN x, GEN y)
+ GEN nfmul(GEN nf, GEN x, GEN y)
+ GEN nfmuli(GEN nf, GEN x, GEN y)
+ GEN nfnorm(GEN nf, GEN x)
+ GEN nfpow(GEN nf, GEN x, GEN k)
+ GEN nfpow_u(GEN nf, GEN z, ulong n)
+ GEN nfpowmodideal(GEN nf, GEN x, GEN k, GEN ideal)
+ GEN nfsign(GEN nf, GEN alpha)
+ GEN nfsign_arch(GEN nf, GEN alpha, GEN arch)
+ GEN nfsign_from_logarch(GEN Larch, GEN invpi, GEN archp)
+ GEN nfsqr(GEN nf, GEN x)
+ GEN nfsqri(GEN nf, GEN x)
+ GEN nftrace(GEN nf, GEN x)
+ long nfval(GEN nf, GEN x, GEN vp)
+ GEN polmod_nffix(const char *f, GEN rnf, GEN x, int lift)
+ GEN polmod_nffix2(const char *f, GEN T, GEN relpol, GEN x, int lift)
+ int pr_equal(GEN nf, GEN P, GEN Q)
+ GEN rnfalgtobasis(GEN rnf, GEN x)
+ GEN rnfbasistoalg(GEN rnf, GEN x)
+ GEN rnfeltnorm(GEN rnf, GEN x)
+ GEN rnfelttrace(GEN rnf, GEN x)
+ GEN set_sign_mod_divisor(GEN nf, GEN x, GEN y, GEN idele, GEN sarch)
+ GEN vec01_to_indices(GEN arch)
GEN vecmodii(GEN a, GEN b)
- GEN ideallog(GEN nf,GEN x,GEN bigideal)
- GEN zidealstar(GEN nf, GEN x)
- GEN znlog(GEN x, GEN g)
+ GEN ideallog(GEN nf, GEN x, GEN bigideal)
+
+ GEN multable(GEN nf, GEN x)
+ GEN tablemul(GEN TAB, GEN x, GEN y)
+ GEN tablemul_ei(GEN M, GEN x, long i)
+ GEN tablemul_ei_ej(GEN M, long i, long j)
+ GEN tablemulvec(GEN M, GEN x, GEN v)
+ GEN tablesqr(GEN tab, GEN x)
+ GEN ei_multable(GEN nf, long i)
+ long ZC_nfval(GEN nf, GEN x, GEN P)
+ long ZC_nfvalrem(GEN nf, GEN x, GEN P, GEN *t)
+ GEN zk_multable(GEN nf, GEN x)
+ GEN zk_scalar_or_multable(GEN, GEN x)
+ int ZC_prdvd(GEN nf, GEN x, GEN P)
# base4.c
- GEN nfreduce(GEN nf, GEN x, GEN ideal)
+ GEN RM_round_maxrank(GEN G)
+ GEN ZM_famat_limit(GEN fa, GEN limit)
+ GEN famat_inv(GEN f)
+ GEN famat_inv_shallow(GEN f)
+ GEN famat_makecoprime(GEN nf, GEN g, GEN e, GEN pr, GEN prk, GEN EX)
+ GEN famat_mul(GEN f, GEN g)
+ GEN famat_pow(GEN f, GEN n)
+ GEN famat_sqr(GEN f)
+ GEN famat_reduce(GEN fa)
+ GEN famat_to_nf(GEN nf, GEN f)
+ GEN famat_to_nf_modideal_coprime(GEN nf, GEN g, GEN e, GEN id, GEN EX)
+ GEN famat_to_nf_moddivisor(GEN nf, GEN g, GEN e, GEN bid)
+ GEN famatsmall_reduce(GEN fa)
GEN idealtwoelt(GEN nf, GEN ix)
GEN idealtwoelt0(GEN nf, GEN ix, GEN a)
GEN idealtwoelt2(GEN nf, GEN x, GEN a)
GEN idealadd(GEN nf, GEN x, GEN y)
GEN idealaddmultoone(GEN nf, GEN list)
GEN idealaddtoone(GEN nf, GEN x, GEN y)
+ GEN idealaddtoone_i(GEN nf, GEN x, GEN y)
GEN idealaddtoone0(GEN nf, GEN x, GEN y)
GEN idealappr(GEN nf, GEN x)
GEN idealappr0(GEN nf, GEN x, long fl)
GEN idealapprfact(GEN nf, GEN x)
GEN idealchinese(GEN nf, GEN x, GEN y)
GEN idealcoprime(GEN nf, GEN x, GEN y)
+ GEN idealcoprimefact(GEN nf, GEN x, GEN fy)
GEN idealdiv(GEN nf, GEN x, GEN y)
- GEN idealdiv0(GEN nf, GEN x, GEN y,long flag)
+ GEN idealdiv0(GEN nf, GEN x, GEN y, long flag)
GEN idealdivexact(GEN nf, GEN x, GEN y)
GEN idealdivpowprime(GEN nf, GEN x, GEN vp, GEN n)
GEN idealmulpowprime(GEN nf, GEN x, GEN vp, GEN n)
GEN idealfactor(GEN nf, GEN x)
GEN idealhnf(GEN nf, GEN x)
+ GEN idealhnf_principal(GEN nf, GEN x)
+ GEN idealhnf_shallow(GEN nf, GEN x)
+ GEN idealhnf_two(GEN nf, GEN vp)
GEN idealhnf0(GEN nf, GEN a, GEN b)
GEN idealintersect(GEN nf, GEN x, GEN y)
GEN idealinv(GEN nf, GEN ix)
- GEN idealred0(GEN nf, GEN ix, GEN vdir)
+ GEN idealred0(GEN nf, GEN I, GEN vdir)
GEN idealmul(GEN nf, GEN ix, GEN iy)
- GEN idealmul0(GEN nf, GEN ix, GEN iy, long flag, long prec)
+ GEN idealmul0(GEN nf, GEN ix, GEN iy, long flag)
+ GEN idealmul_HNF(GEN nf, GEN ix, GEN iy)
GEN idealmulred(GEN nf, GEN ix, GEN iy)
GEN idealnorm(GEN nf, GEN x)
+ GEN idealnumden(GEN nf, GEN x)
GEN idealpow(GEN nf, GEN ix, GEN n)
- GEN idealpow0(GEN nf, GEN ix, GEN n, long flag, long prec)
- GEN idealpowred(GEN nf, GEN ix, GEN n,long prec)
+ GEN idealpow0(GEN nf, GEN ix, GEN n, long flag)
+ GEN idealpowred(GEN nf, GEN ix, GEN n)
GEN idealpows(GEN nf, GEN ideal, long iexp)
+ GEN idealprodprime(GEN nf, GEN L)
+ GEN idealsqr(GEN nf, GEN x)
long idealtyp(GEN *ideal, GEN *arch)
- long isideal(GEN nf,GEN x)
- GEN minideal(GEN nf,GEN ix,GEN vdir,long prec)
- GEN mul_content(GEN cx, GEN cy)
- GEN nfdetint(GEN nf,GEN pseudo)
+ long idealval(GEN nf, GEN ix, GEN vp)
+ long isideal(GEN nf, GEN x)
+ GEN idealmin(GEN nf, GEN ix, GEN vdir)
+ GEN nf_get_Gtwist(GEN nf, GEN vdir)
+ GEN nf_get_Gtwist1(GEN nf, long i)
+ GEN nfC_nf_mul(GEN nf, GEN v, GEN x)
+ GEN nfdetint(GEN nf, GEN pseudo)
+ GEN nfdivmodpr(GEN nf, GEN x, GEN y, GEN modpr)
GEN nfhnf(GEN nf, GEN x)
+ GEN nfhnfmod(GEN nf, GEN x, GEN d)
GEN nfkermodpr(GEN nf, GEN x, GEN modpr)
+ GEN nfmulmodpr(GEN nf, GEN x, GEN y, GEN modpr)
+ GEN nfpowmodpr(GEN nf, GEN x, GEN k, GEN modpr)
+ GEN nfreduce(GEN nf, GEN x, GEN ideal)
GEN nfsnf(GEN nf, GEN x)
GEN nfsolvemodpr(GEN nf, GEN a, GEN b, GEN modpr)
+ GEN to_famat(GEN x, GEN y)
+ GEN to_famat_shallow(GEN x, GEN y)
GEN vecdiv(GEN x, GEN y)
GEN vecinv(GEN x)
GEN vecmul(GEN x, GEN y)
@@ -812,169 +1964,225 @@ cdef extern from 'pari/pari.h':
# base5.c
- GEN matalgtobasis(GEN nf, GEN x)
- GEN matbasistoalg(GEN nf, GEN x)
- GEN rnfalgtobasis(GEN rnf, GEN x)
- GEN rnfbasistoalg(GEN rnf, GEN x)
- GEN rnfelementabstorel(GEN rnf, GEN x)
- GEN rnfelementdown(GEN rnf, GEN x)
- GEN rnfelementreltoabs(GEN rnf, GEN x)
- GEN rnfelementup(GEN rnf, GEN x)
+ GEN eltreltoabs(GEN rnfeq, GEN x)
+ GEN eltabstorel(GEN eq, GEN P)
+ GEN eltabstorel_lift(GEN rnfeq, GEN P)
+ void nf_nfzk(GEN nf, GEN rnfeq, GEN *zknf, GEN *czknf)
+ GEN nfeltup(GEN nf, GEN x, GEN zknf, GEN czknf)
+ GEN rnfeltabstorel(GEN rnf, GEN x)
+ GEN rnfeltdown(GEN rnf, GEN x)
+ GEN rnfeltreltoabs(GEN rnf, GEN x)
+ GEN rnfeltup(GEN rnf, GEN x)
GEN rnfidealabstorel(GEN rnf, GEN x)
GEN rnfidealdown(GEN rnf, GEN x)
- GEN rnfidealhermite(GEN rnf, GEN x)
- GEN rnfidealmul(GEN rnf,GEN x,GEN y)
+ GEN rnfidealhnf(GEN rnf, GEN x)
+ GEN rnfidealmul(GEN rnf, GEN x, GEN y)
GEN rnfidealnormabs(GEN rnf, GEN x)
GEN rnfidealnormrel(GEN rnf, GEN x)
GEN rnfidealreltoabs(GEN rnf, GEN x)
- GEN rnfidealtwoelement(GEN rnf,GEN x)
+ GEN rnfidealtwoelement(GEN rnf, GEN x)
GEN rnfidealup(GEN rnf, GEN x)
GEN rnfinit(GEN nf, GEN pol)
+ # bb_group.c
+
+ GEN dlog_get_ordfa(GEN o)
+ GEN dlog_get_ord(GEN o)
+ GEN gen_PH_log(GEN a, GEN g, GEN ord, void *E, bb_group *grp)
+ GEN gen_Shanks_sqrtn(GEN a, GEN n, GEN q, GEN *zetan, void *E, bb_group *grp)
+ GEN gen_gener(GEN o, void *E, bb_group *grp)
+ GEN gen_ellgens(GEN d1, GEN d2, GEN m, void *E, bb_group *grp,
+ GEN pairorder(void *E, GEN P, GEN Q, GEN m, GEN F))
+ GEN gen_ellgroup(GEN N, GEN F, GEN *pt_m, void *E, bb_group *grp,
+ GEN pairorder(void *E, GEN P, GEN Q, GEN m, GEN F))
+ GEN gen_factored_order(GEN a, GEN o, void *E, bb_group *grp)
+ GEN gen_order(GEN x, GEN o, void *E, bb_group *grp)
+ GEN gen_select_order(GEN o, void *E, bb_group *grp)
+
+ GEN gen_plog(GEN x, GEN g0, GEN q, void *E, bb_group *grp)
+ GEN gen_pow(GEN x, GEN n, void *E, GEN (*sqr)(void*, GEN), GEN (*mul)(void*, GEN, GEN))
+ GEN gen_pow_i(GEN x, GEN n, void *E, GEN (*sqr)(void*, GEN), GEN (*mul)(void*, GEN, GEN))
+ GEN gen_pow_fold(GEN x, GEN n, void *E, GEN (*sqr)(void*, GEN), GEN (*msqr)(void*, GEN))
+ GEN gen_pow_fold_i(GEN x, GEN n, void *E, GEN (*sqr)(void*, GEN), GEN (*msqr)(void*, GEN))
+ GEN gen_powers(GEN x, long l, int use_sqr, void *E, GEN (*sqr)(void*, GEN), GEN (*mul)(void*, GEN, GEN), GEN (*one)(void*))
+ GEN gen_powu(GEN x, ulong n, void *E, GEN (*sqr)(void*, GEN), GEN (*mul)(void*, GEN, GEN))
+ GEN gen_powu_i(GEN x, ulong n, void *E, GEN (*sqr)(void*, GEN), GEN (*mul)(void*, GEN, GEN))
+ GEN gen_powu_fold(GEN x, ulong n, void *E, GEN (*sqr)(void*, GEN), GEN (*msqr)(void*, GEN))
+ GEN gen_powu_fold_i(GEN x, ulong n, void *E, GEN (*sqr)(void*, GEN), GEN (*msqr)(void*, GEN))
+
# bibli1.c
- GEN ZM_zc_mul(GEN x, GEN y)
- GEN ZM_zm_mul(GEN x, GEN y)
- GEN T2_from_embed(GEN x, long r1)
+ int QR_init(GEN x, GEN *pB, GEN *pQ, GEN *pL, long prec)
+ GEN R_from_QR(GEN x, long prec)
+ int RgM_QR_init(GEN x, GEN *pB, GEN *pQ, GEN *pL, long prec)
+ GEN Xadic_lindep(GEN x)
GEN algdep(GEN x, long n)
GEN algdep0(GEN x, long n, long bit)
- GEN factoredpolred(GEN x, GEN p)
- GEN factoredpolred2(GEN x, GEN p)
- GEN kerint(GEN x)
- GEN lindep(GEN x)
+ void forqfvec0(GEN a, GEN BORNE, GEN code)
+ GEN gaussred_from_QR(GEN x, long prec)
GEN lindep0(GEN x, long flag)
+ GEN lindep(GEN x)
GEN lindep2(GEN x, long bit)
- GEN lll(GEN x, long prec)
- GEN lllgen(GEN x)
- GEN lllgram(GEN x, long prec)
- GEN lllgramgen(GEN x)
- GEN lllgramint(GEN x)
- GEN lllgramkerim(GEN x)
- GEN lllgramkerimgen(GEN x)
- GEN lllint(GEN x)
- GEN lllintpartial(GEN mat)
- GEN lllkerim(GEN x)
- GEN lllkerimgen(GEN x)
- GEN matkerint0(GEN x,long flag)
+ GEN mathouseholder(GEN Q, GEN v)
+ GEN matqr(GEN x, long flag, long prec)
GEN minim(GEN a, GEN borne, GEN stockmax)
- GEN qfrep0(GEN a, GEN borne, long flag)
- GEN qfminim0(GEN a, GEN borne, GEN stockmax,long flag, long prec)
+ GEN minim_raw(GEN a, GEN borne, GEN stockmax)
GEN minim2(GEN a, GEN borne, GEN stockmax)
- GEN ordred(GEN x)
+ GEN padic_lindep(GEN x)
GEN perf(GEN a)
- GEN polred(GEN x)
- GEN polred0(GEN x, long flag, GEN p)
- GEN polred2(GEN x)
- GEN polredabs(GEN x)
- GEN polredabs0(GEN x, long flag)
- GEN polredabs2(GEN x)
- GEN polredabsall(GEN x, long flun)
- GEN polredbest(GEN x, long flag)
- GEN qflll0(GEN x, long flag)
- GEN qflllgram0(GEN x, long flag)
- GEN smallpolred(GEN x)
- GEN smallpolred2(GEN x)
- char *stackmalloc(size_t N)
- GEN zncoppersmith(GEN P0, GEN N, GEN X, GEN B)
+ GEN qfrep0(GEN a, GEN borne, long flag)
+ GEN qfminim0(GEN a, GEN borne, GEN stockmax, long flag, long prec)
+ GEN seralgdep(GEN s, long p, long r)
+ GEN zncoppersmith(GEN P0, GEN N, GEN X, GEN B)
# bibli2.c
+ GEN QXQ_reverse(GEN a, GEN T)
+ GEN RgV_polint(GEN X, GEN Y, long v)
+ GEN RgXQ_reverse(GEN a, GEN T)
+ GEN ZV_indexsort(GEN L)
+ long ZV_search(GEN x, GEN y)
+ GEN ZV_sort(GEN L)
+ GEN ZV_sort_uniq(GEN L)
+ GEN ZV_union_shallow(GEN x, GEN y)
GEN binomial(GEN x, long k)
+ GEN binomialuu(ulong n, ulong k)
+ int cmp_nodata(void *data, GEN x, GEN y)
int cmp_prime_ideal(GEN x, GEN y)
int cmp_prime_over_p(GEN x, GEN y)
+ int cmp_RgX(GEN x, GEN y)
+ int cmp_universal(GEN x, GEN y)
GEN convol(GEN x, GEN y)
+ int gen_cmp_RgX(void *data, GEN x, GEN y)
GEN polcyclo(long n, long v)
- GEN polcyclo_eval(long n, GEN v)
+ GEN polcyclo_eval(long n, GEN x)
GEN dirdiv(GEN x, GEN y)
GEN dirmul(GEN x, GEN y)
- GEN dirzetak(GEN nf, GEN b)
- long gen_search(GEN x, GEN y, int flag, int (*cmp)(GEN,GEN))
- GEN gen_setminus(GEN set1, GEN set2, int (*cmp)(GEN,GEN))
- GEN gen_sort(GEN x, int flag, int (*cmp)(GEN,GEN))
- GEN genrand(GEN N)
- GEN getheap()
- GEN getrand()
+ GEN gen_indexsort(GEN x, void *E, int (*cmp)(void*, GEN, GEN))
+ GEN gen_indexsort_uniq(GEN x, void *E, int (*cmp)(void*, GEN, GEN))
+ long gen_search(GEN x, GEN y, long flag, void *data, int (*cmp)(void*, GEN, GEN))
+ GEN gen_setminus(GEN set1, GEN set2, int (*cmp)(GEN, GEN))
+ GEN gen_sort(GEN x, void *E, int (*cmp)(void*, GEN, GEN))
+ void gen_sort_inplace(GEN x, void *E, int (*cmp)(void*, GEN, GEN), GEN *perm)
+ GEN gen_sort_uniq(GEN x, void *E, int (*cmp)(void*, GEN, GEN))
long getstack()
long gettime()
+ long getabstime()
GEN gprec(GEN x, long l)
+ GEN gprec_wtrunc(GEN x, long pr)
GEN gprec_w(GEN x, long pr)
- GEN ggrando(GEN x, long n)
GEN gtoset(GEN x)
GEN indexlexsort(GEN x)
GEN indexsort(GEN x)
+ GEN indexvecsort(GEN x, GEN k)
GEN laplace(GEN x)
- GEN pollegendre(long n, long v)
GEN lexsort(GEN x)
GEN mathilbert(long n)
GEN matqpascal(long n, GEN q)
+ GEN merge_factor(GEN fx, GEN fy, void *data, int (*cmp)(void *, GEN, GEN))
+ GEN merge_sort_uniq(GEN x, GEN y, void *data, int (*cmp)(void *, GEN, GEN))
+ GEN modreverse(GEN x)
GEN numtoperm(long n, GEN x)
GEN permtonum(GEN x)
+ GEN polhermite(long n, long v)
+ GEN polhermite_eval(long n, GEN x)
+ GEN pollegendre(long n, long v)
+ GEN pollegendre_eval(long n, GEN x)
GEN polint(GEN xa, GEN ya, GEN x, GEN *dy)
+ GEN polchebyshev(long n, long kind, long v)
+ GEN polchebyshev_eval(long n, long kind, GEN x)
+ GEN polchebyshev1(long n, long v)
+ GEN polchebyshev2(long n, long v)
GEN polrecip(GEN x)
- GEN modreverse(GEN x)
- GEN roots_to_pol(GEN a, long v)
+ GEN setbinop(GEN f, GEN x, GEN y)
GEN setintersect(GEN x, GEN y)
long setisset(GEN x)
GEN setminus(GEN x, GEN y)
- void setrand(GEN seed)
long setsearch(GEN x, GEN y, long flag)
GEN setunion(GEN x, GEN y)
- GEN indexlexsort(GEN x)
- GEN indexsort(GEN x)
GEN sort(GEN x)
- long tablesearch(GEN T, GEN x, int (*cmp)(GEN,GEN))
- GEN tayl(GEN x, long v, long precdl)
- GEN polchebyshev1(long n, long v)
+ GEN sort_factor(GEN y, void *data, int (*cmp)(void*, GEN, GEN))
+ GEN stirling(long n, long m, long flag)
+ GEN stirling1(ulong n, ulong m)
+ GEN stirling2(ulong n, ulong m)
+ long tablesearch(GEN T, GEN x, int (*cmp)(GEN, GEN))
+ GEN vecbinome(long n)
+ long vecsearch(GEN v, GEN x, GEN k)
GEN vecsort(GEN x, GEN k)
GEN vecsort0(GEN x, GEN k, long flag)
+ long zv_search(GEN x, long y)
+
+ # bit.c
+
+ GEN binaire(GEN x)
+ long bittest(GEN x, long n)
+ GEN gbitand(GEN x, GEN y)
+ GEN gbitneg(GEN x, long n)
+ GEN gbitnegimply(GEN x, GEN y)
+ GEN gbitor(GEN x, GEN y)
+ GEN gbittest(GEN x, long n)
+ GEN gbitxor(GEN x, GEN y)
+ long hammingweight(GEN n)
+ GEN ibitand(GEN x, GEN y)
+ GEN ibitnegimply(GEN x, GEN y)
+ GEN ibitor(GEN x, GEN y)
+ GEN ibitxor(GEN x, GEN y)
# buch1.c
- GEN buchimag(GEN D, GEN gcbach, GEN gcbach2, GEN gCO)
- GEN buchreal(GEN D, GEN gsens, GEN gcbach, GEN gcbach2, GEN gRELSUP, long prec)
- GEN cgetalloc(long t, size_t l)
- GEN quadclassunit0(GEN x, long flag,GEN data, long prec)
+ GEN Buchquad(GEN D, double c1, double c2, long prec)
+ GEN quadclassunit0(GEN x, long flag, GEN data, long prec)
GEN quadhilbert(GEN D, long prec)
- GEN quadray(GEN bnf, GEN f, GEN flag, long prec)
+ GEN quadray(GEN bnf, GEN f, long prec)
# buch2.c
- GEN bnfinit0(GEN P,long flag,GEN data,long prec)
- GEN check_and_build_obj(GEN S, int tag, GEN (*build)(GEN))
- GEN isprincipal(GEN bignf, GEN x)
- GEN bnfisprincipal0(GEN bignf, GEN x,long flall)
- GEN isprincipalfact(GEN bnf,GEN P, GEN e, GEN C, long flag)
- GEN isprincipalforce(GEN bignf,GEN x)
- GEN isprincipalgen(GEN bignf, GEN x)
- GEN isprincipalgenforce(GEN bignf,GEN x)
+ GEN bnfcompress(GEN bnf)
+ GEN bnfinit0(GEN P, long flag, GEN data, long prec)
+ GEN bnfnewprec(GEN nf, long prec)
+ GEN bnfnewprec_shallow(GEN nf, long prec)
+ GEN bnrnewprec(GEN bnr, long prec)
+ GEN bnrnewprec_shallow(GEN bnr, long prec)
+ GEN Buchall(GEN P, long flag, long prec)
+ GEN Buchall_param(GEN P, double bach, double bach2, long nbrelpid, long flun, long prec)
+ GEN isprincipal(GEN bnf, GEN x)
+ GEN bnfisprincipal0(GEN bnf, GEN x, long flall)
+ GEN isprincipalfact(GEN bnf, GEN C, GEN L, GEN f, long flag)
+ GEN isprincipalfact_or_fail(GEN bnf, GEN C, GEN P, GEN e)
GEN bnfisunit(GEN bignf, GEN x)
- GEN regulator(GEN P,GEN data,long prec)
GEN signunits(GEN bignf)
+ GEN nfsign_units(GEN bnf, GEN archp, int add_zu)
# buch3.c
- GEN bnrconductor(GEN arg0,GEN arg1,GEN arg2,GEN flag)
- GEN bnrconductorofchar(GEN bnr,GEN chi)
- GEN bnrdisc0(GEN arg0, GEN arg1, GEN arg2, long flag)
- GEN bnrdisclist0(GEN bnf,GEN borne, GEN arch, long all)
- long bnrisconductor(GEN arg0,GEN arg1,GEN arg2)
+ GEN ABC_to_bnr(GEN A, GEN B, GEN C, GEN *H, int gen)
+ GEN Buchray(GEN bnf, GEN module, long flag)
+ GEN bnrclassno(GEN bignf, GEN ideal)
+ GEN bnrclassno0(GEN A, GEN B, GEN C)
+ GEN bnrclassnolist(GEN bnf, GEN listes)
+ GEN bnrconductor0(GEN A, GEN B, GEN C, long flag)
+ GEN bnrconductor(GEN bnr, GEN H0, long flag)
+ GEN bnrconductorofchar(GEN bnr, GEN chi)
+ GEN bnrdisc0(GEN A, GEN B, GEN C, long flag)
+ GEN bnrdisc(GEN bnr, GEN H, long flag)
+ GEN bnrdisclist0(GEN bnf, GEN borne, GEN arch)
+ GEN bnrinit0(GEN bignf, GEN ideal, long flag)
+ long bnrisconductor0(GEN A, GEN B, GEN C)
+ long bnrisconductor(GEN bnr, GEN H)
+ GEN bnrisprincipal(GEN bnf, GEN x, long flag)
+ GEN bnrsurjection(GEN bnr1, GEN bnr2)
GEN buchnarrow(GEN bignf)
long bnfcertify(GEN bnf)
- GEN conductor(GEN bnr,GEN subgroup,long all)
+ long bnfcertify0(GEN bnf, long flag)
GEN decodemodule(GEN nf, GEN fa)
- GEN discrayabs(GEN bnr,GEN subgroup)
- GEN discrayabscond(GEN bnr,GEN subgroup)
- GEN discrayabslist(GEN bnf,GEN listes)
- GEN discrayabslistarch(GEN bnf, GEN arch, long bound)
- GEN discrayabslistlong(GEN bnf, long bound)
- GEN discrayrel(GEN bnr,GEN subgroup)
- GEN discrayrelcond(GEN bnr,GEN subgroup)
- GEN isprincipalray(GEN bignf, GEN x)
- GEN bnrisprincipal(GEN bignf, GEN x,long flall)
- GEN isprincipalraygen(GEN bignf, GEN x)
- GEN bnrclassno(GEN bignf,GEN ideal)
- GEN bnrclassnolist(GEN bnf,GEN listes)
- GEN rnfconductor(GEN bnf, GEN polrel, long flag)
+ GEN discrayabslist(GEN bnf, GEN listes)
+ GEN discrayabslistarch(GEN bnf, GEN arch, ulong bound)
+ GEN discrayabslistlong(GEN bnf, ulong bound)
+ GEN idealmoddivisor(GEN bnr, GEN x)
+ GEN isprincipalray(GEN bnf, GEN x)
+ GEN isprincipalraygen(GEN bnf, GEN x)
+ GEN rnfconductor(GEN bnf, GEN polrel)
+ long rnfisabelian(GEN nf, GEN pol)
GEN rnfnormgroup(GEN bnr, GEN polrel)
GEN subgrouplist0(GEN bnr, GEN indexbound, long all)
@@ -982,146 +2190,312 @@ cdef extern from 'pari/pari.h':
GEN bnfisnorm(GEN bnf, GEN x, long flag)
GEN rnfisnorm(GEN S, GEN x, long flag)
- GEN rnfisnorminit(GEN T, GEN relpol, int galois)
- GEN bnfissunit(GEN bnf,GEN suni,GEN x)
- GEN bnfsunit(GEN bnf,GEN s,long PREC)
- long nfhilbert(GEN bnf,GEN a,GEN b)
- long nfhilbert0(GEN bnf,GEN a,GEN b,GEN p)
+ GEN rnfisnorminit(GEN bnf, GEN relpol, int galois)
+ GEN bnfissunit(GEN bnf, GEN suni, GEN x)
+ GEN bnfsunit(GEN bnf, GEN s, long PREC)
+ long nfhilbert(GEN bnf, GEN a, GEN b)
+ long nfhilbert0(GEN bnf, GEN a, GEN b, GEN p)
+ long hyperell_locally_soluble(GEN pol, GEN p)
+ long nf_hyperell_locally_soluble(GEN nf, GEN pol, GEN p)
# compile.c
+ GEN closure_deriv(GEN G)
+ long localvars_find(GEN pack, entree *ep)
+ GEN localvars_read_str(const char *str, GEN pack)
+ GEN snm_closure(entree *ep, GEN data)
+ GEN strtoclosure(const char *s, long n, ...)
GEN strtofunction(const char *s)
+ # concat.c
+
+ GEN concat(GEN x, GEN y)
+ GEN concat1(GEN x)
+ GEN matconcat(GEN v)
+ GEN shallowconcat(GEN x, GEN y)
+ GEN shallowconcat1(GEN x)
+ GEN shallowmatconcat(GEN v)
+ GEN vconcat(GEN A, GEN B)
+
# default.c
extern int d_SILENT, d_ACKNOWLEDGE, d_INITRC, d_RETURN
- GEN default0(char *a, char *b)
- long getrealprecision()
- GEN sd_TeXstyle(char *v, long flag)
- GEN sd_breakloop(char *v, long flag)
- GEN sd_colors(char *v, long flag)
- GEN sd_compatible(char *v, long flag)
- GEN sd_datadir(char *v, long flag)
- GEN sd_debug(char *v, long flag)
- GEN sd_debugfiles(char *v, long flag)
- GEN sd_debugmem(char *v, long flag)
- GEN sd_echo(char *v, long flag)
- GEN sd_factor_add_primes(char *v, long flag)
- GEN sd_factor_proven(char *v, long flag)
- GEN sd_format(char *v, long flag)
- GEN sd_graphcolormap(char *v, long flag)
- GEN sd_graphcolors(char *v, long flag)
- GEN sd_help(char *v, long flag)
- GEN sd_histsize(char *v, long flag)
- GEN sd_lines(char *v, long flag)
- GEN sd_log(char *v, long flag)
- GEN sd_logfile(char *v, long flag)
- GEN sd_new_galois_format(char *v, long flag)
- GEN sd_output(char *v, long flag)
- GEN sd_parisize(char *v, long flag)
- GEN sd_path(char *v, long flag)
- GEN sd_prettyprinter(char *v, long flag)
- GEN sd_primelimit(char *v, long flag)
- GEN sd_prompt(char *v, long flag)
- GEN sd_prompt_cont(char *v, long flag)
- GEN sd_psfile(char *v, long flag)
- GEN sd_realprecision(char *v, long flag)
- GEN sd_recover(char *v, long flag)
- GEN sd_rl(char *v, long flag)
- GEN sd_secure(char *v, long flag)
- GEN sd_seriesprecision(char *v, long flag)
- GEN sd_simplify(char *v, long flag)
- GEN sd_strictmatch(char *v, long flag)
- GEN sd_timer(char *v, long flag)
- long setrealprecision(long n, long *prec)
+
+ GEN default0(const char *a, char *b)
+ long getrealprecision()
+ int pari_is_default(const char *s)
+ GEN sd_TeXstyle(const char *v, long flag)
+ GEN sd_colors(const char *v, long flag)
+ GEN sd_compatible(const char *v, long flag)
+ GEN sd_datadir(const char *v, long flag)
+ GEN sd_debug(const char *v, long flag)
+ GEN sd_debugfiles(const char *v, long flag)
+ GEN sd_debugmem(const char *v, long flag)
+ GEN sd_factor_add_primes(const char *v, long flag)
+ GEN sd_factor_proven(const char *v, long flag)
+ GEN sd_format(const char *v, long flag)
+ GEN sd_histsize(const char *v, long flag)
+ GEN sd_log(const char *v, long flag)
+ GEN sd_logfile(const char *v, long flag)
+ GEN sd_nbthreads(const char *v, long flag)
+ GEN sd_new_galois_format(const char *v, long flag)
+ GEN sd_output(const char *v, long flag)
+ GEN sd_parisize(const char *v, long flag)
+ GEN sd_path(const char *v, long flag)
+ GEN sd_prettyprinter(const char *v, long flag)
+ GEN sd_primelimit(const char *v, long flag)
+ GEN sd_realprecision(const char *v, long flag)
+ GEN sd_secure(const char *v, long flag)
+ GEN sd_seriesprecision(const char *v, long flag)
+ GEN sd_simplify(const char *v, long flag)
+ GEN sd_sopath(char *v, int flag)
+ GEN sd_strictargs(const char *v, long flag)
+ GEN sd_strictmatch(const char *v, long flag)
+ GEN sd_string(const char *v, long flag, char *s, char **f)
+ GEN sd_threadsize(const char *v, long flag)
+ GEN sd_toggle(const char *v, long flag, char *s, int *ptn)
+ GEN sd_ulong(const char *v, long flag, char *s, ulong *ptn, ulong Min, ulong Max, char **msg)
+ GEN setdefault(const char *s, char *v, long flag)
+ long setrealprecision(long n, long *prec)
# ellanal.c
GEN ellanalyticrank(GEN e, GEN eps, long prec)
GEN ellL1(GEN e, long r, long prec)
+ # elldata.c
+
+ GEN ellconvertname(GEN s)
+ GEN elldatagenerators(GEN E)
+ GEN ellidentify(GEN E)
+ GEN ellsearch(GEN A)
+ GEN ellsearchcurve(GEN name)
+ void forell(void *E, long call(void*, GEN), long a, long b)
+
# elliptic.c
- GEN addell(GEN e, GEN z1, GEN z2)
+ extern int t_ELL_Rg, t_ELL_Q, t_ELL_Qp, t_ELL_Fp, t_ELL_Fq
GEN akell(GEN e, GEN n)
GEN anell(GEN e, long n)
- GEN ellap(GEN e, GEN p)
+ GEN anellsmall(GEN e, long n)
GEN bilhell(GEN e, GEN z1, GEN z2, long prec)
+ void checkell(GEN e)
+ void checkell_Fq(GEN e)
+ void checkell_Q(GEN e)
+ void checkell_Qp(GEN e)
+ void checkellpt(GEN z)
+ void checkell5(GEN e)
+ GEN ellanal_globalred(GEN e, GEN *gr)
+ GEN ellQ_get_N(GEN e)
+ void ellQ_get_Nfa(GEN e, GEN *N, GEN *faN)
+ GEN ellQp_Tate_uniformization(GEN E, long prec)
+ GEN ellQp_u(GEN E, long prec)
+ GEN ellQp_u2(GEN E, long prec)
+ GEN ellQp_q(GEN E, long prec)
+ GEN ellQp_ab(GEN E, long prec)
+ GEN ellQp_root(GEN E, long prec)
+ GEN ellR_ab(GEN E, long prec)
+ GEN ellR_eta(GEN E, long prec)
+ GEN ellR_omega(GEN x, long prec)
+ GEN ellR_roots(GEN E, long prec)
+ GEN elladd(GEN e, GEN z1, GEN z2)
+ GEN ellap(GEN e, GEN p)
+ GEN ellcard(GEN E, GEN p)
GEN ellchangecurve(GEN e, GEN ch)
- GEN ellap0(GEN e, GEN p, long flag)
+ GEN elldivpol(GEN e, long n, long v)
GEN elleisnum(GEN om, long k, long flag, long prec)
GEN elleta(GEN om, long prec)
- GEN ellheight0(GEN e, GEN a, long flag,long prec)
- GEN ellinit0(GEN x,long flag,long prec)
+ GEN ellff_get_card(GEN E)
+ GEN ellff_get_gens(GEN E)
+ GEN ellff_get_group(GEN E)
+ GEN ellff_get_o(GEN x)
+ GEN ellff_get_p(GEN E)
+ GEN ellfromj(GEN j)
+ GEN ellgenerators(GEN E)
+ GEN ellglobalred(GEN e1)
+ GEN ellgroup(GEN E, GEN p)
+ GEN ellgroup0(GEN E, GEN p, long flag)
+ GEN ellheight0(GEN e, GEN a, long flag, long prec)
+ GEN ellheegner(GEN e)
+ GEN ellinit(GEN x, GEN p, long prec)
+ GEN ellisoncurve(GEN e, GEN z)
+ GEN elllseries(GEN e, GEN s, GEN A, long prec)
+ GEN elllocalred(GEN e, GEN p1)
+ GEN elllog(GEN e, GEN a, GEN g, GEN o)
GEN ellminimalmodel(GEN E, GEN *ptv)
+ GEN ellmul(GEN e, GEN z, GEN n)
+ GEN ellneg(GEN e, GEN z)
+ GEN ellorder(GEN e, GEN p, GEN o)
+ GEN ellordinate(GEN e, GEN x, long prec)
+ GEN ellperiods(GEN w, long flag, long prec)
+ GEN ellrandom(GEN e)
long ellrootno(GEN e, GEN p)
+ long ellrootno_global(GEN e)
GEN ellsigma(GEN om, GEN z, long flag, long prec)
+ GEN ellsub(GEN e, GEN z1, GEN z2)
+ GEN elltaniyama(GEN e, long prec)
+ GEN elltatepairing(GEN E, GEN t, GEN s, GEN m)
GEN elltors0(GEN e, long flag)
- GEN ellwp0(GEN e, GEN z, long flag, long precdl, long prec)
+ GEN ellweilpairing(GEN E, GEN t, GEN s, GEN m)
+ GEN ellwp(GEN w, GEN z, long prec)
+ GEN ellwp0(GEN w, GEN z, long flag, long prec)
+ GEN ellwpseries(GEN e, long v, long PRECDL)
GEN ellzeta(GEN om, GEN z, long prec)
+ GEN ellchangeinvert(GEN w)
+ GEN ellchangepoint(GEN x, GEN ch)
+ GEN ellchangepointinv(GEN x, GEN ch)
+ GEN elltors(GEN e)
+ GEN expIxy(GEN x, GEN y, long prec)
+ GEN genus2red(GEN Q, GEN P, GEN p)
GEN ghell(GEN e, GEN a, long prec)
- GEN ellglobalred(GEN e1)
- GEN elllocalred(GEN e, GEN p1)
- GEN elllseries(GEN e, GEN s, GEN A, long prec)
GEN mathell(GEN e, GEN x, long prec)
int oncurve(GEN e, GEN z)
- GEN ellordinate(GEN e, GEN x, long prec)
GEN orderell(GEN e, GEN p)
- GEN ellchangepoint(GEN x, GEN ch)
GEN pointell(GEN e, GEN z, long prec)
- GEN powell(GEN e, GEN z, GEN n)
- GEN subell(GEN e, GEN z1, GEN z2)
- GEN taniyama(GEN e)
- GEN weipell(GEN e, long precdl)
GEN zell(GEN e, GEN z, long prec)
+ # ellsea.c
+
+ GEN Fp_ellcard_SEA(GEN a4, GEN a6, GEN p, long early_abort)
+ GEN Fq_ellcard_SEA(GEN a4, GEN a6, GEN q, GEN T, GEN p, long early_abort)
+ GEN ellmodulareqn(long l, long vx, long vy)
+ GEN ellsea(GEN E, GEN p, long early_abort)
+
# es.c
+ GEN GENtoGENstr_nospace(GEN x)
GEN GENtoGENstr(GEN x)
char* GENtoTeXstr(GEN x)
char* GENtostr(GEN x)
+ char* GENtostr_unquoted(GEN x)
GEN Str(GEN g)
GEN Strchr(GEN g)
GEN Strexpand(GEN g)
GEN Strtex(GEN g)
void brute(GEN g, char format, long dec)
void dbgGEN(GEN x, long nb)
+ void error0(GEN g)
+ void dbg_pari_heap()
int file_is_binary(FILE *f)
- void gpwritebin(char *filename, GEN x)
- GEN gp_read_file(char *filename)
- GEN gp_read_str(char *s)
- void killallfiles(int check)
+ void err_flush()
+ void err_printf(const char* pat, ...)
+ GEN gp_getenv(const char *s)
+ GEN gp_read_file(char *s)
GEN gp_read_stream(FILE *f)
+ GEN gp_readvec_file(char *s)
+ GEN gp_readvec_stream(FILE *f)
+ void gpinstall(const char *s, char *code,
+ char *gpname, char *lib)
+ GEN gsprintf(const char *fmt, ...)
+ GEN gvsprintf(const char *fmt, va_list ap)
+ char* itostr(GEN x)
void matbrute(GEN g, char format, long dec)
- char* os_getenv(char *s)
+ char* os_getenv(const char *s)
void (*os_signal(int sig, void (*f)(int)))(int)
void outmat(GEN x)
void output(GEN x)
- char* pari_strdup(char *s)
- char* pari_strndup(char *s, long n)
- char* pari_unique_filename(char *s)
- void pari_unlink(char *s)
+ char* RgV_to_str(GEN g, long flag)
+ void pari_add_hist(GEN z, long t)
+ void pari_ask_confirm(const char *s)
+ void pari_fclose(pariFILE *f)
void pari_flush()
- void pari_putc(char c)
- void pari_puts(char *s)
+ pariFILE* pari_fopen(const char *s, char *mode)
+ pariFILE* pari_fopen_or_fail(const char *s, char *mode)
+ pariFILE* pari_fopengz(const char *s)
+ void pari_fprintf(FILE *file, char *fmt, ...)
+ void pari_fread_chars(void *b, size_t n, FILE *f)
+ GEN pari_get_hist(long p)
+ long pari_get_histtime(long p)
+ char* pari_get_homedir(const char *user)
+ int pari_is_dir(const char *name)
+ int pari_is_file(const char *name)
int pari_last_was_newline()
void pari_set_last_newline(int last)
- #void print(GEN g) # syntax error
+ ulong pari_nb_hist()
+ void pari_printf(const char *fmt, ...)
+ void pari_putc(char c)
+ void pari_puts(const char *s)
+ pariFILE* pari_safefopen(const char *s, char *mode)
+ char* pari_sprintf(const char *fmt, ...)
+ int pari_stdin_isatty()
+ char* pari_strdup(const char *s)
+ char* pari_strndup(const char *s, long n)
+ char* pari_unique_dir(const char *s)
+ char* pari_unique_filename(const char *s)
+ void pari_unlink(const char *s)
+ void pari_vfprintf(FILE *file, char *fmt, va_list ap)
+ void pari_vprintf(const char *fmt, va_list ap)
+ char* pari_vsprintf(const char *fmt, va_list ap)
+ char* path_expand(const char *s)
+ void out_print0(PariOUT *out, char *sep, GEN g, long flag)
+ void out_printf(PariOUT *out, char *fmt, ...)
+ void out_putc(PariOUT *out, char c)
+ void out_puts(PariOUT *out, char *s)
+ void out_term_color(PariOUT *out, long c)
+ void out_vprintf(PariOUT *out, char *fmt, va_list ap)
+ char* pari_sprint0(const char *msg, GEN g, long flag)
+ #void print(GEN g)
+ extern int f_RAW, f_PRETTYMAT, f_PRETTY, f_TEX
+ void print0(GEN g, long flag)
void print1(GEN g)
+ void printf0(const char *fmt, GEN args)
+ void printsep(const char *s, GEN g, long flag)
+ void printsep1(const char *s, GEN g, long flag)
void printtex(GEN g)
- GEN readbin(char *name, FILE *f)
- void switchin(char *name)
- void switchout(char *name)
+ char* stack_sprintf(const char *fmt, ...)
+ char* stack_strcat(const char *s, char *t)
+ char* stack_strdup(const char *s)
+ void strftime_expand(const char *s, char *buf, long max)
+ GEN Strprintf(const char *fmt, GEN args)
+ FILE* switchin(const char *name)
+ void switchout(const char *name)
+ void term_color(long c)
+ char* term_get_color(char *s, long c)
void texe(GEN g, char format, long dec)
- char* type_name(long t)
- void write0(char *s, GEN g)
- void write1(char *s, GEN g)
- void writetex(char *s, GEN g)
+ char* type_name(long t)
+ void warning0(GEN g)
+ void write0(const char *s, GEN g)
+ void write1(const char *s, GEN g)
+ void writebin(const char *name, GEN x)
+ void writetex(const char *s, GEN g)
# eval.c
+ extern int br_NONE, br_BREAK, br_NEXT, br_MULTINEXT, br_RETURN
+ void bincopy_relink(GEN C, GEN vi)
+ GEN break0(long n)
GEN closure_callgen1(GEN C, GEN x)
+ GEN closure_callgen2(GEN C, GEN x, GEN y)
+ GEN closure_callgenall(GEN C, long n, ...)
GEN closure_callgenvec(GEN C, GEN args)
+ void closure_callvoid1(GEN C, GEN x)
+ long closure_context(long start, long level)
+ void closure_disassemble(GEN n)
+ void closure_err(long level)
+ GEN closure_evalbrk(GEN C, long *status)
+ GEN closure_evalgen(GEN C)
+ GEN closure_evalnobrk(GEN C)
+ GEN closure_evalres(GEN C)
+ void closure_evalvoid(GEN C)
+ GEN closure_trapgen(GEN C, long numerr)
+ GEN copybin_unlink(GEN C)
+ GEN get_lex(long vn)
+ GEN gp_call(void *E, GEN x)
+ long gp_callbool(void *E, GEN x)
+ long gp_callvoid(void *E, GEN x)
+ GEN gp_eval(void *E, GEN x)
+ long gp_evalbool(void *E, GEN x)
+ GEN gp_evalupto(void *E, GEN x)
+ long gp_evalvoid(void *E, GEN x)
+ long loop_break()
+ GEN next0(long n)
+ GEN pareval(GEN C)
+ GEN parsum(GEN a, GEN b, GEN code, GEN x)
+ GEN parvector(long n, GEN code)
+ void pop_lex(long n)
+ void push_lex(GEN a, GEN C)
+ GEN return0(GEN x)
+ void set_lex(long vn, GEN x)
# FF.c
@@ -1132,12 +2506,22 @@ cdef extern from 'pari/pari.h':
GEN FF_Z_mul(GEN a, GEN b)
GEN FF_add(GEN a, GEN b)
GEN FF_charpoly(GEN x)
- int FF_equal0(GEN x)
- int FF_equal1(GEN x)
- int FF_equalm1(GEN x)
GEN FF_conjvec(GEN x)
GEN FF_div(GEN a, GEN b)
+ GEN FF_ellcard(GEN E)
+ GEN FF_ellgens(GEN E)
+ GEN FF_ellgroup(GEN E)
+ GEN FF_elllog(GEN E, GEN P, GEN Q, GEN o)
+ GEN FF_ellmul(GEN E, GEN P, GEN n)
+ GEN FF_ellorder(GEN E, GEN P, GEN o)
+ GEN FF_ellrandom(GEN E)
+ GEN FF_elltatepairing(GEN E, GEN P, GEN Q, GEN m)
+ GEN FF_ellweilpairing(GEN E, GEN P, GEN Q, GEN m)
int FF_equal(GEN a, GEN b)
+ int FF_equal0(GEN x)
+ int FF_equal1(GEN x)
+ int FF_equalm1(GEN x)
+ long FF_f(GEN x)
GEN FF_inv(GEN a)
long FF_issquare(GEN x)
long FF_issquareall(GEN x, GEN *pt)
@@ -1155,15 +2539,27 @@ cdef extern from 'pari/pari.h':
GEN FF_p_i(GEN x)
GEN FF_pow(GEN x, GEN n)
GEN FF_primroot(GEN x, GEN *o)
+ GEN FF_q(GEN x)
int FF_samefield(GEN x, GEN y)
GEN FF_sqr(GEN a)
GEN FF_sqrt(GEN a)
GEN FF_sqrtn(GEN x, GEN n, GEN *zetan)
GEN FF_sub(GEN x, GEN y)
+ GEN FF_to_F2xq(GEN x)
+ GEN FF_to_F2xq_i(GEN x)
+ GEN FF_to_Flxq(GEN x)
+ GEN FF_to_Flxq_i(GEN x)
GEN FF_to_FpXQ(GEN x)
GEN FF_to_FpXQ_i(GEN x)
GEN FF_trace(GEN x)
GEN FF_zero(GEN a)
+ GEN FFM_FFC_mul(GEN M, GEN C, GEN ff)
+ GEN FFM_det(GEN M, GEN ff)
+ GEN FFM_image(GEN M, GEN ff)
+ GEN FFM_inv(GEN M, GEN ff)
+ GEN FFM_ker(GEN M, GEN ff)
+ GEN FFM_mul(GEN M, GEN N, GEN ff)
+ long FFM_rank(GEN M, GEN ff)
GEN FFX_factor(GEN f, GEN x)
GEN FFX_roots(GEN f, GEN x)
GEN Z_FF_div(GEN a, GEN b)
@@ -1172,11 +2568,19 @@ cdef extern from 'pari/pari.h':
GEN fforder(GEN x, GEN o)
GEN ffprimroot(GEN x, GEN *o)
GEN ffrandom(GEN ff)
- int is_Z_factor(GEN f)
+ int Rg_is_FF(GEN c, GEN *ff)
+ int RgC_is_FFC(GEN x, GEN *ff)
+ int RgM_is_FFM(GEN x, GEN *ff)
+ GEN p_to_FF(GEN p, long v)
# galconj.c
GEN checkgal(GEN gal)
+ GEN checkgroup(GEN g, GEN *S)
+ GEN embed_disc(GEN r, long r1, long prec)
+ GEN embed_roots(GEN r, long r1)
+ GEN galois_group(GEN gal)
+ GEN galoisconj(GEN nf, GEN d)
GEN galoisconj0(GEN nf, long flag, GEN d, long prec)
GEN galoisexport(GEN gal, long format)
GEN galoisfixedfield(GEN gal, GEN v, long flag, long y)
@@ -1191,113 +2595,174 @@ cdef extern from 'pari/pari.h':
GEN vandermondeinverse(GEN L, GEN T, GEN den, GEN prep)
# gen1.c
-
+ GEN conjvec(GEN x, long prec)
GEN gadd(GEN x, GEN y)
GEN gaddsg(long x, GEN y)
+ GEN gconj(GEN x)
GEN gdiv(GEN x, GEN y)
+ GEN gdivgs(GEN x, long s)
+ GEN ginv(GEN x)
GEN gmul(GEN x, GEN y)
+ GEN gmul2n(GEN x, long n)
+ GEN gmulsg(long s, GEN y)
GEN gsqr(GEN x)
GEN gsub(GEN x, GEN y)
+ GEN gsubsg(long x, GEN y)
+ GEN inv_ser(GEN b)
+ GEN mulcxI(GEN x)
+ GEN mulcxmI(GEN x)
+ GEN ser_normalize(GEN x)
+
+ # galpol.c
+
+ GEN galoisnbpol(long a)
+ GEN galoisgetpol(long a, long b, long s)
# gen2.c
- GEN ZX_mul(GEN x, GEN y)
+ GEN gassoc_proto(GEN f(GEN, GEN), GEN, GEN)
+ GEN map_proto_G(GEN f(GEN), GEN x)
+ GEN map_proto_lG(long f(GEN), GEN x)
+ GEN map_proto_lGL(long f(GEN, long), GEN x, long y)
+
+ long Q_pval(GEN x, GEN p)
+ long Q_pvalrem(GEN x, GEN p, GEN *y)
+ long RgX_val(GEN x)
+ long RgX_valrem(GEN x, GEN *z)
+ long RgX_valrem_inexact(GEN x, GEN *Z)
+ int ZV_Z_dvd(GEN v, GEN p)
+ long ZV_pval(GEN x, GEN p)
+ long ZV_pvalrem(GEN x, GEN p, GEN *px)
+ long ZV_lval(GEN x, ulong p)
+ long ZV_lvalrem(GEN x, ulong p, GEN *px)
+ long ZX_lvalrem(GEN x, ulong p, GEN *px)
+ long ZX_lval(GEN x, ulong p)
+ long ZX_pval(GEN x, GEN p)
+ long ZX_pvalrem(GEN x, GEN p, GEN *px)
+ long Z_lval(GEN n, ulong p)
+ long Z_lvalrem(GEN n, ulong p, GEN *py)
+ long Z_lvalrem_stop(GEN *n, ulong p, int *stop)
+ long Z_pval(GEN n, GEN p)
+ long Z_pvalrem(GEN x, GEN p, GEN *py)
GEN cgetp(GEN x)
+ GEN cvstop2(long s, GEN y)
GEN cvtop(GEN x, GEN p, long l)
GEN cvtop2(GEN x, GEN y)
GEN gabs(GEN x, long prec)
void gaffect(GEN x, GEN y)
void gaffsg(long s, GEN x)
- GEN gclone(GEN x)
int gcmp(GEN x, GEN y)
- int gcmpsg(long x, GEN y)
int gequal0(GEN x)
int gequal1(GEN x)
+ int gequalX(GEN x)
int gequalm1(GEN x)
+ int gcmpsg(long x, GEN y)
GEN gcvtop(GEN x, GEN p, long r)
int gequal(GEN x, GEN y)
int gequalsg(long s, GEN x)
long gexpo(GEN x)
- long ggval(GEN x, GEN p)
+ long gvaluation(GEN x, GEN p)
+ int gidentical(GEN x, GEN y)
long glength(GEN x)
GEN gmax(GEN x, GEN y)
+ GEN gmaxgs(GEN x, long y)
GEN gmin(GEN x, GEN y)
+ GEN gmings(GEN x, long y)
GEN gneg(GEN x)
GEN gneg_i(GEN x)
- GEN greffe(GEN x, long l, long use_stack)
+ GEN RgX_to_ser(GEN x, long l)
+ GEN RgX_to_ser_inexact(GEN x, long l)
int gsigne(GEN x)
- GEN gtofp(GEN z, long prec)
GEN gtolist(GEN x)
long gtolong(GEN x)
int lexcmp(GEN x, GEN y)
- GEN listcreate()
GEN listinsert(GEN list, GEN object, long index)
- void listkill(GEN list)
+ void listpop(GEN L, long index)
GEN listput(GEN list, GEN object, long index)
- GEN listsort(GEN list, long flag)
+ void listsort(GEN list, long flag)
GEN matsize(GEN x)
+ GEN mklistcopy(GEN x)
GEN normalize(GEN x)
GEN normalizepol(GEN x)
+ GEN normalizepol_approx(GEN x, long lx)
+ GEN normalizepol_lg(GEN x, long lx)
+ ulong padic_to_Fl(GEN x, ulong p)
+ GEN padic_to_Fp(GEN x, GEN Y)
+ GEN quadtofp(GEN x, long l)
+ GEN rfrac_to_ser(GEN x, long l)
long sizedigit(GEN x)
long u_lval(ulong x, ulong p)
long u_lvalrem(ulong x, ulong p, ulong *py)
+ long u_lvalrem_stop(ulong *n, ulong p, int *stop)
+ long u_pval(ulong x, GEN p)
long u_pvalrem(ulong x, GEN p, ulong *py)
+ long vecindexmax(GEN x)
+ long vecindexmin(GEN x)
+ GEN vecmax0(GEN x, GEN *pv)
GEN vecmax(GEN x)
+ GEN vecmin0(GEN x, GEN *pv)
GEN vecmin(GEN x)
- long Z_lval(GEN n, ulong p)
- long Z_lvalrem(GEN n, ulong p, GEN *py)
+ long z_lval(long s, ulong p)
+ long z_lvalrem(long s, ulong p, long *py)
long z_pval(long n, GEN p)
- long Z_pval(GEN n, GEN p)
- long Z_pvalrem(GEN x, GEN p, GEN *py)
+ long z_pvalrem(long n, GEN p, long *py)
# gen3.c
+ GEN padic_to_Q(GEN x)
+ GEN padic_to_Q_shallow(GEN x)
+ GEN QpV_to_QV(GEN v)
+ GEN RgM_mulreal(GEN x, GEN y)
+ GEN RgX_RgM_eval_col(GEN x, GEN M, long c)
+ GEN RgX_deflate_max(GEN x0, long *m)
+ GEN RgX_integ(GEN x)
GEN ceil_safe(GEN x)
GEN ceilr(GEN x)
GEN centerlift(GEN x)
- GEN centerlift0(GEN x,long v)
+ GEN centerlift0(GEN x, long v)
GEN compo(GEN x, long n)
- GEN deg1pol(GEN x1, GEN x0,long v)
+ GEN deg1pol(GEN x1, GEN x0, long v)
+ GEN deg1pol_shallow(GEN x1, GEN x0, long v)
long degree(GEN x)
GEN denom(GEN x)
GEN deriv(GEN x, long v)
- GEN RgX_deriv(GEN x)
GEN derivser(GEN x)
+ GEN diffop(GEN x, GEN v, GEN dv)
+ GEN diffop0(GEN x, GEN v, GEN dv, long n)
GEN diviiround(GEN x, GEN y)
GEN divrem(GEN x, GEN y, long v)
- GEN gand(GEN x, GEN y)
+ GEN floor_safe(GEN x)
GEN gceil(GEN x)
GEN gcvtoi(GEN x, long *e)
+ GEN gdeflate(GEN x, long v, long d)
GEN gdivent(GEN x, GEN y)
+ GEN gdiventgs(GEN x, long y)
+ GEN gdiventsg(long x, GEN y)
GEN gdiventres(GEN x, GEN y)
- GEN gdivgs(GEN x, long s)
GEN gdivmod(GEN x, GEN y, GEN *pr)
GEN gdivround(GEN x, GEN y)
+ int gdvd(GEN x, GEN y)
GEN geq(GEN x, GEN y)
GEN geval(GEN x)
GEN gfloor(GEN x)
+ GEN gtrunc2n(GEN x, long s)
GEN gfrac(GEN x)
GEN gge(GEN x, GEN y)
GEN ggrando(GEN x, long n)
GEN ggt(GEN x, GEN y)
GEN gimag(GEN x)
- GEN ginv(GEN x)
GEN gle(GEN x, GEN y)
GEN glt(GEN x, GEN y)
GEN gmod(GEN x, GEN y)
- GEN gmodulo(GEN x,GEN y)
GEN gmodgs(GEN x, long y)
- GEN gmodulo(GEN x,GEN y)
+ GEN gmodsg(long x, GEN y)
+ GEN gmodulo(GEN x, GEN y)
GEN gmodulsg(long x, GEN y)
GEN gmodulss(long x, long y)
- GEN gmul2n(GEN x, long n)
- GEN gmulsg(long s, GEN y)
GEN gne(GEN x, GEN y)
GEN gnot(GEN x)
- GEN gor(GEN x, GEN y)
GEN gpolvar(GEN y)
long gprecision(GEN x)
- GEN gram_matrix(GEN M)
GEN greal(GEN x)
GEN grndtoi(GEN x, long *e)
GEN ground(GEN x)
@@ -1307,6 +2772,8 @@ cdef extern from 'pari/pari.h':
GEN gsubstvec(GEN x, GEN v, GEN y)
GEN gtocol(GEN x)
GEN gtocol0(GEN x, long n)
+ GEN gtocolrev(GEN x)
+ GEN gtocolrev0(GEN x, long n)
GEN gtopoly(GEN x, long v)
GEN gtopolyrev(GEN x, long v)
GEN gtoser(GEN x, long v, long precdl)
@@ -1317,106 +2784,288 @@ cdef extern from 'pari/pari.h':
GEN gtovecsmall(GEN x)
GEN gtovecsmall0(GEN x, long n)
GEN gtrunc(GEN x)
- int gvar(GEN x)
- int gvar2(GEN x)
+ long gvar(GEN x)
+ long gvar2(GEN x)
GEN hqfeval(GEN q, GEN x)
GEN imag_i(GEN x)
- GEN int2n(long n)
GEN integ(GEN x, long v)
+ GEN integser(GEN x)
int iscomplex(GEN x)
int isexactzero(GEN g)
+ int isrationalzeroscalar(GEN g)
int isinexact(GEN x)
int isinexactreal(GEN x)
- long isint(GEN n, long *ptk)
+ int isint(GEN n, GEN *ptk)
+ int isrationalzero(GEN g)
int issmall(GEN n, long *ptk)
GEN lift(GEN x)
- GEN lift0(GEN x,long v)
- GEN lift_intern0(GEN x,long v)
- GEN truncr(GEN x)
+ GEN lift0(GEN x, long v)
+ GEN liftall(GEN x)
+ GEN liftall_shallow(GEN x)
+ GEN liftint(GEN x)
+ GEN liftint_shallow(GEN x)
+ GEN liftpol(GEN x)
+ GEN liftpol_shallow(GEN x)
GEN mkcoln(long n, ...)
GEN mkintn(long n, ...)
GEN mkpoln(long n, ...)
GEN mkvecn(long n, ...)
+ GEN mkvecsmalln(long n, ...)
+ GEN mulreal(GEN x, GEN y)
GEN numer(GEN x)
- GEN padicappr(GEN f, GEN a)
long padicprec(GEN x, GEN p)
- GEN polcoeff0(GEN x,long n,long v)
+ long padicprec_relative(GEN x)
+ GEN polcoeff0(GEN x, long n, long v)
GEN polcoeff_i(GEN x, long n, long v)
- long poldegree(GEN x,long v)
+ long poldegree(GEN x, long v)
+ long RgX_degree(GEN x, long v)
GEN poleval(GEN x, GEN y)
- GEN pollead(GEN x,long v)
+ GEN pollead(GEN x, long v)
long precision(GEN x)
- GEN precision0(GEN x,long n)
+ GEN precision0(GEN x, long n)
+ GEN qf_apply_RgM(GEN q, GEN M)
+ GEN qf_apply_ZM(GEN q, GEN M)
+ GEN qfbil(GEN x, GEN y, GEN q)
GEN qfeval(GEN q, GEN x)
+ GEN qfevalb(GEN q, GEN x, GEN y)
+ GEN qfnorm(GEN x, GEN q)
GEN real_i(GEN x)
- GEN real2n(long n, long prec)
- GEN recip(GEN x)
GEN round0(GEN x, GEN *pte)
GEN roundr(GEN x)
+ GEN roundr_safe(GEN x)
GEN scalarpol(GEN x, long v)
+ GEN scalarpol_shallow(GEN x, long v)
GEN scalarser(GEN x, long v, long prec)
+ GEN ser_unscale(GEN P, GEN h)
+ GEN serreverse(GEN x)
GEN simplify(GEN x)
+ GEN simplify_shallow(GEN x)
GEN tayl(GEN x, long v, long precdl)
GEN toser_i(GEN x)
GEN trunc0(GEN x, GEN *pte)
+ GEN uu32toi(ulong a, ulong b)
# groupid.c
long group_ident(GEN G, GEN S)
+ long group_ident_trans(GEN G, GEN S)
# hash.c
- ulong hash_GEN(GEN x)
+ hashtable *hash_create(ulong minsize, ulong (*hash)(void*), int (*eq)(void*, void*), int use_stack)
+ void hash_insert(hashtable *h, void *k, void *v)
+ hashentry *hash_search(hashtable *h, void *k)
+ hashentry *hash_remove(hashtable *h, void *k)
+ void hash_destroy(hashtable *h)
+ ulong hash_str(const char *str)
+ ulong hash_str2(const char *s)
+ ulong hash_GEN(GEN x)
+
+ # hnf_snf.c
+
+ GEN Frobeniusform(GEN V, long n)
+ GEN RgM_hnfall(GEN A, GEN *pB, long remove)
+ GEN ZM_hnf(GEN x)
+ GEN ZM_hnfall(GEN A, GEN *ptB, long remove)
+ GEN ZM_hnfcenter(GEN M)
+ GEN ZM_hnflll(GEN A, GEN *ptB, int remove)
+ GEN ZV_gcdext(GEN A)
+ GEN ZM_hnfmod(GEN x, GEN d)
+ GEN ZM_hnfmodall(GEN x, GEN dm, long flag)
+ GEN ZM_hnfmodid(GEN x, GEN d)
+ GEN ZM_hnfperm(GEN A, GEN *ptU, GEN *ptperm)
+ void ZM_snfclean(GEN d, GEN u, GEN v)
+ GEN ZM_snf(GEN x)
+ GEN ZM_snf_group(GEN H, GEN *newU, GEN *newUi)
+ GEN ZM_snfall(GEN x, GEN *ptU, GEN *ptV)
+ GEN ZM_snfall_i(GEN x, GEN *ptU, GEN *ptV, int return_vec)
+ GEN zlm_echelon(GEN x, long early_abort, ulong p, ulong pm)
+ GEN ZpM_echelon(GEN x, long early_abort, GEN p, GEN pm)
+ GEN gsmith(GEN x)
+ GEN gsmithall(GEN x)
+ GEN hnf(GEN x)
+ GEN hnf_divscale(GEN A, GEN B, GEN t)
+ GEN hnf_solve(GEN A, GEN B)
+ GEN hnf_invimage(GEN A, GEN b)
+ GEN hnfall(GEN x)
+ int hnfdivide(GEN A, GEN B)
+ GEN hnflll(GEN x)
+ GEN hnfmerge_get_1(GEN A, GEN B)
+ GEN hnfmod(GEN x, GEN d)
+ GEN hnfmodid(GEN x, GEN p)
+ GEN hnfperm(GEN x)
+ GEN matfrobenius(GEN M, long flag, long v)
+ GEN mathnf0(GEN x, long flag)
+ GEN matsnf0(GEN x, long flag)
+ GEN smith(GEN x)
+ GEN smithall(GEN x)
+ GEN smithclean(GEN z)
# ifactor1.c
+ GEN Z_factor(GEN n)
+ GEN Z_factor_limit(GEN n, ulong all)
+ GEN Z_factor_until(GEN n, GEN limit)
+ long Z_issmooth(GEN m, ulong lim)
+ GEN Z_issmooth_fact(GEN m, ulong lim)
+ long Z_issquarefree(GEN x)
+ GEN absi_factor(GEN n)
+ GEN absi_factor_limit(GEN n, ulong all)
+ long bigomega(GEN n)
+ GEN core(GEN n)
+ ulong coreu(ulong n)
+ GEN eulerphi(GEN n)
+ ulong eulerphiu(ulong n)
+ ulong eulerphiu_fact(GEN f)
+ GEN factorint(GEN n, long flag)
+ GEN factoru(ulong n)
+ int ifac_isprime(GEN x)
+ int ifac_next(GEN *part, GEN *p, long *e)
+ int ifac_read(GEN part, GEN *p, long *e)
+ void ifac_skip(GEN part)
+ GEN ifac_start(GEN n, int moebius)
int is_357_power(GEN x, GEN *pt, ulong *mask)
- int is_pth_power(GEN x, GEN *pt, ulong *curexp, ulong cutoffbits)
+ int is_pth_power(GEN x, GEN *pt, forprime_t *T, ulong cutoffbits)
+ long ispowerful(GEN n)
+ long issquarefree(GEN x)
+ long istotient(GEN n, GEN *px)
+ long moebius(GEN n)
+ long moebiusu(ulong n)
GEN nextprime(GEN n)
+ GEN numdiv(GEN n)
+ long omega(GEN n)
GEN precprime(GEN n)
+ GEN sumdiv(GEN n)
+ GEN sumdivk(GEN n, long k)
+ ulong tridiv_bound(GEN n)
+ int uis_357_power(ulong x, ulong *pt, ulong *mask)
+ int uis_357_powermod(ulong x, ulong *mask)
+ long uissquarefree(ulong n)
+ long uissquarefree_fact(GEN f)
+ ulong unextprime(ulong n)
+ ulong uprecprime(ulong n)
+ GEN usumdivkvec(ulong n, GEN K)
# init.c
- long allocatemoremem(size_t newsize)
- GEN changevar(GEN x, GEN y)
- void pari_err(long numerr, ...)
- long err_catch(long errnum, jmp_buf *penv)
+ void allocatemem(ulong newsize)
+ long timer_delay(pari_timer *T)
+ long timer_get(pari_timer *T)
+ void timer_start(pari_timer *T)
+ int chk_gerepileupto(GEN x)
+ GENbin* copy_bin(GEN x)
+ GENbin* copy_bin_canon(GEN x)
+ void dbg_gerepile(pari_sp av)
+ void dbg_gerepileupto(GEN q)
+ GEN errname(GEN err)
+ GEN gclone(GEN x)
+ GEN gcloneref(GEN x)
+ void gclone_refc(GEN x)
GEN gcopy(GEN x)
GEN gcopy_avma(GEN x, pari_sp *AVMA)
+ GEN gcopy_lg(GEN x, long lx)
+ GEN gerepile(pari_sp ltop, pari_sp lbot, GEN q)
+ void gerepileallsp(pari_sp av, pari_sp tetpil, int n, ...)
+ void gerepilecoeffssp(pari_sp av, pari_sp tetpil, long *g, int n)
+ void gerepilemanysp(pari_sp av, pari_sp tetpil, GEN* g[], int n)
+ GEN getheap()
+ void gp_context_save(gp_context* rec)
+ void gp_context_restore(gp_context* rec)
+ long gsizeword(GEN x)
+ long gsizebyte(GEN x)
void gunclone(GEN x)
- void msgtimer(char *format, ...)
- GEN newblock(long n)
+ void gunclone_deep(GEN x)
+ GEN listcopy(GEN x)
+ void timer_printf(pari_timer *T, char *format, ...)
+ void msgtimer(const char *format, ...)
+ long name_numerr(const char *s)
+ GEN newblock(size_t n)
+ char * numerr_name(long errnum)
+ GEN obj_check(GEN S, long K)
+ GEN obj_checkbuild(GEN S, long tag, GEN (*build)(GEN))
+ GEN obj_checkbuild_padicprec(GEN S, long tag, GEN (*build)(GEN, long), long prec)
+ GEN obj_checkbuild_prec(GEN S, long tag, GEN (*build)(GEN, long), long prec)
+ void obj_free(GEN S)
+ GEN obj_init(long d, long n)
+ GEN obj_insert(GEN S, long K, GEN O)
+ GEN obj_insert_shallow(GEN S, long K, GEN O)
+ void pari_add_function(entree *ep)
+ void pari_add_module(entree *ep)
+ void pari_add_defaults_module(entree *ep)
+ void pari_add_oldmodule(entree *ep)
void pari_close()
- void pari_init(size_t parisize, ulong maxprime)
+ void pari_close_opts(ulong init_opts)
+ int pari_daemon()
+ void pari_err(int numerr, ...)
+ GEN pari_err_last()
+ char * pari_err2str(GEN err)
void pari_init_opts(size_t parisize, ulong maxprime, ulong init_opts)
- long gsizebyte(GEN x)
- long gsizeword(GEN x)
+ void pari_init(size_t parisize, ulong maxprime)
+ void pari_stackcheck_init(void *pari_stack_base)
+ void pari_sig_init(void (*f)(int))
+ void pari_thread_alloc(pari_thread *t, size_t s, GEN arg)
+ void pari_thread_close()
+ void pari_thread_free(pari_thread *t)
+ void pari_thread_init()
+ GEN pari_thread_start(pari_thread *t)
+ GEN pari_version()
+ void pari_warn(int numerr, ...)
+ GEN trap0(const char *e, GEN f, GEN r)
+ void shiftaddress(GEN x, long dec)
+ void shiftaddress_canon(GEN x, long dec)
long timer()
long timer2()
+ void traverseheap( void(*f)(GEN, void *), void *data )
# intnum.c
- GEN intcirc(void *E, GEN (*eval) (GEN, void *), GEN a, GEN R, GEN tab, long prec)
- GEN intfouriercos(void *E, GEN (*eval) (GEN, void *), GEN a, GEN b, GEN x, GEN tab, long prec)
- GEN intfourierexp(void *E, GEN (*eval)(GEN, void*), GEN a, GEN b, GEN x, GEN tab, long prec)
- GEN intfouriersin(void *E, GEN (*eval) (GEN, void *), GEN a, GEN b, GEN x, GEN tab, long prec)
- GEN intfuncinit(void *E, GEN (*eval) (GEN, void *), GEN a, GEN b, long m, long flag, long prec)
- GEN intlaplaceinv(void *E, GEN (*eval) (GEN, void *), GEN sig, GEN x, GEN tab, long prec)
- GEN intmellininv(void *E, GEN (*eval) (GEN, void *), GEN sig, GEN x, GEN tab, long prec)
+ GEN intcirc(void *E, GEN (*eval) (void *, GEN), GEN a, GEN R, GEN tab, long prec)
+ GEN intfouriercos(void *E, GEN (*eval) (void *, GEN), GEN a, GEN b, GEN x, GEN tab, long prec)
+ GEN intfourierexp(void *E, GEN (*eval)(void *, GEN), GEN a, GEN b, GEN x, GEN tab, long prec)
+ GEN intfouriersin(void *E, GEN (*eval) (void *, GEN), GEN a, GEN b, GEN x, GEN tab, long prec)
+ GEN intfuncinit(void *E, GEN (*eval) (void *, GEN), GEN a, GEN b, long m, long flag, long prec)
+ GEN intlaplaceinv(void *E, GEN (*eval) (void *, GEN), GEN sig, GEN x, GEN tab, long prec)
+ GEN intmellininv(void *E, GEN (*eval) (void *, GEN), GEN sig, GEN x, GEN tab, long prec)
GEN intmellininvshort(GEN sig, GEN x, GEN tab, long prec)
- GEN intnum(void *E, GEN (*eval) (GEN, void *), GEN a, GEN b, GEN tab, long prec)
+ GEN intnum(void *E, GEN (*eval) (void *, GEN), GEN a, GEN b, GEN tab, long prec)
GEN intnuminit(GEN a, GEN b, long m, long prec)
- GEN intnuminitgen(void *E, GEN (*eval) (GEN, void *), GEN a, GEN b, long m, long flext, long prec)
- GEN intnumromb(void *E, GEN (*eval) (GEN, void *), GEN a, GEN b, long flag, long prec)
+ GEN intnuminitgen(void *E, GEN (*eval) (void *, GEN), GEN a, GEN b, long m, long flext, long prec)
+ GEN intnumromb(void *E, GEN (*eval) (void *, GEN), GEN a, GEN b, long flag, long prec)
long intnumstep(long prec)
- GEN sumnum(void *E, GEN (*f) (GEN, void *), GEN a, GEN sig, GEN tab, long flag, long prec)
- GEN sumnumalt(void *E, GEN (*f) (GEN, void *), GEN a, GEN s, GEN tab, long flag, long prec)
+ GEN sumnum(void *E, GEN (*f) (void *, GEN), GEN a, GEN sig, GEN tab, long flag, long prec)
+ GEN sumnumalt(void *E, GEN (*f) (void *, GEN), GEN a, GEN s, GEN tab, long flag, long prec)
GEN sumnuminit(GEN sig, long m, long sgn, long prec)
+ # krasner.c
+
+ GEN padicfields0(GEN p, GEN n, long flag)
+ GEN padicfields(GEN p, long m, long d, long flag)
+
# kummer.c
GEN rnfkummer(GEN bnr, GEN subgroup, long all, long prec)
+ # lll.c
+
+ GEN ZM_lll_norms(GEN x, double D, long flag, GEN *B)
+ GEN kerint(GEN x)
+ GEN lll(GEN x)
+ GEN lllfp(GEN x, double D, long flag)
+ GEN lllgen(GEN x)
+ GEN lllgram(GEN x)
+ GEN lllgramgen(GEN x)
+ GEN lllgramint(GEN x)
+ GEN lllgramkerim(GEN x)
+ GEN lllgramkerimgen(GEN x)
+ GEN lllint(GEN x)
+ GEN lllintpartial(GEN mat)
+ GEN lllintpartial_inplace(GEN mat)
+ GEN lllkerim(GEN x)
+ GEN lllkerimgen(GEN x)
+ GEN matkerint0(GEN x, long flag)
+ GEN qflll0(GEN x, long flag)
+ GEN qflllgram0(GEN x, long flag)
+
# members.c
GEN member_a1(GEN x)
@@ -1429,6 +3078,7 @@ cdef extern from 'pari/pari.h':
GEN member_b4(GEN x)
GEN member_b6(GEN x)
GEN member_b8(GEN x)
+ GEN member_bid(GEN x)
GEN member_bnf(GEN x)
GEN member_c4(GEN x)
GEN member_c6(GEN x)
@@ -1453,19 +3103,26 @@ cdef extern from 'pari/pari.h':
GEN member_orders(GEN x)
GEN member_p(GEN x)
GEN member_pol(GEN x)
+ GEN member_polabs(GEN x)
GEN member_reg(GEN x)
+ GEN member_r1(GEN x)
+ GEN member_r2(GEN x)
GEN member_roots(GEN x)
GEN member_sign(GEN x)
GEN member_t2(GEN x)
GEN member_tate(GEN x)
GEN member_tufu(GEN x)
GEN member_tu(GEN x)
- GEN member_w(GEN x)
GEN member_zk(GEN x)
GEN member_zkst(GEN bid)
# mp.c
+ GEN addmulii(GEN x, GEN y, GEN z)
+ GEN addmulii_inplace(GEN x, GEN y, GEN z)
+ ulong Fl_inv(ulong x, ulong p)
+ ulong Fl_invsafe(ulong x, ulong p)
+ int Fp_ratlift(GEN x, GEN m, GEN amax, GEN bmax, GEN *a, GEN *b)
int absi_cmp(GEN x, GEN y)
int absi_equal(GEN x, GEN y)
int absr_cmp(GEN x, GEN y)
@@ -1473,35 +3130,44 @@ cdef extern from 'pari/pari.h':
GEN addir_sign(GEN x, long sx, GEN y, long sy)
GEN addrr_sign(GEN x, long sx, GEN y, long sy)
GEN addsi_sign(long x, GEN y, long sy)
+ GEN addui_sign(ulong x, GEN y, long sy)
GEN addsr(long x, GEN y)
- GEN addss(long x, long y)
+ GEN addumului(ulong a, ulong b, GEN Y)
void affir(GEN x, GEN y)
void affrr(GEN x, GEN y)
GEN bezout(GEN a, GEN b, GEN *u, GEN *v)
- long cbezout(long a,long b,long *uu,long *vv)
+ long cbezout(long a, long b, long *uu, long *vv)
int cmpii(GEN x, GEN y)
int cmprr(GEN x, GEN y)
- int cmpsi(long x, GEN y)
- int cmpui(ulong x, GEN y)
+ long dblexpo(double x)
+ ulong dblmantissa(double x)
GEN dbltor(double x)
GEN diviiexact(GEN x, GEN y)
- GEN diviuexact(GEN x, ulong y)
GEN divir(GEN x, GEN y)
GEN divis(GEN y, long x)
GEN divis_rem(GEN x, long y, long *rem)
GEN diviu_rem(GEN y, ulong x, ulong *rem)
+ GEN diviuuexact(GEN x, ulong y, ulong z)
+ GEN diviuexact(GEN x, ulong y)
GEN divri(GEN x, GEN y)
GEN divrr(GEN x, GEN y)
GEN divrs(GEN x, long y)
+ GEN divru(GEN x, ulong y)
GEN divsi(long x, GEN y)
GEN divsr(long x, GEN y)
+ GEN divur(ulong x, GEN y)
GEN dvmdii(GEN x, GEN y, GEN *z)
int equalii(GEN x, GEN y)
+ int equalrr(GEN x, GEN y)
GEN floorr(GEN x)
GEN gcdii(GEN x, GEN y)
+ GEN int2n(long n)
+ GEN int2u(ulong n)
GEN int_normalize(GEN x, long known_zero_words)
int invmod(GEN a, GEN b, GEN *res)
- ulong Fl_inv(ulong x, ulong p)
+ ulong invmod2BIL(ulong b)
+ GEN invr(GEN b)
+ GEN mantissa_real(GEN x, long *e)
GEN modii(GEN x, GEN y)
void modiiz(GEN x, GEN y, GEN z)
GEN mulii(GEN x, GEN y)
@@ -1513,29 +3179,58 @@ cdef extern from 'pari/pari.h':
GEN mului(ulong x, GEN y)
GEN mulur(ulong x, GEN y)
GEN muluu(ulong x, ulong y)
- GEN randomi(GEN x)
- int ratlift(GEN x, GEN m, GEN *a, GEN *b, GEN amax, GEN bmax)
+ GEN muluui(ulong x, ulong y, GEN z)
+ GEN remi2n(GEN x, long n)
double rtodbl(GEN x)
GEN shifti(GEN x, long n)
GEN sqri(GEN x)
- #define sqrti(x) sqrtremi((x),NULL)
+ GEN sqrr(GEN x)
+ GEN sqrs(long x)
+ GEN sqrtr_abs(GEN x)
GEN sqrtremi(GEN S, GEN *R)
+ GEN sqru(ulong x)
GEN subsr(long x, GEN y)
GEN truedvmdii(GEN x, GEN y, GEN *z)
+ GEN truedvmdis(GEN x, long y, GEN *z)
+ GEN truedvmdsi(long x, GEN y, GEN *z)
+ GEN trunc2nr(GEN x, long n)
+ GEN mantissa2nr(GEN x, long n)
+ GEN truncr(GEN x)
ulong umodiu(GEN y, ulong x)
long vals(ulong x)
# nffactor.c
- GEN nffactor(GEN nf,GEN x)
- GEN nffactormod(GEN nf,GEN pol,GEN pr)
- GEN nfroots(GEN nf,GEN pol)
- GEN rnfcharpoly(GEN nf,GEN T,GEN alpha,int n)
- GEN rnfdedekind(GEN nf,GEN T,GEN pr)
+ GEN FpC_ratlift(GEN P, GEN mod, GEN amax, GEN bmax, GEN denom)
+ GEN FpM_ratlift(GEN M, GEN mod, GEN amax, GEN bmax, GEN denom)
+ GEN FpX_ratlift(GEN P, GEN mod, GEN amax, GEN bmax, GEN denom)
+ GEN nffactor(GEN nf, GEN x)
+ GEN nffactormod(GEN nf, GEN pol, GEN pr)
+ GEN nfgcd(GEN P, GEN Q, GEN nf, GEN den)
+ GEN nfgcd_all(GEN P, GEN Q, GEN T, GEN den, GEN *Pnew)
+ GEN nfroots(GEN nf, GEN pol)
+ GEN polfnf(GEN a, GEN t)
+ GEN rootsof1(GEN x)
+ GEN rootsof1_kannan(GEN nf)
+
+ # paricfg.c
+
+ extern char *paricfg_datadir
+ extern char *paricfg_version
+ extern char *paricfg_buildinfo
+ extern long paricfg_version_code
+ extern char *paricfg_vcsversion
+ extern char *paricfg_compiledate
+ extern char *paricfg_mt_engine
# part.c
+ void forpart(void *E, long call(void*, GEN), long k, GEN nbound, GEN abound)
+ void forpart_init(forpart_t *T, long k, GEN abound, GEN nbound)
+ GEN forpart_next(forpart_t *T)
+ GEN forpart_prev(forpart_t *T)
GEN numbpart(GEN x)
+ GEN partitions(long k, GEN nbound, GEN abound)
# perm.c
@@ -1556,234 +3251,293 @@ cdef extern from 'pari/pari.h':
long group_perm_normalize(GEN N, GEN g)
GEN group_quotient(GEN G, GEN H)
GEN group_rightcoset(GEN G, GEN g)
+ GEN group_set(GEN G, long n)
+ long group_subgroup_isnormal(GEN G, GEN H)
GEN group_subgroups(GEN G)
- GEN groupelts_center(GEN S)
GEN groupelts_abelian_group(GEN S)
+ GEN groupelts_center(GEN S)
+ GEN groupelts_set(GEN G, long n)
int perm_commute(GEN p, GEN q)
GEN perm_cycles(GEN v)
long perm_order(GEN perm)
GEN perm_pow(GEN perm, long exp)
GEN quotient_group(GEN C, GEN G)
GEN quotient_perm(GEN C, GEN p)
+ GEN quotient_subgroup_lift(GEN C, GEN H, GEN S)
+ GEN subgroups_tableset(GEN S, long n)
+ long tableset_find_index(GEN tbl, GEN set)
+ GEN trivialgroup()
GEN vecperm_orbits(GEN v, long n)
+ GEN vec_insert(GEN v, long n, GEN x)
+ int vec_is1to1(GEN v)
+ int vec_isconst(GEN v)
+ long vecsmall_duplicate(GEN x)
+ long vecsmall_duplicate_sorted(GEN x)
+ GEN vecsmall_indexsort(GEN V)
void vecsmall_sort(GEN V)
GEN vecsmall_uniq(GEN V)
+ GEN vecsmall_uniq_sorted(GEN V)
GEN vecvecsmall_indexsort(GEN x)
- GEN vecvecsmall_sort(GEN x)
long vecvecsmall_search(GEN x, GEN y, long flag)
+ GEN vecvecsmall_sort(GEN x)
+ GEN vecvecsmall_sort_uniq(GEN x)
+
+ # mt.c
+
+ void mt_broadcast(GEN code)
+ void mt_sigint_block()
+ void mt_sigint_unblock()
+ void mt_queue_end(pari_mt *pt)
+ GEN mt_queue_get(pari_mt *pt, long *jobid, long *pending)
+ void mt_queue_start(pari_mt *pt, GEN worker)
+ void mt_queue_submit(pari_mt *pt, long jobid, GEN work)
+ void pari_mt_init()
+ void pari_mt_close()
# polarit1.c
- long Flx_nbfact(GEN z, ulong p)
- long Flx_nbroots(GEN f, ulong p)
- GEN FpX_degfact(GEN f, GEN p)
- long FpX_is_irred(GEN f, GEN p)
- long FpX_is_squarefree(GEN f, GEN p)
- long FpX_is_totally_split(GEN f, GEN p)
- GEN FpX_factor(GEN f, GEN p)
- long FpX_nbfact(GEN f, GEN p)
- long FpX_nbroots(GEN f, GEN p)
- GEN FpXQX_gcd(GEN P, GEN Q, GEN T, GEN p)
- GEN FqX_factor(GEN x, GEN T, GEN p)
- GEN FqX_gcd(GEN P, GEN Q, GEN T, GEN p)
- long FqX_is_squarefree(GEN P, GEN T, GEN p)
- long FqX_nbfact(GEN u, GEN T, GEN p)
- long FqX_nbroots(GEN f, GEN T, GEN p)
- GEN random_FpX(long d, long v, GEN p)
- GEN FpX_roots(GEN f, GEN p)
- GEN padicappr(GEN f, GEN a)
- GEN factcantor(GEN x, GEN p)
- GEN factmod(GEN f, GEN p)
- GEN factorff(GEN f, GEN p, GEN a)
- GEN factormod0(GEN f, GEN p, long flag)
- GEN factorpadic0(GEN f,GEN p,long r,long flag)
+ GEN ZX_Zp_root(GEN f, GEN a, GEN p, long prec)
+ GEN Zp_appr(GEN f, GEN a)
+ GEN factorpadic0(GEN f, GEN p, long r, long flag)
GEN factorpadic(GEN x, GEN p, long r)
- int gdvd(GEN x, GEN y)
+ GEN gdeuc(GEN x, GEN y)
+ GEN grem(GEN x, GEN y)
+ GEN padicappr(GEN f, GEN a)
GEN poldivrem(GEN x, GEN y, GEN *pr)
- GEN rootmod(GEN f, GEN p)
- GEN rootmod0(GEN f, GEN p,long flag)
- GEN rootmod2(GEN f, GEN p)
GEN rootpadic(GEN f, GEN p, long r)
GEN rootpadicfast(GEN f, GEN p, long e)
- GEN simplefactmod(GEN f, GEN p)
# polarit2.c
GEN Q_content(GEN x)
GEN Q_denom(GEN x)
GEN Q_div_to_int(GEN x, GEN c)
+ GEN Q_gcd(GEN x, GEN y)
+ GEN Q_mul_to_int(GEN x, GEN c)
GEN Q_muli_to_int(GEN x, GEN d)
GEN Q_primitive_part(GEN x, GEN *ptc)
GEN Q_primpart(GEN x)
GEN Q_remove_denom(GEN x, GEN *ptd)
+ GEN RgXQ_charpoly(GEN x, GEN T, long v)
+ GEN RgXQ_inv(GEN x, GEN y)
+ GEN RgX_disc(GEN x)
GEN RgX_extgcd(GEN x, GEN y, GEN *U, GEN *V)
- GEN ZX_squff(GEN f, GEN *ex)
+ GEN RgX_extgcd_simple(GEN a, GEN b, GEN *pu, GEN *pv)
+ GEN RgX_gcd(GEN x, GEN y)
+ GEN RgX_gcd_simple(GEN x, GEN y)
+ int RgXQ_ratlift(GEN y, GEN x, long amax, long bmax, GEN *P, GEN *Q)
+ GEN RgX_resultant_all(GEN P, GEN Q, GEN *sol)
+ long RgX_type(GEN x, GEN *ptp, GEN *ptpol, long *ptpa)
+ void RgX_type_decode(long x, long *t1, long *t2)
+ int RgX_type_is_composite(long t)
+ GEN ZX_content(GEN x)
GEN centermod(GEN x, GEN p)
GEN centermod_i(GEN x, GEN p, GEN ps2)
GEN centermodii(GEN x, GEN p, GEN po2)
GEN content(GEN x)
GEN deg1_from_roots(GEN L, long v)
- GEN discsr(GEN x)
- GEN divide_conquer_prod(GEN x, GEN (*mul)(GEN,GEN))
+ GEN divide_conquer_assoc(GEN x, void *data, GEN (*mul)(void*, GEN, GEN))
+ GEN divide_conquer_prod(GEN x, GEN (*mul)(GEN, GEN))
GEN factor(GEN x)
- GEN factor0(GEN x,long flag)
- GEN factorback(GEN fa,GEN nf)
+ GEN factor0(GEN x, long flag)
+ GEN factorback(GEN fa)
+ GEN factorback2(GEN fa, GEN e)
+ GEN famat_mul_shallow(GEN f, GEN g)
GEN gbezout(GEN x, GEN y, GEN *u, GEN *v)
- GEN ggcd0(GEN x, GEN )
- GEN gdeflate(GEN x, long v, long d)
GEN gdivexact(GEN x, GEN y)
+ GEN gen_factorback(GEN L, GEN e, GEN (*_mul)(void*, GEN, GEN), GEN (*_pow)(void*, GEN, GEN), void *data)
GEN ggcd(GEN x, GEN y)
+ GEN ggcd0(GEN x, GEN y)
GEN ginvmod(GEN x, GEN y)
- GEN gisirreducible(GEN x)
GEN glcm(GEN x, GEN y)
GEN glcm0(GEN x, GEN y)
- GEN gen_pow(GEN,GEN,void*,GEN (*sqr)(void*,GEN),GEN (*mul)(void*,GEN,GEN))
- GEN gen_pow_u(GEN x, ulong n, void *data, GEN (*sqr)(void*,GEN), GEN (*mul)(void*,GEN,GEN))
- long logint(GEN B, GEN y, GEN *ptq)
+ GEN gp_factor0(GEN x, GEN flag)
+ GEN idealfactorback(GEN nf, GEN L, GEN e, int red)
+ long isirreducible(GEN x)
GEN newtonpoly(GEN x, GEN p)
- GEN nfgcd(GEN P, GEN Q, GEN nf, GEN den)
- GEN nfisincl(GEN a, GEN b)
- GEN nfisisom(GEN a, GEN b)
+ GEN nffactorback(GEN nf, GEN L, GEN e)
GEN nfrootsQ(GEN x)
GEN poldisc0(GEN x, long v)
- GEN polfnf(GEN a, GEN t)
- GEN polhensellift(GEN pol, GEN fct, GEN p, long exp)
- GEN polresultant0(GEN x, GEN y,long v,long flag)
+ GEN polresultant0(GEN x, GEN y, long v, long flag)
GEN polsym(GEN x, long n)
GEN primitive_part(GEN x, GEN *c)
GEN primpart(GEN x)
- GEN quadgen(GEN x)
- GEN quadpoly(GEN x)
- GEN quadpoly0(GEN x, long v)
GEN reduceddiscsmith(GEN pol)
GEN resultant2(GEN x, GEN y)
+ GEN resultant_all(GEN u, GEN v, GEN *sol)
+ GEN rnfcharpoly(GEN nf, GEN T, GEN alpha, long v)
GEN roots_from_deg1(GEN x)
- GEN sort_factor(GEN y, int (*cmp)(GEN,GEN))
- GEN sort_factor_gen(GEN y, int (*cmp)(GEN,GEN))
- GEN sort_vecpol(GEN a, int (*cmp)(GEN,GEN))
- GEN srgcd(GEN x, GEN y)
+ GEN roots_to_pol(GEN a, long v)
+ GEN roots_to_pol_r1(GEN a, long v, long r1)
long sturmpart(GEN x, GEN a, GEN b)
GEN subresext(GEN x, GEN y, GEN *U, GEN *V)
- GEN sylvestermatrix(GEN x,GEN y)
- GEN vecbezout(GEN x, GEN y)
- GEN vecbezoutres(GEN x, GEN y)
+ GEN sylvestermatrix(GEN x, GEN y)
+ GEN trivial_fact()
+ GEN gcdext0(GEN x, GEN y)
+ GEN polresultantext0(GEN x, GEN y, long v)
+ GEN polresultantext(GEN x, GEN y)
+ GEN prime_fact(GEN x)
# polarit3.c
- GEN Fp_pows(GEN A, long k, GEN N)
- GEN Fp_powu(GEN x, ulong k, GEN p)
- GEN FpM_red(GEN z, GEN p)
- GEN FpM_to_mod(GEN z, GEN p)
- GEN FpV_polint(GEN xa, GEN ya, GEN p)
- GEN FpV_red(GEN z, GEN p)
- GEN FpV_roots_to_pol(GEN V, GEN p, long v)
- GEN FpV_to_mod(GEN z, GEN p)
- GEN FpX_Fp_add(GEN y,GEN x,GEN p)
- GEN FpX_Fp_mul(GEN y,GEN x,GEN p)
- GEN FpX_add(GEN x,GEN y,GEN p)
- GEN FpX_center(GEN T,GEN mod)
- GEN FpX_chinese_coprime(GEN x,GEN y,GEN Tx,GEN Ty,GEN Tz,GEN p)
- GEN FpX_divrem(GEN x, GEN y, GEN p, GEN *pr)
- GEN FpX_eval(GEN x,GEN y,GEN p)
- GEN FpX_extgcd(GEN x, GEN y, GEN p, GEN *ptu, GEN *ptv)
- GEN FpX_factorff_irred(GEN P, GEN Q, GEN l)
- void FpX_ffintersect(GEN P,GEN Q,long n,GEN l,GEN *SP,GEN *SQ,GEN MA,GEN MB)
- GEN FpX_ffisom(GEN P,GEN Q,GEN l)
- GEN FpX_gcd(GEN x, GEN y, GEN p)
- GEN FpX_mul(GEN x,GEN y,GEN p)
- GEN FpX_neg(GEN x,GEN p)
- GEN FpX_normalize(GEN z, GEN p)
- GEN FpX_red(GEN z, GEN p)
- GEN FpX_sqr(GEN x,GEN p)
- GEN FpX_sub(GEN x,GEN y,GEN p)
- GEN FpX_to_mod(GEN z, GEN p)
- GEN FpXQ_charpoly(GEN x, GEN T, GEN p)
- GEN FpXQ_div(GEN x,GEN y,GEN T,GEN p)
- GEN FpXQ_ffisom_inv(GEN S,GEN Tp, GEN p)
- GEN FpXQ_inv(GEN x,GEN T,GEN p)
- GEN FpXQ_invsafe(GEN x, GEN T, GEN p)
- GEN FpXQ_matrix_pow(long n, long m, GEN y, GEN P, GEN l)
- GEN FpXQ_minpoly(GEN x, GEN T, GEN p)
- GEN FpXQ_mul(GEN y,GEN x,GEN T,GEN p)
- GEN FpXQ_pow(GEN x, GEN n, GEN T, GEN p)
- GEN FpXQ_powers(GEN x, long l, GEN T, GEN p)
- GEN FpXQ_sqr(GEN y, GEN T, GEN p)
- GEN FpXQ_sqrtn(GEN a, GEN n, GEN T, GEN p, GEN *zetan)
- GEN FpXQX_mul(GEN x, GEN y, GEN T, GEN p)
- GEN FpXQX_red(GEN z, GEN T, GEN p)
- GEN FpXQX_sqr(GEN x, GEN T, GEN p)
- GEN FpXQX_extgcd(GEN x, GEN y, GEN T, GEN p, GEN *ptu, GEN *ptv)
- GEN FpXQX_divrem(GEN x, GEN y, GEN T, GEN p, GEN *pr)
- GEN FpXQXV_prod(GEN V, GEN Tp, GEN p)
- GEN FpXV_prod(GEN V, GEN p)
- GEN FpXV_red(GEN z, GEN p)
- GEN FpXX_red(GEN z, GEN p)
- GEN FpX_rescale(GEN P, GEN h, GEN p)
+ GEN Flx_FlxY_resultant(GEN a, GEN b, ulong pp)
+ GEN Flx_factorff_irred(GEN P, GEN Q, ulong p)
+ void Flx_ffintersect(GEN P, GEN Q, long n, ulong l, GEN *SP, GEN *SQ, GEN MA, GEN MB)
+ GEN Flx_ffisom(GEN P, GEN Q, ulong l)
+ GEN Flx_roots_naive(GEN f, ulong p)
+ GEN FlxX_resultant(GEN u, GEN v, ulong p, long sx)
+ GEN Flxq_ffisom_inv(GEN S, GEN Tp, ulong p)
+ GEN FpV_polint(GEN xa, GEN ya, GEN p, long v)
+ GEN FpX_FpXY_resultant(GEN a, GEN b0, GEN p)
+ GEN FpX_factorff_irred(GEN P, GEN Q, GEN p)
+ void FpX_ffintersect(GEN P, GEN Q, long n, GEN l, GEN *SP, GEN *SQ, GEN MA, GEN MB)
+ GEN FpX_ffisom(GEN P, GEN Q, GEN l)
+ GEN FpX_translate(GEN P, GEN c, GEN p)
+ GEN FpXQ_ffisom_inv(GEN S, GEN Tp, GEN p)
+ GEN FpXV_FpC_mul(GEN V, GEN W, GEN p)
+ GEN FpXY_Fq_evaly(GEN Q, GEN y, GEN T, GEN p, long vx)
+ GEN Fq_Fp_mul(GEN x, GEN y, GEN T, GEN p)
+ GEN Fq_add(GEN x, GEN y, GEN T, GEN p)
+ GEN Fq_div(GEN x, GEN y, GEN T, GEN p)
GEN Fq_inv(GEN x, GEN T, GEN p)
GEN Fq_invsafe(GEN x, GEN T, GEN p)
- GEN Fq_add(GEN x, GEN y, GEN T, GEN p)
GEN Fq_mul(GEN x, GEN y, GEN T, GEN p)
+ GEN Fq_mulu(GEN x, ulong y, GEN T, GEN p)
GEN Fq_neg(GEN x, GEN T, GEN p)
GEN Fq_neg_inv(GEN x, GEN T, GEN p)
GEN Fq_pow(GEN x, GEN n, GEN T, GEN p)
- GEN Fq_red(GEN x, GEN T, GEN p)
+ GEN Fq_powu(GEN x, ulong n, GEN pol, GEN p)
GEN Fq_sub(GEN x, GEN y, GEN T, GEN p)
+ GEN Fq_sqr(GEN x, GEN T, GEN p)
+ GEN Fq_sqrt(GEN x, GEN T, GEN p)
+ GEN Fq_sqrtn(GEN x, GEN n, GEN T, GEN p, GEN *zeta)
+ GEN FqC_add(GEN x, GEN y, GEN T, GEN p)
+ GEN FqC_sub(GEN x, GEN y, GEN T, GEN p)
+ GEN FqC_Fq_mul(GEN x, GEN y, GEN T, GEN p)
+ GEN FqC_to_FlxC(GEN v, GEN T, GEN pp)
GEN FqM_to_FlxM(GEN x, GEN T, GEN pp)
GEN FqV_roots_to_pol(GEN V, GEN T, GEN p, long v)
GEN FqV_red(GEN z, GEN T, GEN p)
- GEN FqX_Fq_mul(GEN P, GEN U, GEN T, GEN p)
- GEN FqX_div(GEN x, GEN y, GEN T, GEN p)
- GEN FqX_divrem(GEN x, GEN y, GEN T, GEN p, GEN *z)
+ GEN FqV_to_FlxV(GEN v, GEN T, GEN pp)
+ GEN FqX_Fq_add(GEN y, GEN x, GEN T, GEN p)
+ GEN FqX_Fq_mul_to_monic(GEN P, GEN U, GEN T, GEN p)
+ GEN FqX_eval(GEN x, GEN y, GEN T, GEN p)
GEN FqX_normalize(GEN z, GEN T, GEN p)
- GEN FqX_red(GEN z, GEN T, GEN p)
- GEN FqX_rem(GEN x, GEN y, GEN T, GEN p)
- GEN FqX_mul(GEN x, GEN y, GEN T, GEN p)
- GEN FqX_sqr(GEN x, GEN T, GEN p)
+ GEN FqX_translate(GEN P, GEN c, GEN T, GEN p)
+ GEN FqXQ_powers(GEN x, long l, GEN S, GEN T, GEN p)
+ GEN FqXQ_matrix_pow(GEN y, long n, long m, GEN S, GEN T, GEN p)
+ GEN FqXY_eval(GEN Q, GEN y, GEN x, GEN T, GEN p)
+ GEN FqXY_evalx(GEN Q, GEN x, GEN T, GEN p)
+ GEN QX_disc(GEN x)
+ GEN QX_gcd(GEN a, GEN b)
+ GEN QX_resultant(GEN A, GEN B)
+ GEN QXQ_intnorm(GEN A, GEN B)
GEN QXQ_inv(GEN A, GEN B)
+ GEN QXQ_norm(GEN A, GEN B)
+ int Rg_is_Fp(GEN x, GEN *p)
+ int Rg_is_FpXQ(GEN x, GEN *pT, GEN *pp)
+ GEN Rg_to_Fp(GEN x, GEN p)
+ GEN Rg_to_FpXQ(GEN x, GEN T, GEN p)
+ GEN RgC_to_Flc(GEN x, ulong p)
+ GEN RgC_to_FpC(GEN x, GEN p)
+ int RgM_is_FpM(GEN x, GEN *p)
+ GEN RgM_to_Flm(GEN x, ulong p)
+ GEN RgM_to_FpM(GEN x, GEN p)
+ int RgV_is_FpV(GEN x, GEN *p)
+ GEN RgV_to_FpV(GEN x, GEN p)
+ int RgX_is_FpX(GEN x, GEN *p)
+ GEN RgX_to_FpX(GEN x, GEN p)
+ int RgX_is_FpXQX(GEN x, GEN *pT, GEN *pp)
+ GEN RgX_to_FpXQX(GEN x, GEN T, GEN p)
+ GEN RgX_to_FqX(GEN x, GEN T, GEN p)
+ GEN ZX_ZXY_rnfequation(GEN A, GEN B, long *Lambda)
+ GEN ZXQ_charpoly(GEN A, GEN T, long v)
GEN ZX_disc(GEN x)
int ZX_is_squarefree(GEN x)
+ GEN ZX_gcd(GEN A, GEN B)
+ GEN ZX_gcd_all(GEN A, GEN B, GEN *Anew)
GEN ZX_resultant(GEN A, GEN B)
- long brent_kung_optpow(long d, long n)
+ int Z_incremental_CRT(GEN *H, ulong Hp, GEN *q, ulong p)
+ GEN Z_init_CRT(ulong Hp, ulong p)
+ int ZM_incremental_CRT(GEN *H, GEN Hp, GEN *q, ulong p)
+ GEN ZM_init_CRT(GEN Hp, ulong p)
+ int ZX_incremental_CRT(GEN *ptH, GEN Hp, GEN *q, ulong p)
+ GEN ZX_init_CRT(GEN Hp, ulong p, long v)
+ GEN characteristic(GEN x)
GEN ffinit(GEN p, long n, long v)
+ GEN ffnbirred(GEN p, long n)
+ GEN ffnbirred0(GEN p, long n, long flag)
+ GEN ffsumnbirred(GEN p, long n)
+ bb_field *get_Fq_field(void **E, GEN T, GEN p)
+ GEN init_Fq(GEN p, long n, long v)
+ GEN pol_x_powers(long N, long v)
+ GEN residual_characteristic(GEN x)
+
+ # prime.c
+
+ long BPSW_isprime(GEN x)
+ long BPSW_psp(GEN N)
+ GEN addprimes(GEN primes)
+ GEN gisprime(GEN x, long flag)
+ GEN gispseudoprime(GEN x, long flag)
+ GEN gprimepi_upper_bound(GEN x)
+ GEN gprimepi_lower_bound(GEN x)
+ long isprime(GEN x)
+ long ispseudoprime(GEN x, long flag)
+ long millerrabin(GEN n, long k)
+ GEN prime(long n)
+ GEN primepi(GEN x)
+ double primepi_upper_bound(double x)
+ double primepi_lower_bound(double x)
+ GEN primes(long n)
+ GEN primes_interval(GEN a, GEN b)
+ GEN primes_interval_zv(ulong a, ulong b)
+ GEN primes_upto_zv(ulong b)
+ GEN primes0(GEN n)
+ GEN primes_zv(long m)
+ GEN randomprime(GEN N)
+ GEN removeprimes(GEN primes)
+ int uislucaspsp(ulong n)
+ int uisprime(ulong n)
+ ulong uprime(long n)
+ ulong uprimepi(ulong n)
- # RgX.c
+ # qfisom.c
- int RgX_is_rational(GEN x)
- GEN RgM_to_RgXV(GEN x, long v)
- GEN RgM_to_RgXX(GEN x, long v,long w)
- GEN RgM_zc_mul(GEN x, GEN y)
- GEN RgM_zm_mul(GEN x, GEN y)
- GEN RgV_to_RgX(GEN x, long v)
- GEN RgV_zc_mul(GEN x, GEN y)
- GEN RgV_zm_mul(GEN x, GEN y)
- GEN RgX_divrem(GEN x,GEN y,GEN *r)
- GEN RgX_mul(GEN x,GEN y)
- GEN RgX_mulspec(GEN a, GEN b, long na, long nb)
- GEN RgXQX_divrem(GEN x,GEN y,GEN T,GEN *r)
- GEN RgXQX_mul(GEN x,GEN y,GEN T)
- GEN RgXQX_red(GEN P, GEN T)
- GEN RgXQX_RgXQ_mul(GEN x, GEN y, GEN T)
- GEN RgX_Rg_mul(GEN y, GEN x)
- GEN RgX_shift(GEN x, long n)
- GEN RgX_sqr(GEN x)
- GEN RgX_sqrspec(GEN a, long na)
- GEN RgXV_to_RgM(GEN v, long n)
- GEN RgX_to_RgV(GEN x, long N)
- GEN RgXX_to_RgM(GEN v, long n)
- GEN RgXY_swap(GEN x, long n, long w)
+ GEN qfauto(GEN g, GEN flags)
+ GEN qfauto0(GEN g, GEN flags)
+ GEN qfautoexport(GEN g, long flag)
+ GEN qfisom(GEN g, GEN h, GEN flags)
+ GEN qfisom0(GEN g, GEN h, GEN flags)
+ GEN qfisominit(GEN g, GEN flags)
+ GEN qfisominit0(GEN g, GEN flags)
+
+ # random.c
+
+ GEN genrand(GEN N)
+ GEN getrand()
+ ulong pari_rand()
+ GEN randomi(GEN x)
+ GEN randomr(long prec)
+ ulong random_Fl(ulong n)
+ void setrand(GEN seed)
# rootpol.c
- GEN cleanroots(GEN x,long l)
+ GEN QX_complex_roots(GEN p, long l)
+ GEN ZX_graeffe(GEN p)
+ GEN cleanroots(GEN x, long l)
int isrealappr(GEN x, long l)
- GEN roots(GEN x,long l)
- GEN roots0(GEN x,long flag,long l)
+ GEN polgraeffe(GEN p)
+ GEN polmod_to_embed(GEN x, long prec)
+ GEN roots(GEN x, long l)
# subcyclo.c
+ GEN factor_Aurifeuille(GEN p, long n)
+ GEN factor_Aurifeuille_prime(GEN p, long n)
GEN galoissubcyclo(GEN N, GEN sg, long flag, long v)
GEN polsubcyclo(long n, long d, long v)
- GEN znstar_small(GEN zn)
# subfield.c
@@ -1792,7 +3546,7 @@ cdef extern from 'pari/pari.h':
# subgroup.c
GEN subgrouplist(GEN cyc, GEN bound)
- void traversesubgroups(GEN cyc, GEN B, void fun(GEN,void*), void *E)
+ void forsubgroup(void *E, long fun(void*, GEN), GEN cyc, GEN B)
# stark.c
@@ -1802,23 +3556,34 @@ cdef extern from 'pari/pari.h':
# sumiter.c
- GEN derivnum(void *E, GEN (*eval)(GEN,void*), GEN x, long prec)
- GEN direuler(void *E, GEN (*eval)(GEN,void*), GEN ga, GEN gb, GEN c)
- GEN forvec_start(GEN x, long flag, GEN *d, GEN (**next)(GEN,GEN))
+ GEN derivnum(void *E, GEN (*eval)(void *, GEN), GEN x, long prec)
+ GEN derivfun(void *E, GEN (*eval)(void *, GEN), GEN x, long prec)
+ GEN direuler(void *E, GEN (*eval)(void *, GEN), GEN ga, GEN gb, GEN c)
+ int forcomposite_init(forcomposite_t *C, GEN a, GEN b)
+ GEN forcomposite_next(forcomposite_t *C)
+ GEN forprime_next(forprime_t *T)
+ int forprime_init(forprime_t *T, GEN a, GEN b)
+ int forvec_init(forvec_t *T, GEN x, long flag)
+ GEN forvec_next(forvec_t *T)
GEN polzag(long n, long m)
- GEN prodeuler(void *E, GEN (*eval)(GEN,void*), GEN ga, GEN gb, long prec)
- GEN prodinf(void *E, GEN (*eval)(GEN,void*), GEN a, long prec)
- GEN prodinf1(void *E, GEN (*eval)(GEN,void*), GEN a, long prec)
- GEN sumalt(void *E, GEN (*eval)(GEN,void*), GEN a, long prec)
- GEN sumalt2(void *E, GEN (*eval)(GEN,void*), GEN a, long prec)
- GEN sumpos(void *E, GEN (*eval)(GEN,void*), GEN a, long prec)
- GEN sumpos2(void *E, GEN (*eval)(GEN,void*), GEN a, long prec)
- GEN suminf(void *E, GEN (*eval)(GEN,void*), GEN a, long prec)
- GEN zbrent(void *E, GEN (*eval)(GEN,void*), GEN a, GEN b, long prec)
+ GEN prodeuler(void *E, GEN (*eval)(void *, GEN), GEN ga, GEN gb, long prec)
+ GEN prodinf(void *E, GEN (*eval)(void *, GEN), GEN a, long prec)
+ GEN prodinf1(void *E, GEN (*eval)(void *, GEN), GEN a, long prec)
+ GEN sumalt(void *E, GEN (*eval)(void *, GEN), GEN a, long prec)
+ GEN sumalt2(void *E, GEN (*eval)(void *, GEN), GEN a, long prec)
+ GEN sumpos(void *E, GEN (*eval)(void *, GEN), GEN a, long prec)
+ GEN sumpos2(void *E, GEN (*eval)(void *, GEN), GEN a, long prec)
+ GEN suminf(void *E, GEN (*eval)(void *, GEN), GEN a, long prec)
+ ulong u_forprime_next(forprime_t *T)
+ int u_forprime_init(forprime_t *T, ulong a, ulong b)
+ void u_forprime_restrict(forprime_t *T, ulong c)
+ int u_forprime_arith_init(forprime_t *T, ulong a, ulong b, ulong c, ulong q)
+ GEN zbrent(void *E, GEN (*eval)(void *, GEN), GEN a, GEN b, long prec)
# thue.c
GEN bnfisintnorm(GEN x, GEN y)
+ GEN bnfisintnormabs(GEN bnf, GEN a)
GEN thue(GEN thueres, GEN rhs, GEN ne)
GEN thueinit(GEN pol, long flag, long prec)
@@ -1827,14 +3592,26 @@ cdef extern from 'pari/pari.h':
GEN Pi2n(long n, long prec)
GEN PiI2(long prec)
GEN PiI2n(long n, long prec)
+ GEN Qp_exp(GEN x)
+ GEN Qp_log(GEN x)
+ GEN Qp_sqrt(GEN x)
+ GEN Qp_sqrtn(GEN x, GEN n, GEN *zetan)
+ long Zn_ispower(GEN a, GEN q, GEN K, GEN *pt)
long Zn_issquare(GEN x, GEN n)
GEN Zn_sqrt(GEN x, GEN n)
- void consteuler(long prec)
- void constpi(long prec)
- GEN exp_Ir(GEN x)
+ GEN Zp_teichmuller(GEN x, GEN p, long n, GEN q)
+ GEN agm(GEN x, GEN y, long prec)
+ GEN constcatalan(long prec)
+ GEN consteuler(long prec)
+ GEN constlog2(long prec)
+ GEN constpi(long prec)
+ GEN cxexpm1(GEN z, long prec)
+ GEN expIr(GEN x)
+ GEN exp1r_abs(GEN x)
GEN gcos(GEN x, long prec)
GEN gcotan(GEN x, long prec)
GEN gexp(GEN x, long prec)
+ GEN gexpm1(GEN x, long prec)
GEN glog(GEN x, long prec)
GEN gpow(GEN x, GEN n, long prec)
GEN gpowgs(GEN x, long n)
@@ -1843,72 +3620,100 @@ cdef extern from 'pari/pari.h':
GEN gsqrt(GEN x, long prec)
GEN gsqrtn(GEN x, GEN n, GEN *zetan, long prec)
GEN gtan(GEN x, long prec)
+ GEN logr_abs(GEN x)
GEN mpcos(GEN x)
GEN mpeuler(long prec)
+ GEN mpcatalan(long prec)
+ void mpsincosm1(GEN x, GEN *s, GEN *c)
GEN mpexp(GEN x)
- GEN mpexp1(GEN x)
+ GEN mpexpm1(GEN x)
GEN mplog(GEN x)
GEN mplog2(long prec)
GEN mppi(long prec)
GEN mpsin(GEN x)
void mpsincos(GEN x, GEN *s, GEN *c)
+ GEN powis(GEN x, long n)
+ GEN powiu(GEN p, ulong k)
+ GEN powrfrac(GEN x, long n, long d)
+ GEN powrs(GEN x, long n)
+ GEN powrshalf(GEN x, long s)
+ GEN powru(GEN x, ulong n)
+ GEN powruhalf(GEN x, ulong s)
+ GEN powuu(ulong p, ulong k)
GEN powgi(GEN x, GEN n)
+ GEN serchop0(GEN s)
+ GEN sqrtnint(GEN a, long n)
GEN teich(GEN x)
+ GEN trans_eval(const char *fun, GEN (*f) (GEN, long), GEN x, long prec)
+ ulong upowuu(ulong p, ulong k)
+ ulong usqrtn(ulong a, ulong n)
+ ulong usqrt(ulong a)
# trans2.c
+ GEN Qp_gamma(GEN x)
GEN bernfrac(long n)
+ GEN bernpol(long k, long v)
GEN bernreal(long n, long prec)
- GEN bernvec(long nomb)
- GEN gach(GEN x, long prec)
+ GEN gacosh(GEN x, long prec)
GEN gacos(GEN x, long prec)
GEN garg(GEN x, long prec)
- GEN gash(GEN x, long prec)
+ GEN gasinh(GEN x, long prec)
GEN gasin(GEN x, long prec)
GEN gatan(GEN x, long prec)
- GEN gath(GEN x, long prec)
- GEN gch(GEN x, long prec)
- GEN ggamd(GEN x, long prec)
+ GEN gatanh(GEN x, long prec)
+ GEN gcosh(GEN x, long prec)
+ GEN ggammah(GEN x, long prec)
GEN ggamma(GEN x, long prec)
GEN glngamma(GEN x, long prec)
GEN gpsi(GEN x, long prec)
- GEN gsh(GEN x, long prec)
- GEN gth(GEN x, long prec)
+ GEN gsinh(GEN x, long prec)
+ GEN gtanh(GEN x, long prec)
void mpbern(long nomb, long prec)
+ GEN mpfactr(long n, long prec)
+ GEN sumformal(GEN T, long v)
# trans3.c
- GEN agm(GEN x, GEN y, long prec)
GEN dilog(GEN x, long prec)
GEN eint1(GEN x, long prec)
GEN eta(GEN x, long prec)
- GEN eta0(GEN x, long flag,long prec)
+ GEN eta0(GEN x, long flag, long prec)
GEN gerfc(GEN x, long prec)
GEN gpolylog(long m, GEN x, long prec)
GEN gzeta(GEN x, long prec)
GEN hyperu(GEN a, GEN b, GEN gx, long prec)
GEN incgam(GEN a, GEN x, long prec)
- GEN incgam0(GEN a, GEN x, GEN z,long prec)
+ GEN incgam0(GEN a, GEN x, GEN z, long prec)
GEN incgamc(GEN a, GEN x, long prec)
GEN hbessel1(GEN n, GEN z, long prec)
GEN hbessel2(GEN n, GEN z, long prec)
GEN ibessel(GEN n, GEN z, long prec)
GEN jbessel(GEN n, GEN z, long prec)
GEN jbesselh(GEN n, GEN z, long prec)
+ GEN mpeint1(GEN x, GEN expx)
+ GEN mplambertW(GEN y)
+ GEN mpveceint1(GEN C, GEN eC, long n)
+ GEN powruvec(GEN e, ulong n)
GEN nbessel(GEN n, GEN z, long prec)
GEN jell(GEN x, long prec)
GEN kbessel(GEN nu, GEN gx, long prec)
- GEN polylog(long m, GEN x, long prec)
GEN polylog0(long m, GEN x, long flag, long prec)
+ GEN sumdedekind_coprime(GEN h, GEN k)
+ GEN sumdedekind(GEN h, GEN k)
GEN szeta(long x, long prec)
GEN theta(GEN q, GEN z, long prec)
GEN thetanullk(GEN q, long k, long prec)
GEN trueeta(GEN x, long prec)
- GEN veceint1(GEN C, GEN nmax, long prec)
+ GEN u_sumdedekind_coprime(long h, long k)
+ GEN veceint1(GEN nmax, GEN C, long prec)
GEN vecthetanullk(GEN q, long k, long prec)
- GEN weber0(GEN x, long flag,long prec)
+ GEN vecthetanullk_tau(GEN tau, long k, long prec)
+ GEN weber0(GEN x, long flag, long prec)
GEN weberf(GEN x, long prec)
+ GEN weberf1(GEN x, long prec)
GEN weberf2(GEN x, long prec)
+ GEN glambertW(GEN y, long prec)
# gmp/int.h
long* int_MSW(GEN x)
@@ -1916,8 +3721,15 @@ cdef extern from 'pari/pari.h':
long* int_precW(long * xp)
long* int_nextW(long * xp)
- # misc...
- extern char* diffptr
+ # paristio.h
+
+ struct PariOUT:
+ void (*putch)(char)
+ void (*puts)(char*)
+ void (*flush)()
+ extern PariOUT* pariOut
+ extern PariOUT* pariErr
+ extern byteptr diffptr
cdef extern from 'stdsage.h':
GEN set_gel(GEN x, long n, GEN z) # gel(x,n) = z
@@ -1929,15 +3741,6 @@ cdef extern from 'stdsage.h':
include 'declinl.pxi'
-cdef extern from *: # paristio.h
- struct PariOUT:
- void (*putch)(char)
- void (*puts)(char*)
- void (*flush)()
- extern PariOUT* pariOut
- extern PariOUT* pariErr
-
-
cdef extern from 'pari/paripriv.h':
int gpd_QUIET, gpd_TEST, gpd_EMACS, gpd_TEXMACS
diff --git a/src/sage/libs/pari/gen.pyx b/src/sage/libs/pari/gen.pyx
index 71b3f14..981bd1f 100644
--- a/src/sage/libs/pari/gen.pyx
+++ b/src/sage/libs/pari/gen.pyx
@@ -23,6 +23,8 @@ AUTHORS:
- Peter Bruin (2013-11-17): move PariInstance to a separate file
(#15185)
+ - Jeroen Demeyer (2014-02-09): upgrade to PARI 2.7 (#15767)
+
"""
#*****************************************************************************
@@ -332,7 +334,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: K.getattr("reg")
Traceback (most recent call last):
...
- PariError: _.reg: incorrect type in reg
+ PariError: _.reg: incorrect type in reg (t_VEC)
sage: K.getattr("zzz")
Traceback (most recent call last):
...
@@ -385,14 +387,15 @@ cdef class gen(sage.structure.element.RingElement):
sage: bnr.nf_get_pol()
x^4 - 4*x^2 + 1
- For relative extensions, this returns the absolute polynomial,
- not the relative one::
+ For relative number fields, this returns the relative
+ polynomial. However, beware that ``pari(L)`` returns an absolute
+ number field::
sage: L.<b> = K.extension(x^2 - 5)
- sage: pari(L).nf_get_pol() # Absolute polynomial
+ sage: pari(L).nf_get_pol() # Absolute
y^8 - 28*y^6 + 208*y^4 - 408*y^2 + 36
- sage: L.pari_rnf().nf_get_pol()
- x^8 - 28*x^6 + 208*x^4 - 408*x^2 + 36
+ sage: L.pari_rnf().nf_get_pol() # Relative
+ x^2 - 5
TESTS::
@@ -408,7 +411,8 @@ cdef class gen(sage.structure.element.RingElement):
sage: pari("[0]").nf_get_pol()
Traceback (most recent call last):
...
- PariError: incorrect type in pol
+ PariError: incorrect type in pol (t_VEC)
+
"""
pari_catch_sig_on()
return P.new_gen(member_pol(self.g))
@@ -555,7 +559,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: K.<i> = QuadraticField(-1)
sage: F = pari(K).idealfactor(K.ideal(5)); F
- [[5, [-2, 1]~, 1, 1, [2, 1]~], 1; [5, [2, 1]~, 1, 1, [-2, 1]~], 1]
+ [[5, [-2, 1]~, 1, 1, [2, -1; 1, 2]], 1; [5, [2, 1]~, 1, 1, [-2, -1; 1, -2]], 1]
sage: F[0,0].pr_get_p()
5
"""
@@ -1152,9 +1156,11 @@ cdef class gen(sage.structure.element.RingElement):
-36bb1e3929d1a8fe2802f083
"""
cdef GEN x
- cdef long lx, *xp
+ cdef long lx
+ cdef long *xp
cdef long w
- cdef char *s, *sp
+ cdef char *s
+ cdef char *sp
cdef char *hexdigits
hexdigits = "0123456789abcdef"
cdef int i, j
@@ -1379,7 +1385,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: complex(g)
Traceback (most recent call last):
...
- PariError: incorrect type in greal/gimag
+ PariError: incorrect type in greal/gimag (t_INTMOD)
"""
cdef double re, im
pari_catch_sig_on()
@@ -1735,7 +1741,9 @@ cdef class gen(sage.structure.element.RingElement):
moebius(x): Moebius function of x.
"""
pari_catch_sig_on()
- return P.new_gen(gmoebius(x.g))
+ r = moebius(x.g)
+ pari_catch_sig_off()
+ return r
def sign(gen x):
"""
@@ -1757,7 +1765,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: pari(I).sign()
Traceback (most recent call last):
...
- PariError: incorrect type in gsigne
+ PariError: incorrect type in gsigne (t_COMPLEX)
"""
pari_catch_sig_on()
@@ -2055,7 +2063,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: pari('x+y').Pol('y')
Traceback (most recent call last):
...
- PariError: variable must have higher priority in gtopoly
+ PariError: incorrect priority in gtopoly: variable x < y
INPUT:
@@ -2174,7 +2182,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: pari(3).Qfb(7, 2) # discriminant is 25
Traceback (most recent call last):
...
- PariError: square discriminant in Qfb
+ PariError: domain error in Qfb: issquare(disc) = 1
"""
cdef gen t0 = objtogen(b)
cdef gen t1 = objtogen(c)
@@ -2281,17 +2289,17 @@ cdef class gen(sage.structure.element.RingElement):
EXAMPLES::
sage: pari([1,5,2]).Set()
- ["1", "2", "5"]
+ [1, 2, 5]
sage: pari([]).Set() # the empty set
[]
sage: pari([1,1,-1,-1,3,3]).Set()
- ["-1", "1", "3"]
+ [-1, 1, 3]
sage: pari(1).Set()
- ["1"]
+ [1]
sage: pari('1/(x*y)').Set()
- ["1/(y*x)"]
+ [1/(y*x)]
sage: pari('["bc","ab","bc"]').Set()
- ["\"ab\"", "\"bc\""]
+ ["ab", "bc"]
"""
pari_catch_sig_on()
return P.new_gen(gtoset(x.g))
@@ -2557,9 +2565,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: pari(1234).Vecsmall()
Vecsmall([1234])
sage: pari('x^2 + 2*x + 3').Vecsmall()
- Traceback (most recent call last):
- ...
- PariError: incorrect type in vectosmall
+ Vecsmall([1, 2, 3])
We demonstate the `n` argument::
@@ -2595,7 +2601,7 @@ cdef class gen(sage.structure.element.RingElement):
EXAMPLES::
sage: pari(0).binary()
- [0]
+ []
sage: pari(-5).binary()
[1, 0, 1]
sage: pari(5).binary()
@@ -2967,7 +2973,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: pari('x').component(0)
Traceback (most recent call last):
...
- PariError: nonexistent component
+ PariError: non-existent component: index < 1
"""
pari_catch_sig_on()
return P.new_gen(compo(x.g, n))
@@ -2999,7 +3005,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: pari('Mod(x,x^3-3)').conj()
Traceback (most recent call last):
...
- PariError: incorrect type in gconj
+ PariError: incorrect type in gconj (t_POLMOD)
"""
pari_catch_sig_on()
return P.new_gen(gconj(x.g))
@@ -3023,7 +3029,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: pari('Mod(1+x,x^2-2)').conjvec()
[-0.414213562373095, 2.41421356237310]~
sage: pari('Mod(x,x^3-3)').conjvec()
- [1.44224957030741, -0.721124785153704 + 1.24902476648341*I, -0.721124785153704 - 1.24902476648341*I]~
+ [1.44224957030741, -0.721124785153704 - 1.24902476648341*I, -0.721124785153704 + 1.24902476648341*I]~
sage: pari('Mod(1+x,x^2-2)').conjvec(precision=192)[0].sage()
-0.414213562373095048801688724209698078569671875376948073177
"""
@@ -3098,7 +3104,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: pari('"hello world"').floor()
Traceback (most recent call last):
...
- PariError: incorrect type in gfloor
+ PariError: incorrect type in gfloor (t_STR)
"""
pari_catch_sig_on()
return P.new_gen(gfloor(x.g))
@@ -3124,7 +3130,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: pari('sqrt(-2)').frac()
Traceback (most recent call last):
...
- PariError: incorrect type in gfloor
+ PariError: incorrect type in gfloor (t_COMPLEX)
"""
pari_catch_sig_on()
return P.new_gen(gfrac(x.g))
@@ -3281,7 +3287,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: y.padicprec(17)
Traceback (most recent call last):
...
- PariError: not the same prime in padicprec
+ PariError: inconsistent moduli in padicprec: 11 != 17
This works for polynomials too::
@@ -3740,7 +3746,7 @@ cdef class gen(sage.structure.element.RingElement):
"""
cdef gen t0 = objtogen(p)
pari_catch_sig_on()
- v = ggval(x.g, t0.g)
+ v = gvaluation(x.g, t0.g)
pari_catch_sig_off()
return v
@@ -3881,7 +3887,7 @@ cdef class gen(sage.structure.element.RingElement):
0.881373587019543 + 1.57079632679490*I
"""
pari_catch_sig_on()
- return P.new_gen(gach(x.g, prec_bits_to_words(precision)))
+ return P.new_gen(gacosh(x.g, prec_bits_to_words(precision)))
def agm(gen x, y, unsigned long precision=0):
r"""
@@ -3972,7 +3978,7 @@ cdef class gen(sage.structure.element.RingElement):
1.52857091948100 + 0.427078586392476*I
"""
pari_catch_sig_on()
- return P.new_gen(gash(x.g, prec_bits_to_words(precision)))
+ return P.new_gen(gasinh(x.g, prec_bits_to_words(precision)))
def atan(gen x, unsigned long precision=0):
r"""
@@ -4015,7 +4021,7 @@ cdef class gen(sage.structure.element.RingElement):
0.549306144334055 - 1.57079632679490*I
"""
pari_catch_sig_on()
- return P.new_gen(gath(x.g, prec_bits_to_words(precision)))
+ return P.new_gen(gatanh(x.g, prec_bits_to_words(precision)))
def bernfrac(gen x):
r"""
@@ -4064,10 +4070,14 @@ cdef class gen(sage.structure.element.RingElement):
EXAMPLES::
sage: pari(8).bernvec()
+ doctest:...: DeprecationWarning: bernvec() is deprecated, use repeated calls to bernfrac() instead
+ See http://trac.sagemath.org/15767 for details.
[1, 1/6, -1/30, 1/42, -1/30, 5/66, -691/2730, 7/6, -3617/510]
sage: [pari(2*n).bernfrac() for n in range(9)]
[1, 1/6, -1/30, 1/42, -1/30, 5/66, -691/2730, 7/6, -3617/510]
"""
+ from sage.misc.superseded import deprecation
+ deprecation(15767, 'bernvec() is deprecated, use repeated calls to bernfrac() instead')
pari_catch_sig_on()
return P.new_gen(bernvec(x))
@@ -4152,8 +4162,7 @@ cdef class gen(sage.structure.element.RingElement):
EXAMPLES::
sage: pari(2).besseljh(3)
- 0.4127100324 # 32-bit
- 0.412710032209716 # 64-bit
+ 0.412710032209716
"""
cdef gen t0 = objtogen(x)
pari_catch_sig_on()
@@ -4291,7 +4300,7 @@ cdef class gen(sage.structure.element.RingElement):
1 + 1/2*x^2 + 1/24*x^4 + 1/720*x^6 + O(x^8)
"""
pari_catch_sig_on()
- return P.new_gen(gch(x.g, prec_bits_to_words(precision)))
+ return P.new_gen(gcosh(x.g, prec_bits_to_words(precision)))
def cotan(gen x, unsigned long precision=0):
"""
@@ -4470,7 +4479,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: pari(-1).gamma()
Traceback (most recent call last):
...
- PariError: non-positive integer argument in ggamma
+ PariError: domain error in gamma: argument = non-positive integer
"""
pari_catch_sig_on()
return P.new_gen(ggamma(s.g, prec_bits_to_words(precision)))
@@ -4495,7 +4504,7 @@ cdef class gen(sage.structure.element.RingElement):
0.575315188063452 + 0.0882106775440939*I
"""
pari_catch_sig_on()
- return P.new_gen(ggamd(s.g, prec_bits_to_words(precision)))
+ return P.new_gen(ggammah(s.g, prec_bits_to_words(precision)))
def hyperu(gen a, b, x, unsigned long precision=0):
r"""
@@ -4614,19 +4623,13 @@ cdef class gen(sage.structure.element.RingElement):
def lngamma(gen x, unsigned long precision=0):
r"""
- This method is deprecated, please use :meth:`.log_gamma` instead.
-
- See the :meth:`.log_gamma` method for documentation and examples.
+ Alias for :meth:`log_gamma`.
EXAMPLES::
sage: pari(100).lngamma()
- doctest:...: DeprecationWarning: The method lngamma() is deprecated. Use log_gamma() instead.
- See http://trac.sagemath.org/6992 for details.
359.134205369575
"""
- from sage.misc.superseded import deprecation
- deprecation(6992, "The method lngamma() is deprecated. Use log_gamma() instead.")
return x.log_gamma(precision)
def log_gamma(gen x, unsigned long precision=0):
@@ -4741,7 +4744,7 @@ cdef class gen(sage.structure.element.RingElement):
0.634963914784736 + 1.29845758141598*I
"""
pari_catch_sig_on()
- return P.new_gen(gsh(x.g, prec_bits_to_words(precision)))
+ return P.new_gen(gsinh(x.g, prec_bits_to_words(precision)))
def sqr(gen x):
"""
@@ -4834,11 +4837,11 @@ cdef class gen(sage.structure.element.RingElement):
sage: s^5
2.00000000000000
sage: z^5
- 1.00000000000000 + 5.42101086 E-19*I # 32-bit
- 1.00000000000000 + 5.96311194867027 E-19*I # 64-bit
+ 1.00000000000000 - 2.710505431 E-20*I # 32-bit
+ 1.00000000000000 - 2.71050543121376 E-20*I # 64-bit
sage: (s*z)^5
- 2.00000000000000 + 1.409462824 E-18*I # 32-bit
- 2.00000000000000 + 9.21571846612679 E-19*I # 64-bit
+ 2.00000000000000 + 0.E-19*I # 32-bit
+ 2.00000000000000 - 1.08420217248550 E-19*I # 64-bit
"""
# TODO: ??? lots of good examples in the PARI docs ???
cdef GEN zetan
@@ -4890,7 +4893,7 @@ cdef class gen(sage.structure.element.RingElement):
1.55740772465490
"""
pari_catch_sig_on()
- return P.new_gen(gth(x.g, prec_bits_to_words(precision)))
+ return P.new_gen(gtanh(x.g, prec_bits_to_words(precision)))
def teichmuller(gen x):
r"""
@@ -4964,8 +4967,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: C.<i> = ComplexField()
sage: pari(i).weber()
- 1.18920711500272 + 0.E-19*I # 32-bit
- 1.18920711500272 + 2.71050543121376 E-20*I # 64-bit
+ 1.18920711500272
sage: pari(i).weber(1)
1.09050773266526
sage: pari(i).weber(2)
@@ -5246,17 +5248,19 @@ cdef class gen(sage.structure.element.RingElement):
4
"""
pari_catch_sig_on()
- return P.new_gen(gnumbdiv(n.g))
+ return P.new_gen(numdiv(n.g))
def phi(gen n):
"""
- Return the Euler phi function of n. EXAMPLES::
+ Return the Euler phi function of n.
+
+ EXAMPLES::
sage: pari(10).phi()
4
"""
pari_catch_sig_on()
- return P.new_gen(geulerphi(n.g))
+ return P.new_gen(eulerphi(n.g))
def primepi(gen self):
"""
@@ -5390,11 +5394,9 @@ cdef class gen(sage.structure.element.RingElement):
INPUT:
- - ``self`` - a list of 5 coefficients
+ - ``self`` -- a list of 5 coefficients
- - ``flag (optional, default: 0)`` - if 0, ask for a PARI ell
- structure with 19 components; if 1, ask for a shorted PARI
- sell structure with only the first 13 components.
+ - ``flag`` -- ignored (for backwards compatibility)
- ``precision (optional, default: 0)`` - the real
precision to be used in the computation of the components of the
@@ -5412,80 +5414,62 @@ cdef class gen(sage.structure.element.RingElement):
OUTPUT:
+ - ``gen`` - a PARI ell structure.
- - ``gen`` - either a PARI ell structure with 19 components
- (if flag=0), or a PARI sell structure with 13 components
- (if flag=1).
-
-
- EXAMPLES: An elliptic curve with integer coefficients::
+ EXAMPLES:
+
+ An elliptic curve with integer coefficients::
sage: e = pari([0,1,0,1,0]).ellinit(); e
- [0, 1, 0, 1, 0, 4, 2, 0, -1, -32, 224, -48, 2048/3, [0.E-28, -0.500000000000000 - 0.866025403784439*I, -0.500000000000000 + 0.866025403784439*I]~, 3.37150070962519, -1.68575035481260 - 2.15651564749964*I, 1.37451455785745 - 1.084202173 E-19*I, -0.687257278928726 + 0.984434956803824*I, 7.27069403586288] # 32-bit
- [0, 1, 0, 1, 0, 4, 2, 0, -1, -32, 224, -48, 2048/3, [0.E-38, -0.500000000000000 - 0.866025403784439*I, -0.500000000000000 + 0.866025403784439*I]~, 3.37150070962519, -1.68575035481260 - 2.15651564749964*I, 1.37451455785745 - 5.42101086242752 E-19*I, -0.687257278928726 + 0.984434956803824*I, 7.27069403586288] # 64-bit
-
- Its inexact components have the default precision of 53 bits::
-
- sage: RR(e[14])
- 3.37150070962519
-
- We can compute this to higher precision::
-
- sage: R = RealField(150)
- sage: e = pari([0,1,0,1,0]).ellinit(precision=150)
- sage: R(e[14])
- 3.3715007096251920857424073155981539790016018
-
- Using flag=1 returns a short elliptic curve PARI object::
-
- sage: pari([0,1,0,1,0]).ellinit(flag=1)
- [0, 1, 0, 1, 0, 4, 2, 0, -1, -32, 224, -48, 2048/3]
+ [0, 1, 0, 1, 0, 4, 2, 0, -1, -32, 224, -48, 2048/3, Vecsmall([1]), [Vecsmall([64, -1])], [0, 0, 0, 0, 0, 0, 0, 0]]
The coefficients can be any ring elements that convert to PARI::
- sage: pari([0,1/2,0,-3/4,0]).ellinit(flag=1)
- [0, 1/2, 0, -3/4, 0, 2, -3/2, 0, -9/16, 40, -116, 117/4, 256000/117]
- sage: pari([0,0.5,0,-0.75,0]).ellinit(flag=1)
- [0, 0.500000000000000, 0, -0.750000000000000, 0, 2.00000000000000, -1.50000000000000, 0, -0.562500000000000, 40.0000000000000, -116.000000000000, 29.2500000000000, 2188.03418803419]
- sage: pari([0,I,0,1,0]).ellinit(flag=1)
- [0, I, 0, 1, 0, 4*I, 2, 0, -1, -64, 352*I, -80, 16384/5]
- sage: pari([0,x,0,2*x,1]).ellinit(flag=1)
- [0, x, 0, 2*x, 1, 4*x, 4*x, 4, -4*x^2 + 4*x, 16*x^2 - 96*x, -64*x^3 + 576*x^2 - 864, 64*x^4 - 576*x^3 + 576*x^2 - 432, (256*x^6 - 4608*x^5 + 27648*x^4 - 55296*x^3)/(4*x^4 - 36*x^3 + 36*x^2 - 27)]
+ sage: pari([0,1/2,0,-3/4,0]).ellinit()
+ [0, 1/2, 0, -3/4, 0, 2, -3/2, 0, -9/16, 40, -116, 117/4, 256000/117, Vecsmall([1]), [Vecsmall([64, 1])], [0, 0, 0, 0, 0, 0, 0, 0]]
+ sage: pari([0,0.5,0,-0.75,0]).ellinit()
+ [0, 0.500000000000000, 0, -0.750000000000000, 0, 2.00000000000000, -1.50000000000000, 0, -0.562500000000000, 40.0000000000000, -116.000000000000, 29.2500000000000, 2188.03418803419, Vecsmall([0]), [Vecsmall([64, 1])], [0, 0, 0, 0]]
+ sage: pari([0,I,0,1,0]).ellinit()
+ [0, I, 0, 1, 0, 4*I, 2, 0, -1, -64, 352*I, -80, 16384/5, Vecsmall([0]), [Vecsmall([64, 0])], [0, 0, 0, 0]]
+ sage: pari([0,x,0,2*x,1]).ellinit()
+ [0, x, 0, 2*x, 1, 4*x, 4*x, 4, -4*x^2 + 4*x, 16*x^2 - 96*x, -64*x^3 + 576*x^2 - 864, 64*x^4 - 576*x^3 + 576*x^2 - 432, (256*x^6 - 4608*x^5 + 27648*x^4 - 55296*x^3)/(4*x^4 - 36*x^3 + 36*x^2 - 27), Vecsmall([0]), [Vecsmall([64, 0])], [0, 0, 0, 0]]
"""
+ if flag:
+ from sage.misc.superseded import deprecation
+ deprecation(15767, 'The flag argument to ellinit() is deprecated and not used anymore')
pari_catch_sig_on()
- return P.new_gen(ellinit0(self.g, flag, prec_bits_to_words(precision)))
+ return P.new_gen(ellinit(self.g, NULL, prec_bits_to_words(precision)))
def ellglobalred(self):
"""
- e.ellglobalred(): return information related to the global minimal
- model of the elliptic curve e.
+ Return information related to the global minimal model of the
+ elliptic curve e.
INPUT:
+ - ``e`` -- elliptic curve (returned by ellinit)
- - ``e`` - elliptic curve (returned by ellinit)
+ OUTPUT: A vector [N, [u,r,s,t], c, faN, L] with
+ - ``N`` - the (arithmetic) conductor of `e`
- OUTPUT:
-
-
- - ``gen`` - the (arithmetic) conductor of e
-
- - ``gen`` - a vector giving the coordinate change over
+ - ``[u,r,s,t]`` - a vector giving the coordinate change over
Q from e to its minimal integral model (see also ellminimalmodel)
- - ``gen`` - the product of the local Tamagawa numbers
- of e
+ - ``c`` - the product of the local Tamagawa numbers of `e`.
+ - ``faN`` is the factorization of `N`
+
+ - ``L[i]`` is ``elllocalred(E, faN[i,1])``
EXAMPLES::
sage: e = pari([0, 5, 2, -1, 1]).ellinit()
sage: e.ellglobalred()
- [20144, [1, -2, 0, -1], 1]
+ [20144, [1, -2, 0, -1], 1, [2, 4; 1259, 1], [[4, 2, 0, 1], [1, 5, 0, 1]]]
sage: e = pari(EllipticCurve('17a').a_invariants()).ellinit()
sage: e.ellglobalred()
- [17, [1, 0, 0, 0], 4]
+ [17, [1, 0, 0, 0], 4, Mat([17, 1]), [[1, 8, 0, 4]]]
"""
pari_catch_sig_on()
return P.new_gen(ellglobalred(self.g))
@@ -5507,11 +5491,11 @@ cdef class gen(sage.structure.element.RingElement):
OUTPUT: point on E
- EXAMPLES: First we create an elliptic curve::
+ EXAMPLES:
+
+ First we create an elliptic curve::
sage: e = pari([0, 1, 1, -2, 0]).ellinit()
- sage: str(e)[:65] # first part of output
- '[0, 1, 1, -2, 0, 4, -4, 1, -3, 112, -856, 389, 1404928/389, [0.90'
Next we add two points on the elliptic curve. Notice that the
Python lists are automatically converted to PARI objects so you
@@ -5525,7 +5509,7 @@ cdef class gen(sage.structure.element.RingElement):
cdef gen t0 = objtogen(z0)
cdef gen t1 = objtogen(z1)
pari_catch_sig_on()
- return P.new_gen(addell(self.g, t0.g, t1.g))
+ return P.new_gen(elladd(self.g, t0.g, t1.g))
def ellak(self, n):
r"""
@@ -5767,18 +5751,16 @@ cdef class gen(sage.structure.element.RingElement):
INPUT:
-
- ``e`` - elliptic curve
- ``ch`` - change of coordinates vector with 4
entries
-
EXAMPLES::
sage: e = pari([1,2,3,4,5]).ellinit()
sage: e.ellglobalred()
- [10351, [1, -1, 0, -1], 1]
+ [10351, [1, -1, 0, -1], 1, [11, 1; 941, 1], [[1, 5, 0, 1], [1, 5, 0, 1]]]
sage: f = e.ellchangecurve([1,-1,0,-1])
sage: f[:5]
[1, -1, 0, 4, 3]
@@ -5804,10 +5786,6 @@ cdef class gen(sage.structure.element.RingElement):
6.28318530717959*I
sage: w1*eta2-w2*eta1 == pari(2*pi*I)
True
- sage: pari([0,0,0,-82,0]).ellinit(flag=1).elleta()
- Traceback (most recent call last):
- ...
- PariError: incorrect type in elleta
"""
pari_catch_sig_on()
return P.new_gen(elleta(self.g, prec_bits_to_words(precision)))
@@ -5850,7 +5828,8 @@ cdef class gen(sage.structure.element.RingElement):
sage: e.ellheight([1,0], flag=1)
0.476711659343740
sage: e.ellheight([1,0], precision=128).sage()
- 0.47671165934373953737948605888465305932
+ 0.47671165934373953737948605888465305945902294217 # 32-bit
+ 0.476711659343739537379486058884653059459022942211150879336 # 64-bit
"""
cdef gen t0 = objtogen(a)
pari_catch_sig_on()
@@ -5879,13 +5858,6 @@ cdef class gen(sage.structure.element.RingElement):
sage: e = pari([0,1,1,-2,0]).ellinit().ellminimalmodel()[0]
sage: e.ellheightmatrix([[1,0], [-1,1]])
[0.476711659343740, 0.418188984498861; 0.418188984498861, 0.686667083305587]
-
- It is allowed to call :meth:`ellinit` with ``flag=1``::
-
- sage: E = pari([0,1,1,-2,0]).ellinit(flag=1)
- sage: E.ellheightmatrix([[1,0], [-1,1]], precision=128).sage()
- [0.47671165934373953737948605888465305932 0.41818898449886058562988945821587638244]
- [0.41818898449886058562988945821587638244 0.68666708330558658572355210295409678904]
"""
cdef gen t0 = objtogen(x)
pari_catch_sig_on()
@@ -6100,9 +6072,9 @@ cdef class gen(sage.structure.element.RingElement):
sage: e.elllseries(2.1)
0.402838047956645
sage: e.elllseries(1, precision=128)
- 2.87490929644255 E-38
+ 2.98766720445395 E-38
sage: e.elllseries(1, precision=256)
- 3.00282377034977 E-77
+ 5.48956813891054 E-77
sage: e.elllseries(-2)
0
sage: e.elllseries(2.1, A=1.1)
@@ -6217,8 +6189,6 @@ cdef class gen(sage.structure.element.RingElement):
[]
sage: e.ellordinate(5.0)
[11.3427192823270, -12.3427192823270]
- sage: e.ellordinate(RR(-3))
- [-1/2 + 3.42782730020052*I, -1/2 - 3.42782730020052*I]
"""
cdef gen t0 = objtogen(x)
pari_catch_sig_on()
@@ -6311,26 +6281,19 @@ cdef class gen(sage.structure.element.RingElement):
cdef gen t0 = objtogen(z)
cdef gen t1 = objtogen(n)
pari_catch_sig_on()
- return P.new_gen(powell(self.g, t0.g, t1.g))
+ return P.new_gen(ellmul(self.g, t0.g, t1.g))
- def ellrootno(self, p=1):
+ def ellrootno(self, p=None):
"""
- e.ellrootno(p): return the (local or global) root number of the
- `L`-series of the elliptic curve e
-
- If p is a prime number, the local root number at p is returned. If
- p is 1, the global root number is returned. Note that the global
- root number is the sign of the functional equation of the
- `L`-series, and therefore conjecturally equal to the parity
- of the rank of e.
+ Return the root number for the L-function of the elliptic curve
+ E/Q at a prime p (including 0, for the infinite place); return
+ the global root number if p is omitted.
INPUT:
-
- ``e`` - elliptic curve over `\QQ`
- - ``p (default = 1)`` - 1 or a prime number
-
+ - ``p`` - a prime number or ``None``.
OUTPUT: 1 or -1
@@ -6344,9 +6307,19 @@ cdef class gen(sage.structure.element.RingElement):
sage: e.ellrootno(1009)
1
"""
- cdef gen t0 = objtogen(p)
+ cdef gen t0
+ cdef GEN g0
+ if p is None:
+ g0 = NULL
+ elif p == 1:
+ from sage.misc.superseded import deprecation
+ deprecation(15767, 'The argument p=1 in ellrootno() is deprecated, use p=None instead')
+ g0 = NULL
+ else:
+ t0 = objtogen(p)
+ g0 = t0.g
pari_catch_sig_on()
- rootno = ellrootno(self.g, t0.g)
+ rootno = ellrootno(self.g, g0)
pari_catch_sig_off()
return rootno
@@ -6392,11 +6365,11 @@ cdef class gen(sage.structure.element.RingElement):
cdef gen t0 = objtogen(z0)
cdef gen t1 = objtogen(z1)
pari_catch_sig_on()
- return P.new_gen(subell(self.g, t0.g, t1.g))
+ return P.new_gen(ellsub(self.g, t0.g, t1.g))
- def elltaniyama(self):
+ def elltaniyama(self, long n=16):
pari_catch_sig_on()
- return P.new_gen(taniyama(self.g))
+ return P.new_gen(elltaniyama(self.g, n))
def elltors(self, long flag=0):
"""
@@ -6438,7 +6411,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: e = pari([1,0,1,-19,26]).ellinit()
sage: e.elltors()
- [12, [6, 2], [[-2, 8], [3, -2]]]
+ [12, [6, 2], [[1, 2], [3, -2]]]
"""
pari_catch_sig_on()
return P.new_gen(elltors0(self.g, flag))
@@ -6467,8 +6440,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: e = pari([0,0,0,1,0]).ellinit()
sage: e.ellzeta(1)
- 1.06479841295883 + 0.E-19*I # 32-bit
- 1.06479841295883 + 5.42101086242752 E-20*I # 64-bit
+ 1.06479841295883
sage: C.<i> = ComplexField()
sage: e.ellzeta(i-1)
-0.350122658523049 - 0.350122658523049*I
@@ -6498,8 +6470,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: e = pari([0,0,0,1,0]).ellinit()
sage: C.<i> = ComplexField()
sage: e.ellztopoint(1+i)
- [0.E-19 - 1.02152286795670*I, -0.149072813701096 - 0.149072813701096*I] # 32-bit
- [7.96075508054992 E-21 - 1.02152286795670*I, -0.149072813701096 - 0.149072813701096*I] # 64-bit
+ [0.E-19 - 1.02152286795670*I, -0.149072813701096 - 0.149072813701096*I]
Complex numbers belonging to the period lattice of e are of course
sent to the point at infinity on e::
@@ -6511,7 +6482,7 @@ cdef class gen(sage.structure.element.RingElement):
pari_catch_sig_on()
return P.new_gen(pointell(self.g, t0.g, prec_bits_to_words(precision)))
- def omega(self):
+ def omega(self, unsigned long precision=0):
"""
e.omega(): return basis for the period lattice of the elliptic
curve e.
@@ -6520,9 +6491,10 @@ cdef class gen(sage.structure.element.RingElement):
sage: e = pari([0, -1, 1, -10, -20]).ellinit()
sage: e.omega()
- [1.26920930427955, -0.634604652139777 - 1.45881661693850*I]
+ [1.26920930427955, 0.634604652139777 - 1.45881661693850*I]
"""
- return self[14:16]
+ pari_catch_sig_on()
+ return P.new_gen(ellR_omega(self.g, prec_bits_to_words(precision)))
def disc(self):
"""
@@ -6536,7 +6508,8 @@ cdef class gen(sage.structure.element.RingElement):
sage: _.factor()
[-1, 1; 11, 5]
"""
- return self[11]
+ pari_catch_sig_on()
+ return P.new_gen(member_disc(self.g))
def j(self):
"""
@@ -6550,7 +6523,8 @@ cdef class gen(sage.structure.element.RingElement):
sage: _.factor()
[-1, 1; 2, 12; 11, -5; 31, 3]
"""
- return self[12]
+ pari_catch_sig_on()
+ return P.new_gen(member_j(self.g))
def ellj(self, unsigned long precision=0):
"""
@@ -6569,7 +6543,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: pari(-I).ellj()
Traceback (most recent call last):
...
- PariError: argument '-I' does not belong to upper half-plane
+ PariError: domain error in modular function: Im(argument) <= 0
"""
pari_catch_sig_on()
return P.new_gen(jell(self.g, prec_bits_to_words(precision)))
@@ -6867,7 +6841,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: K.<i> = QuadraticField(-1)
sage: F = pari(K).idealprimedec(5); F
- [[5, [-2, 1]~, 1, 1, [2, 1]~], [5, [2, 1]~, 1, 1, [-2, 1]~]]
+ [[5, [-2, 1]~, 1, 1, [2, -1; 1, 2]], [5, [2, 1]~, 1, 1, [-2, -1; 1, -2]]]
sage: F[0].pr_get_p()
5
"""
@@ -6909,7 +6883,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: nf = F._pari_()
sage: I = pari('[1, -1, 2]~')
sage: nf.idealstar(I)
- [[[43, 9, 5; 0, 1, 0; 0, 0, 1], [0]], [42, [42]], Mat([[43, [9, 1, 0]~, 1, 1, [-5, -9, 1]~], 1]), [[[[42], [[3, 0, 0]~], [[3, 0, 0]~], [Vecsmall([])], 1]], [[], [], []]], Mat(1)]
+ [[[43, 9, 5; 0, 1, 0; 0, 0, 1], [0]], [42, [42]], Mat([[43, [9, 1, 0]~, 1, 1, [-5, 2, -18; -9, -5, 2; 1, -9, -5]], 1]), [[[[42], [3], [3], [Vecsmall([])], 1]], [[], [], []]], Mat(1)]
"""
cdef gen t0 = objtogen(I)
pari_catch_sig_on()
@@ -6953,18 +6927,30 @@ cdef class gen(sage.structure.element.RingElement):
def nfbasis(self, long flag=0, fa=None):
"""
- nfbasis(x, flag, fa): integral basis of the field QQ[a], where ``a`` is
- a root of the polynomial x.
+ Integral basis of the field `\QQ[a]`, where ``a`` is a root of
+ the polynomial x.
- Binary digits of ``flag`` mean:
+ INPUT:
+
+ - ``flag``: if set to 1 and ``fa`` is not given: assume that no
+ square of a prime > 500000 divides the discriminant of ``x``.
+
+ - ``fa``: If present, encodes a subset of primes at which to
+ check for maximality. This must be one of the three following
+ things:
+
+ - an integer: check all primes up to ``fa`` using trial
+ division.
- - 1: assume that no square of a prime>primelimit divides the
- discriminant of ``x``.
- - 2: use round 2 algorithm instead of round 4.
+ - a vector: a list of primes to check.
+
+ - a matrix: a partial factorization of the discriminant
+ of ``x``.
+
+ .. NOTE::
- If present, ``fa`` provides the matrix of a partial factorization of
- the discriminant of ``x``, useful if one wants only an order maximal at
- certain primes only.
+ In earlier versions of Sage, other bits in ``flag`` were
+ defined but these are now simply ignored.
EXAMPLES::
@@ -6981,29 +6967,34 @@ cdef class gen(sage.structure.element.RingElement):
[1, x]
sage: pari(f).nfbasis() # Correct result
[1, 1/10000000019*x]
- sage: pari(f).nfbasis(fa = "[2,2; %s,2]"%p) # Correct result and faster
+ sage: pari(f).nfbasis(fa=10^6) # Check primes up to 10^6: wrong result
+ [1, x]
+ sage: pari(f).nfbasis(fa="[2,2; %s,2]"%p) # Correct result and faster
+ [1, 1/10000000019*x]
+ sage: pari(f).nfbasis(fa=[2,p]) # Equivalent with the above
[1, 1/10000000019*x]
-
- TESTS:
-
- ``flag`` = 2 should give the same result::
-
- sage: pari('x^3 - 17').nfbasis(flag = 2)
- [1, x, 1/3*x^2 - 1/3*x + 1/3]
"""
+ if flag < 0 or flag > 1:
+ flag = flag & 1
+ from sage.misc.superseded import deprecation
+ deprecation(15767, 'In nfbasis(), flag must be 0 or 1, other bits are deprecated and ignored')
+
cdef gen t0
- if not fa:
- pari_catch_sig_on()
- return P.new_gen(nfbasis0(self.g, flag, NULL))
- else:
+ cdef GEN g0
+ if fa is not None:
t0 = objtogen(fa)
- pari_catch_sig_on()
- return P.new_gen(nfbasis0(self.g, flag, t0.g))
+ g0 = t0.g
+ elif flag:
+ g0 = utoi(500000)
+ else:
+ g0 = NULL
+ pari_catch_sig_on()
+ return P.new_gen(nfbasis(self.g, NULL, g0))
def nfbasis_d(self, long flag=0, fa=None):
"""
- nfbasis_d(x): Return a basis of the number field defined over QQ
- by x and its discriminant.
+ Like :meth:`nfbasis`, but return a tuple ``(B, D)`` where `B`
+ is the integral basis and `D` the discriminant.
EXAMPLES::
@@ -7022,15 +7013,23 @@ cdef class gen(sage.structure.element.RingElement):
sage: pari([-2,0,0,1]).Polrev().nfbasis_d()
([1, x, x^2], -108)
"""
+ if flag < 0 or flag > 1:
+ flag = flag & 1
+ from sage.misc.superseded import deprecation
+ deprecation(15767, 'In nfbasis_d(), flag must be 0 or 1, other bits are deprecated and ignored')
+
cdef gen t0
+ cdef GEN g0
cdef GEN disc
- if not fa:
- pari_catch_sig_on()
- B = P.new_gen_noclear(nfbasis(self.g, &disc, flag, NULL))
- else:
+ if fa is not None:
t0 = objtogen(fa)
- pari_catch_sig_on()
- B = P.new_gen_noclear(nfbasis(self.g, &disc, flag, t0.g))
+ g0 = t0.g
+ elif flag & 1:
+ g0 = utoi(500000)
+ else:
+ g0 = NULL
+ pari_catch_sig_on()
+ B = P.new_gen_noclear(nfbasis(self.g, &disc, g0))
D = P.new_gen(disc)
return B, D
@@ -7247,18 +7246,13 @@ cdef class gen(sage.structure.element.RingElement):
sage: A = matrix(F,[[1,2,a,3],[3,0,a+2,0],[0,0,a,2],[3+a,a,0,1]])
sage: I = [F.ideal(-2*a+1),F.ideal(7), F.ideal(3),F.ideal(1)]
sage: Fp.nfhnf([pari(A),[pari(P) for P in I]])
- [[1, [-969/5, -1/15]~, [15, -2]~, [-1938, -3]~; 0, 1, 0, 0; 0, 0, 1, 0;
- 0, 0, 0, 1], [[3997, 1911; 0, 7], [15, 6; 0, 3], [1, 0; 0, 1], [1, 0; 0,
- 1]]]
+ [[1, [-969/5, -1/15]~, [15, -2]~, [-1938, -3]~; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [[3997, 1911; 0, 7], [15, 6; 0, 3], 1, 1]]
sage: K.<b> = NumberField(x^3-2)
sage: Kp = pari(K)
sage: A = matrix(K,[[1,0,0,5*b],[1,2*b^2,b,57],[0,2,1,b^2-3],[2,0,0,b]])
sage: I = [K.ideal(2),K.ideal(3+b^2),K.ideal(1),K.ideal(1)]
sage: Kp.nfhnf([pari(A),[pari(P) for P in I]])
- [[1, -225, 72, -31; 0, 1, [0, -1, 0]~, [0, 0, -1/2]~; 0, 0, 1, [0, 0,
- -1/2]~; 0, 0, 0, 1], [[1116, 756, 612; 0, 18, 0; 0, 0, 18], [2, 0, 0; 0,
- 2, 0; 0, 0, 2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [2, 0, 0; 0, 1, 0; 0, 0,
- 1]]]
+ [[1, -225, 72, -31; 0, 1, [0, -1, 0]~, [0, 0, -1/2]~; 0, 0, 1, [0, 0, -1/2]~; 0, 0, 0, 1], [[1116, 756, 612; 0, 18, 0; 0, 0, 18], 2, 1, [2, 0, 0; 0, 1, 0; 0, 0, 1]]]
An example where the ring of integers of the number field is not a PID::
@@ -7267,15 +7261,11 @@ cdef class gen(sage.structure.element.RingElement):
sage: A = matrix(K,[[1,0,0,5*b],[1,2*b^2,b,57],[0,2,1,b^2-3],[2,0,0,b]])
sage: I = [K.ideal(2),K.ideal(3+b^2),K.ideal(1),K.ideal(1)]
sage: Kp.nfhnf([pari(A),[pari(P) for P in I]])
- [[1, [15, 6]~, [0, -54]~, [113, 72]~; 0, 1, [-4, -1]~, [0, -1]~; 0, 0,
- 1, 0; 0, 0, 0, 1], [[360, 180; 0, 180], [6, 4; 0, 2], [1, 0; 0, 1], [1,
- 0; 0, 1]]]
+ [[1, [15, 6]~, [0, -54]~, [113, 72]~; 0, 1, [-4, -1]~, [0, -1]~; 0, 0, 1, 0; 0, 0, 0, 1], [[360, 180; 0, 180], [6, 4; 0, 2], 1, 1]]
sage: A = matrix(K,[[1,0,0,5*b],[1,2*b,b,57],[0,2,1,b-3],[2,0,b,b]])
sage: I = [K.ideal(2).factor()[0][0],K.ideal(3+b),K.ideal(1),K.ideal(1)]
sage: Kp.nfhnf([pari(A),[pari(P) for P in I]])
- [[1, [7605, 4]~, [5610, 5]~, [7913, -6]~; 0, 1, 0, -1; 0, 0, 1, 0; 0, 0,
- 0, 1], [[19320, 13720; 0, 56], [2, 1; 0, 1], [1, 0; 0, 1], [1, 0; 0,
- 1]]]
+ [[1, [7605, 4]~, [5610, 5]~, [7913, -6]~; 0, 1, 0, -1; 0, 0, 1, 0; 0, 0, 0, 1], [[19320, 13720; 0, 56], [2, 1; 0, 1], 1, 1]]
AUTHORS:
@@ -7302,41 +7292,19 @@ cdef class gen(sage.structure.element.RingElement):
EXAMPLES::
sage: pari('x^3 - 17').nfinit()
- [x^3 - 17, [1, 1], -867, 3, [[1, 1.68006..., 2.57128...; 1, -0.340034... + 2.65083...*I, -1.28564... - 2.22679...*I], [1, 1.68006..., 2.57128...; 1, 2.31080..., -3.51243...; 1, -2.99087..., 0.941154...], [1, 2, 3; 1, 2, -4; 1, -3, 1], [3, 1, 0; 1, -11, 17; 0, 17, 0], [51, 0, 16; 0, 17, 3; 0, 0, 1], [17, 0, -1; 0, 0, 3; -1, 3, 2], [51, [-17, 6, -1; 0, -18, 3; 1, 0, -16]]], [2.57128..., -1.28564... - 2.22679...*I], [1, 1/3*x^2 - 1/3*x + 1/3, x], [1, 0, -1; 0, 0, 3; 0, 1, 1], [1, 0, 0, 0, -4, 6, 0, 6, -1; 0, 1, 0, 1, 1, -1, 0, -1, 3; 0, 0, 1, 0, 2, 0, 1, 0, 1]]
-
- TESTS:
+ [x^3 - 17, [1, 1], -867, 3, [[1, 1.68006914259990, 2.57128159065824; 1, -0.340034571299952 - 2.65083754153991*I, -1.28564079532912 + 2.22679517779329*I], [1, 1.68006914259990, 2.57128159065824; 1, -2.99087211283986, 0.941154382464174; 1, 2.31080297023995, -3.51243597312241], [1, 2, 3; 1, -3, 1; 1, 2, -4], [3, 1, 0; 1, -11, 17; 0, 17, 0], [51, 0, 16; 0, 17, 3; 0, 0, 1], [17, 0, -1; 0, 0, 3; -1, 3, 2], [51, [-17, 6, -1; 0, -18, 3; 1, 0, -16]], [3, 17]], [2.57128159065824, -1.28564079532912 + 2.22679517779329*I], [1, 1/3*x^2 - 1/3*x + 1/3, x], [1, 0, -1; 0, 0, 3; 0, 1, 1], [1, 0, 0, 0, -4, 6, 0, 6, -1; 0, 1, 0, 1, 1, -1, 0, -1, 3; 0, 0, 1, 0, 2, 0, 1, 0, 1]]
- This example only works after increasing precision::
+ TESTS::
- sage: pari('x^2 + 10^100 + 1').nfinit(precision=64)
- Traceback (most recent call last):
- ...
- PariError: precision too low in floorr (precision loss in truncation)
sage: pari('x^2 + 10^100 + 1').nfinit()
[...]
-
- Throw a PARI error which is not of type ``precer``::
-
sage: pari('1.0').nfinit()
Traceback (most recent call last):
...
- PariError: incorrect type in checknf
+ PariError: incorrect type in checknf [please apply nfinit()] (t_REAL)
"""
- # If explicit precision is given, use only that
- if precision:
- pari_catch_sig_on()
- return P.new_gen(nfinit0(self.g, flag, prec_bits_to_words(precision)))
-
- # Otherwise, start with 64 bits of precision and increase as needed:
- precision = 64
- while True:
- try:
- return self.nfinit(flag, precision)
- except PariError as err:
- if err.errnum() == precer:
- precision *= 2
- else:
- raise
+ pari_catch_sig_on()
+ return P.new_gen(nfinit0(self.g, flag, prec_bits_to_words(precision)))
def nfisisom(self, gen other):
"""
@@ -7389,7 +7357,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: nf = pari('x^2 + 1').nfinit()
sage: nf.nfrootsof1()
- [4, -x]
+ [4, x]
"""
pari_catch_sig_on()
return P.new_gen(rootsof1(self.g))
@@ -7427,12 +7395,12 @@ cdef class gen(sage.structure.element.RingElement):
def rnfeltabstorel(self, x):
cdef gen t0 = objtogen(x)
pari_catch_sig_on()
- return P.new_gen(rnfelementabstorel(self.g, t0.g))
+ return P.new_gen(rnfeltabstorel(self.g, t0.g))
def rnfeltreltoabs(self, x):
cdef gen t0 = objtogen(x)
pari_catch_sig_on()
- return P.new_gen(rnfelementreltoabs(self.g, t0.g))
+ return P.new_gen(rnfeltreltoabs(self.g, t0.g))
def rnfequation(self, poly, long flag=0):
cdef gen t0 = objtogen(poly)
@@ -7460,10 +7428,10 @@ cdef class gen(sage.structure.element.RingElement):
sage: P = pari('[[[1, 0]~, [0, 0]~; [0, 0]~, [1, 0]~], [[2, 0; 0, 2], [2, 0; 0, 1/2]]]')
- And this is the HNF of the inert ideal (2) in nf:
+ And this is the inert ideal (2) in nf:
sage: rnf.rnfidealdown(P)
- [2, 0; 0, 2]
+ 2
"""
cdef gen t0 = objtogen(x)
pari_catch_sig_on()
@@ -7472,7 +7440,7 @@ cdef class gen(sage.structure.element.RingElement):
def rnfidealhnf(self, x):
cdef gen t0 = objtogen(x)
pari_catch_sig_on()
- return P.new_gen(rnfidealhermite(self.g, t0.g))
+ return P.new_gen(rnfidealhnf(self.g, t0.g))
def rnfidealnormrel(self, x):
cdef gen t0 = objtogen(x)
@@ -7523,11 +7491,11 @@ cdef class gen(sage.structure.element.RingElement):
sage: pari(-23).quadhilbert()
x^3 - x^2 + 1
sage: pari(145).quadhilbert()
- x^4 - x^3 - 3*x^2 + x + 1
+ x^4 - 6*x^2 - 5*x - 1
sage: pari(-12).quadhilbert() # Not fundamental
Traceback (most recent call last):
...
- PariError: quadray needs a fundamental discriminant
+ PariError: domain error in quadray: isfundamental(D) = 0
"""
pari_catch_sig_on()
# Precision argument is only used for real quadratic extensions
@@ -7612,7 +7580,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: pari('1/x').eval(0)
Traceback (most recent call last):
...
- PariError: division by zero
+ PariError: impossible inverse in gdiv: 0
sage: pari('1/x + O(x^2)').eval(0)
Traceback (most recent call last):
...
@@ -7620,11 +7588,11 @@ cdef class gen(sage.structure.element.RingElement):
sage: pari('1/x + O(x^2)').eval(pari('O(x^3)'))
Traceback (most recent call last):
...
- PariError: division by zero
+ PariError: impossible inverse in gdiv: O(x^3)
sage: pari('O(x^0)').eval(0)
Traceback (most recent call last):
...
- PariError: non existent component in truecoeff
+ PariError: domain error in polcoeff: t_SER = O(x^0)
Evaluating multivariate polynomials::
@@ -7690,9 +7658,9 @@ cdef class gen(sage.structure.element.RingElement):
sage: K.<a> = NumberField(x^2 + 1)
sage: nf = K._pari_()
sage: nf
- [y^2 + 1, [0, 1], -4, 1, [Mat([1, 0.E-19 - 1.00000000000000*I]), [1, -1.00000000000000; 1, 1.00000000000000], [1, -1; 1, 1], [2, 0; 0, -2], [2, 0; 0, 2], [1, 0; 0, -1], [1, [0, -1; 1, 0]]], [0.E-19 - 1.00000000000000*I], [1, y], [1, 0; 0, 1], [1, 0, 0, -1; 0, 1, 1, 0]]
+ [y^2 + 1, [0, 1], -4, 1, [Mat([1, 0.E-19 + 1.00000000000000*I]), [1, 1.00000000000000; 1, -1.00000000000000], [1, 1; 1, -1], [2, 0; 0, -2], [2, 0; 0, 2], [1, 0; 0, -1], [1, [0, -1; 1, 0]], []], [0.E-19 + 1.00000000000000*I], [1, y], [1, 0; 0, 1], [1, 0, 0, -1; 0, 1, 1, 0]]
sage: nf(y='x')
- [x^2 + 1, [0, 1], -4, 1, [Mat([1, 0.E-19 - 1.00000000000000*I]), [1, -1.00000000000000; 1, 1.00000000000000], [1, -1; 1, 1], [2, 0; 0, -2], [2, 0; 0, 2], [1, 0; 0, -1], [1, [0, -1; 1, 0]]], [0.E-19 - 1.00000000000000*I], [1, x], [1, 0; 0, 1], [1, 0, 0, -1; 0, 1, 1, 0]]
+ [x^2 + 1, [0, 1], -4, 1, [Mat([1, 0.E-19 + 1.00000000000000*I]), [1, 1.00000000000000; 1, -1.00000000000000], [1, 1; 1, -1], [2, 0; 0, -2], [2, 0; 0, 2], [1, 0; 0, -1], [1, [0, -1; 1, 0]], []], [0.E-19 + 1.00000000000000*I], [1, x], [1, 0; 0, 1], [1, 0, 0, -1; 0, 1, 1, 0]]
"""
cdef long t = typ(self.g)
cdef gen t0
@@ -7786,7 +7754,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: T(0)
Traceback (most recent call last):
...
- PariError: _/_: division by zero
+ PariError: _/_: impossible inverse in gdiv: 0
sage: pari('() -> 42')(1,2,3)
Traceback (most recent call last):
...
@@ -8012,7 +7980,7 @@ cdef class gen(sage.structure.element.RingElement):
non-constant polynomial, or False if f is reducible or constant.
"""
pari_catch_sig_on()
- cdef long t = itos(gisirreducible(self.g))
+ t = isirreducible(self.g)
P.clear_stack()
return t != 0
@@ -8055,12 +8023,14 @@ cdef class gen(sage.structure.element.RingElement):
def polroots(self, long flag=0, unsigned long precision=0):
"""
- polroots(x,flag=0): complex roots of the polynomial x. flag is
- optional, and can be 0: default, uses Schonhage's method modified
- by Gourdon, or 1: uses a modified Newton method.
+ Complex roots of the given polynomial using Schonhage's method,
+ as modified by Gourdon.
"""
+ if flag:
+ from sage.misc.superseded import deprecation
+ deprecation(15767, 'The flag argument to polroots() is deprecated and not used anymore')
pari_catch_sig_on()
- return P.new_gen(roots0(self.g, flag, prec_bits_to_words(precision)))
+ return P.new_gen(cleanroots(self.g, prec_bits_to_words(precision)))
def polrootsmod(self, p, long flag=0):
cdef gen t0 = objtogen(p)
@@ -8128,7 +8098,7 @@ cdef class gen(sage.structure.element.RingElement):
x + O(x^4)
"""
pari_catch_sig_on()
- return P.new_gen(recip(self.g))
+ return P.new_gen(serreverse(self.g))
def thueinit(self, long flag=0, unsigned long precision=0):
pari_catch_sig_on()
@@ -8332,7 +8302,7 @@ cdef class gen(sage.structure.element.RingElement):
[
[ -5 -10 -2 -7 3]
[ 1 2 1 2 0]
- 10, 5.00000000023283..., [ 1 2 0 1 -1]
+ 10, 5.00000000000000000, [ 1 2 0 1 -1]
]
"""
@@ -8354,14 +8324,31 @@ cdef class gen(sage.structure.element.RingElement):
def qfrep(self, B, long flag=0):
"""
- qfrep(x,B,flag=0): vector of (half) the number of vectors of norms
- from 1 to B for the integral and definite quadratic form x. Binary
- digits of flag mean 1: count vectors of even norm from 1 to 2B, 2:
- return a t_VECSMALL instead of a t_VEC.
+ Vector of (half) the number of vectors of norms from 1 to `B`
+ for the integral and definite quadratic form ``self``.
+ Binary digits of flag mean 1: count vectors of even norm from
+ 1 to `2B`, 2: return a ``t_VECSMALL`` instead of a ``t_VEC``
+ (which is faster).
+
+ EXAMPLES::
+
+ sage: M = pari("[5,1,1;1,3,1;1,1,1]")
+ sage: M.qfrep(20)
+ [1, 1, 2, 2, 2, 4, 4, 3, 3, 4, 2, 4, 6, 0, 4, 6, 4, 5, 6, 4]
+ sage: M.qfrep(20, flag=1)
+ [1, 2, 4, 3, 4, 4, 0, 6, 5, 4, 12, 4, 4, 8, 0, 3, 8, 6, 12, 12]
+ sage: M.qfrep(20, flag=2)
+ Vecsmall([1, 1, 2, 2, 2, 4, 4, 3, 3, 4, 2, 4, 6, 0, 4, 6, 4, 5, 6, 4])
"""
+ # PARI 2.7 always returns a t_VECSMALL, but for backwards
+ # compatibility, we keep returning a t_VEC (unless flag & 2)
cdef gen t0 = objtogen(B)
+ cdef GEN r
pari_catch_sig_on()
- return P.new_gen(qfrep0(self.g, t0.g, flag))
+ r = qfrep0(self.g, t0.g, flag & 1)
+ if (flag & 2) == 0:
+ r = vecsmall_to_vec(r)
+ return P.new_gen(r)
def matsolve(self, B):
"""
@@ -8745,9 +8732,9 @@ cdef class gen(sage.structure.element.RingElement):
cdef gen t0 = objtogen(y)
cdef gen t1 = objtogen(p)
pari_catch_sig_on()
- ret = hilbert0(x.g, t0.g, t1.g)
- pari_catch_sig_off()
- return ret
+ r = hilbert(x.g, t0.g, t1.g)
+ P.clear_stack()
+ return r
def chinese(self, y):
cdef gen t0 = objtogen(y)
@@ -8786,7 +8773,7 @@ cdef class gen(sage.structure.element.RingElement):
Mod(236736367459211723407, 473472734918423446802)
"""
pari_catch_sig_on()
- return P.new_gen(znprimroot0(self.g))
+ return P.new_gen(znprimroot(self.g))
def __abs__(self):
return self.abs()
@@ -8814,8 +8801,8 @@ cdef class gen(sage.structure.element.RingElement):
"""
pari_catch_sig_on()
if add_one:
- return P.new_gen(gnextprime(gaddsg(1,self.g)))
- return P.new_gen(gnextprime(self.g))
+ return P.new_gen(nextprime(gaddsg(1, self.g)))
+ return P.new_gen(nextprime(self.g))
def change_variable_name(self, var):
"""
@@ -8957,12 +8944,12 @@ cdef class gen(sage.structure.element.RingElement):
pari_catch_sig_on()
return P.new_gen(charpoly0(self.g, P.get_var(var), flag))
-
def kronecker(gen self, y):
cdef gen t0 = objtogen(y)
pari_catch_sig_on()
- return P.new_gen(gkronecker(self.g, t0.g))
-
+ r = kronecker(self.g, t0.g)
+ P.clear_stack()
+ return r
def type(gen self):
"""
@@ -9107,7 +9094,7 @@ cdef class gen(sage.structure.element.RingElement):
sage: om = e.omega()
sage: om
[2.49021256085506, -1.97173770155165*I]
- sage: om.elleisnum(2) # was: -5.28864933965426
+ sage: om.elleisnum(2)
10.0672605281120
sage: om.elleisnum(4)
112.000000000000
@@ -9151,7 +9138,7 @@ cdef class gen(sage.structure.element.RingElement):
Compute P(1)::
sage: E.ellwp(1)
- 13.9658695257485 + 0.E-18*I
+ 13.9658695257485
Compute P(1+i), where i = sqrt(-1)::
@@ -9180,11 +9167,18 @@ cdef class gen(sage.structure.element.RingElement):
With flag=1, compute the pair P(z) and P'(z)::
sage: E.ellwp(1, flag=1)
- [13.9658695257485 + 0.E-18*I, 50.5619300880073 ... E-18*I]
+ [13.9658695257485, 50.5619893875144]
"""
cdef gen t0 = objtogen(z)
+ cdef GEN g0 = t0.g
+
+ # Emulate toser_i() but with given precision
pari_catch_sig_on()
- return P.new_gen(ellwp0(self.g, t0.g, flag, n+2, prec_bits_to_words(precision)))
+ if typ(g0) == t_POL:
+ g0 = RgX_to_ser(g0, n+4)
+ elif typ(g0) == t_RFRAC:
+ g0 = rfrac_to_ser(g0, n+4)
+ return P.new_gen(ellwp0(self.g, g0, flag, prec_bits_to_words(precision)))
def ellchangepoint(self, y):
"""
@@ -9368,7 +9362,7 @@ class PariError(RuntimeError):
....: pari('1/0')
....: except PariError as err:
....: print err.errnum()
- 27
+ 30
"""
return self.args[0]
@@ -9414,7 +9408,7 @@ class PariError(RuntimeError):
....: pari('1/0')
....: except PariError as err:
....: print err
- _/_: division by zero
+ _/_: impossible inverse in gdiv: 0
A syntax error::
@@ -9424,7 +9418,7 @@ class PariError(RuntimeError):
PariError: syntax error, unexpected $undefined: !@#$%^&*()
"""
lines = self.errtext().split('\n')
- if self.errnum() == syntaxer:
+ if self.errnum() == e_SYNTAX:
for line in lines:
if "syntax error" in line:
return line.lstrip(" *").rstrip(" .:")
diff --git a/src/sage/libs/pari/gen_py.py b/src/sage/libs/pari/gen_py.py
index 8ea4e5d..28f05f6 100644
--- a/src/sage/libs/pari/gen_py.py
+++ b/src/sage/libs/pari/gen_py.py
@@ -73,11 +73,11 @@ def pari(x):
sage: K.<a> = NumberField(x^3 - 2)
sage: pari(K)
- [y^3 - 2, [1, 1], -108, 1, [[1, 1.25992104989487, 1.58740105196820; 1, -0.629960524947437 - 1.09112363597172*I, -0.793700525984100 + 1.37472963699860*I], [1, 1.25992104989487, 1.58740105196820; 1, -1.72108416091916, 0.581029111014503; 1, 0.461163111024285, -2.16843016298270], [1, 1, 2; 1, -2, 1; 1, 0, -2], [3, 0, 0; 0, 0, 6; 0, 6, 0], [6, 0, 0; 0, 6, 0; 0, 0, 3], [2, 0, 0; 0, 0, 1; 0, 1, 0], [2, [0, 0, 2; 1, 0, 0; 0, 1, 0]]], [1.25992104989487, -0.629960524947437 - 1.09112363597172*I], [1, y, y^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 2, 0, 2, 0; 0, 1, 0, 1, 0, 0, 0, 0, 2; 0, 0, 1, 0, 1, 0, 1, 0, 0]]
+ [y^3 - 2, [1, 1], -108, 1, [[1, 1.25992104989487, 1.58740105196820; 1, -0.629960524947437 + 1.09112363597172*I, -0.793700525984100 - 1.37472963699860*I], [1, 1.25992104989487, 1.58740105196820; 1, 0.461163111024285, -2.16843016298270; 1, -1.72108416091916, 0.581029111014503], [1, 1, 2; 1, 0, -2; 1, -2, 1], [3, 0, 0; 0, 0, 6; 0, 6, 0], [6, 0, 0; 0, 6, 0; 0, 0, 3], [2, 0, 0; 0, 0, 1; 0, 1, 0], [2, [0, 0, 2; 1, 0, 0; 0, 1, 0]], []], [1.25992104989487, -0.629960524947437 + 1.09112363597172*I], [1, y, y^2], [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0, 0, 0, 2, 0, 2, 0; 0, 1, 0, 1, 0, 0, 0, 0, 2; 0, 0, 1, 0, 1, 0, 1, 0, 0]]
sage: E = EllipticCurve('37a1')
sage: pari(E)
- [0, 0, 1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, [0.837565435283323, 0.269594436405445, -1.10715987168877]~, 2.99345864623196, -2.45138938198679*I, 0.942638555913623, 1.32703057887968*I, 7.33813274078958]
+ [0, 0, 1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, Vecsmall([1]), [Vecsmall([64, 1])], [0, 0, 0, 0, 0, 0, 0, 0]]
Conversion from basic Python types::
diff --git a/src/sage/libs/pari/handle_error.pyx b/src/sage/libs/pari/handle_error.pyx
index 81472fb..101028b 100644
--- a/src/sage/libs/pari/handle_error.pyx
+++ b/src/sage/libs/pari/handle_error.pyx
@@ -27,7 +27,7 @@ cdef void _pari_init_error_handling():
....: except PariError as e:
....: print e.errtext()
....:
- *** argument must be positive in polcyclo.
+ *** domain error in polcyclo: index <= 0
"""
global pari_error_string
@@ -73,17 +73,17 @@ cdef int _pari_handle_exception(long err) except 0:
sage: pari(1)/pari(0)
Traceback (most recent call last):
...
- PariError: division by zero
+ PariError: impossible inverse in gdiv: 0
"""
- if err == errpile:
+ if err == e_STACK:
# PARI is out of memory. We double the size of the PARI stack
# and retry the computation.
from sage.libs.pari.all import pari
pari.allocatemem(silent=True)
return 0
- if err == user:
+ if err == e_USER:
raise RuntimeError("PARI user exception\n%s" % pari_error_string)
else:
from sage.libs.pari.all import PariError
diff --git a/src/sage/libs/pari/pari_instance.pxd b/src/sage/libs/pari/pari_instance.pxd
index a7242a0..95db20d 100644
--- a/src/sage/libs/pari/pari_instance.pxd
+++ b/src/sage/libs/pari/pari_instance.pxd
@@ -9,6 +9,7 @@ cpdef long prec_bits_to_words(unsigned long prec_in_bits)
@cython.final
cdef class PariInstance(sage.structure.parent_base.ParentWithBase):
+ cdef long _real_precision
cdef gen PARI_ZERO, PARI_ONE, PARI_TWO
cdef inline gen new_gen(self, GEN x)
cdef inline gen new_gen_noclear(self, GEN x)
diff --git a/src/sage/libs/pari/pari_instance.pyx b/src/sage/libs/pari/pari_instance.pyx
index 7991a62..21e3b36 100644
--- a/src/sage/libs/pari/pari_instance.pyx
+++ b/src/sage/libs/pari/pari_instance.pyx
@@ -20,6 +20,8 @@ AUTHORS:
- Peter Bruin (2013-11-17): split off this file from gen.pyx (#15185)
+- Jeroen Demeyer (2014-02-09): upgrade to PARI 2.7 (#15767)
+
EXAMPLES::
@@ -44,7 +46,7 @@ Arithmetic obeys the usual coercion rules::
GUIDE TO REAL PRECISION AND THE PARI LIBRARY
-The default real precision in communicating with the Pari library
+The default real precision in communicating with the PARI library
is the same as the default Sage real precision, which is 53 bits.
Inexact Pari objects are therefore printed by default to 15 decimal
digits (even if they are actually more precise).
@@ -132,14 +134,15 @@ with a precision of 100 bits::
True
Elliptic curves and precision: If you are working with elliptic
-curves and want to compute with a precision other than the default
-53 bits, you should use the precision parameter of ellinit()::
+curves, you should set the precision for each method::
- sage: R = RealField(150)
- sage: e = pari([0,0,0,-82,0]).ellinit(precision=150)
- sage: eta1 = e.elleta()[0]
- sage: R(eta1)
- 3.6054636014326520859158205642077267748102690
+ sage: e = pari([0,0,0,-82,0]).ellinit()
+ sage: eta1 = e.elleta(precision=100)[0]
+ sage: eta1.sage()
+ 3.6054636014326520859158205642077267748
+ sage: eta1 = e.elleta(precision=180)[0]
+ sage: eta1.sage()
+ 3.60546360143265208591582056420772677481026899659802474544
Number fields and precision: TODO
@@ -157,9 +160,6 @@ include 'pari_err.pxi'
include 'sage/ext/stdsage.pxi'
include 'sage/ext/interrupt.pxi'
-cdef extern from 'c_lib/include/memory.h':
- void init_memory_functions()
-
import sys
cimport libc.stdlib
@@ -348,8 +348,6 @@ pari_catch_sig_off()
pari = pari_instance
-cdef unsigned long num_primes
-
# Callbacks from PARI to print stuff using sys.stdout.write() instead
# of C library functions like puts().
cdef PariOUT sage_pariOut
@@ -432,7 +430,7 @@ cdef class PariInstance(sage.structure.parent_base.ParentWithBase):
if bot:
return # pari already initialized.
- global num_primes, top, bot
+ global top, bot
# The size here doesn't really matter, because we will allocate
# our own stack anyway. We ask PARI not to set up signal and
@@ -445,8 +443,6 @@ cdef class PariInstance(sage.structure.parent_base.ParentWithBase):
# so we need to reset them.
init_memory_functions()
- num_primes = maxprime
-
# Free the PARI stack and allocate our own (using Cython)
pari_free(<void*>bot); bot = 0
init_stack(size)
@@ -465,6 +461,7 @@ cdef class PariInstance(sage.structure.parent_base.ParentWithBase):
pariErr.flush = sage_pariErr_flush
# Display only 15 digits
+ self._real_precision = 15
sd_format("g.15", d_SILENT)
# Init global prec variable (PARI's precision is always a
@@ -585,11 +582,12 @@ cdef class PariInstance(sage.structure.parent_base.ParentWithBase):
sage: pari.set_real_precision(15)
60
"""
- prev = self.get_real_precision()
+ prev = self._real_precision
cdef bytes strn = str(n)
pari_catch_sig_on()
sd_realprecision(strn, d_SILENT)
pari_catch_sig_off()
+ self._real_precision = n
return prev
def get_real_precision(self):
@@ -608,10 +606,7 @@ cdef class PariInstance(sage.structure.parent_base.ParentWithBase):
sage: pari.get_real_precision()
15
"""
- pari_catch_sig_on()
- cdef long prev = itos(sd_realprecision(NULL, d_RETURN))
- pari_catch_sig_off()
- return prev
+ return self._real_precision
def set_series_precision(self, long n):
global precdl
@@ -1147,7 +1142,7 @@ cdef class PariInstance(sage.structure.parent_base.ParentWithBase):
def pari_version(self):
return str(PARIVERSION)
- def init_primes(self, _M):
+ def init_primes(self, unsigned long M):
"""
Recompute the primes table including at least all primes up to M
(but possibly more).
@@ -1156,29 +1151,22 @@ cdef class PariInstance(sage.structure.parent_base.ParentWithBase):
sage: pari.init_primes(200000)
- We make sure that ticket #11741 has been fixed, and double check to
- make sure that diffptr has not been freed::
+ We make sure that ticket :trac:`11741` has been fixed::
- sage: pari.init_primes(2^62)
+ sage: pari.init_primes(2^30)
Traceback (most recent call last):
...
- PariError: not enough memory # 64-bit
- OverflowError: long int too large to convert # 32-bit
- sage: pari.init_primes(200000)
+ ValueError: Cannot compute primes beyond 436273290
"""
- cdef unsigned long M
- cdef char *tmpptr
- M = _M
- global diffptr, num_primes
- if M <= num_primes:
+ # Hardcoded bound in PARI sources
+ if M > 436273290:
+ raise ValueError("Cannot compute primes beyond 436273290")
+
+ if M <= maxprime():
return
pari_catch_sig_on()
- tmpptr = initprimes(M)
+ initprimetable(M)
pari_catch_sig_off()
- pari_free(<void*> diffptr)
- num_primes = M
- diffptr = tmpptr
-
##############################################
## Support for GP Scripts
@@ -1221,19 +1209,18 @@ cdef class PariInstance(sage.structure.parent_base.ParentWithBase):
def _primelimit(self):
"""
- Return the number of primes already computed
- in this Pari instance.
+ Return the number of primes already computed by PARI.
+
+ EXAMPLES::
- EXAMPLES:
sage: pari._primelimit()
- 500000
+ 499979
sage: pari.init_primes(600000)
sage: pari._primelimit()
- 600000
+ 599999
"""
- global num_primes
from sage.rings.all import ZZ
- return ZZ(num_primes)
+ return ZZ(maxprime())
def prime_list(self, long n):
"""
@@ -1302,8 +1289,6 @@ cdef class PariInstance(sage.structure.parent_base.ParentWithBase):
"""
nth_prime(n): returns the n-th prime, where n is a C-int
"""
- global num_primes
-
if n <= 0:
raise ValueError, "nth prime meaningless for non-positive n (=%s)"%n
cdef GEN g
@@ -1311,15 +1296,15 @@ cdef class PariInstance(sage.structure.parent_base.ParentWithBase):
g = prime(n)
return self.new_gen(g)
-
def nth_prime(self, long n):
from sage.libs.pari.all import PariError
try:
return self.__nth_prime(n)
except PariError:
- self.init_primes(max(2*num_primes,20*n))
+ self.init_primes(max(2*maxprime(), 20*n))
return self.nth_prime(n)
+
def euler(self, unsigned long precision=0):
"""
Return Euler's constant to the requested real precision (in bits).
@@ -1488,16 +1473,16 @@ cdef class PariInstance(sage.structure.parent_base.ParentWithBase):
TESTS:
- Check that invalid inputs are handled properly (#11825)::
+ Check that invalid inputs are handled properly (:trac:`11825`)::
sage: pari.setrand(0)
Traceback (most recent call last):
...
- PariError: incorrect type in setrand
+ PariError: incorrect type in setrand (t_INT)
sage: pari.setrand("foobar")
Traceback (most recent call last):
...
- PariError: incorrect type in setrand
+ PariError: incorrect type in setrand (t_POL)
"""
cdef gen t0 = self(seed)
pari_catch_sig_on()
@@ -1579,6 +1564,24 @@ cdef class PariInstance(sage.structure.parent_base.ParentWithBase):
k = k + 1
return A
+ def genus2red(self, Q, P):
+ """
+ Let Q,P be polynomials with integer coefficients. Determine
+ the reduction at p > 2 of the (proper, smooth) hyperelliptic
+ curve C/Q: y^2+Qy = P, of genus 2. (The special fiber X_p of
+ the minimal regular model X of C over Z.)
+
+ EXAMPLES::
+
+ sage: x = polygen(QQ)
+ sage: pari.genus2red(x^3 - 2*x^2 - 2*x + 1, -5*x^5)
+ [1416875, [2, -1; 5, 4; 2267, 1], x^6 - 240*x^4 - 2550*x^3 - 11400*x^2 - 24100*x - 19855, [[2, [2, [Mod(1, 2)]], []], [5, [1, []], ["[V] page 156", [3]]], [2267, [2, [Mod(432, 2267)]], ["[I{1-0-0}] page 170", []]]]]
+ """
+ cdef gen t0 = objtogen(Q)
+ cdef gen t1 = objtogen(P)
+ pari_catch_sig_on()
+ return self.new_gen(genus2red(t0.g, t1.g, NULL))
+
cdef int init_stack(size_t requested_size) except -1:
r"""
diff --git a/src/sage/matrix/matrix_rational_dense.pyx b/src/sage/matrix/matrix_rational_dense.pyx
index cd1ccda..781db98 100644
--- a/src/sage/matrix/matrix_rational_dense.pyx
+++ b/src/sage/matrix/matrix_rational_dense.pyx
@@ -2617,7 +2617,7 @@ cdef class Matrix_rational_dense(matrix_dense.Matrix_dense):
sage: matrix(QQ,2,[1,2,2,4])._invert_pari()
Traceback (most recent call last):
...
- PariError: non invertible matrix in gauss
+ PariError: impossible inverse in ginv: 0
"""
if self._nrows != self._ncols:
raise ValueError("self must be a square matrix")
diff --git a/src/sage/modular/cusps_nf.py b/src/sage/modular/cusps_nf.py
index 214172a..75c4519 100644
--- a/src/sage/modular/cusps_nf.py
+++ b/src/sage/modular/cusps_nf.py
@@ -41,7 +41,7 @@ Different operations with cusps over a number field:
sage: alpha.ideal()
Fractional ideal (7, a + 3)
sage: alpha.ABmatrix()
- [a + 10, 3*a - 1, 7, 2*a]
+ [a + 10, -3*a + 1, 7, -2*a]
sage: alpha.apply([0, 1, -1,0])
Cusp [7: -a - 10] of Number Field in a with defining polynomial x^2 + 5
@@ -895,7 +895,7 @@ class NFCusp(Element):
Given R a Dedekind domain and A, B ideals of R in inverse classes, an
AB-matrix is a matrix realizing the isomorphism between R+R and A+B.
An AB-matrix associated to a cusp [a1: a2] is an AB-matrix with A the
- ideal associated to the cusp (A=<a1, a2>) and first column given by
+ ideal associated to the cusp (A=<a1, a2>) and first column given by
the coefficients of the cusp.
EXAMPLES:
@@ -1295,7 +1295,7 @@ def units_mod_ideal(I):
[1]
sage: I = k.ideal(3)
sage: units_mod_ideal(I)
- [1, -a, -1, a]
+ [1, a, -1, -a]
::
diff --git a/src/sage/modular/modform/constructor.py b/src/sage/modular/modform/constructor.py
index d5e5152..5a2f495 100644
--- a/src/sage/modular/modform/constructor.py
+++ b/src/sage/modular/modform/constructor.py
@@ -430,7 +430,7 @@ def Newforms(group, weight=2, base_ring=None, names=None):
base field that is not minimal for that character::
sage: K.<i> = QuadraticField(-1)
- sage: chi = DirichletGroup(5, K)[3]
+ sage: chi = DirichletGroup(5, K)[1]
sage: len(Newforms(chi, 7, names='a'))
1
sage: x = polygen(K); L.<c> = K.extension(x^2 - 402*i)
diff --git a/src/sage/quadratic_forms/quadratic_form__automorphisms.py b/src/sage/quadratic_forms/quadratic_form__automorphisms.py
index 680df6e..e48729b 100644
--- a/src/sage/quadratic_forms/quadratic_form__automorphisms.py
+++ b/src/sage/quadratic_forms/quadratic_form__automorphisms.py
@@ -220,18 +220,16 @@ def short_vector_list_up_to_length(self, len_bound, up_to_sign_flag=False):
...
ValueError: Quadratic form must be positive definite in order to enumerate short vectors
- Sometimes, PARI does not compute short vectors correctly. It returns too long vectors.
-
- ::
+ Check that PARI doesn't return vectors which are too long::
sage: Q = QuadraticForm(matrix(2, [72, 12, 12, 120]))
sage: len_bound_pari = 2*22953421 - 2; len_bound_pari
45906840
sage: vs = list(Q._pari_().qfminim(len_bound_pari)[2]) # long time (18s on sage.math, 2014)
sage: v = vs[0]; v # long time
- [-65, 623]~
+ [-66, 623]~
sage: v.Vec() * Q._pari_() * v # long time
- 45907800
+ 45902280
"""
if not self.is_positive_definite() :
raise ValueError( "Quadratic form must be positive definite in order to enumerate short vectors" )
@@ -256,11 +254,9 @@ def short_vector_list_up_to_length(self, len_bound, up_to_sign_flag=False):
# Sort the vectors into lists by their length
vec_sorted_list = [list() for i in range(len_bound)]
for i in range(len(parilist)):
- length = ZZ(parilens[i])
- # PARI can sometimes return longer vectors than requested.
- # E.g. : self.matrix() == matrix(2, [72, 12, 12, 120])
- # len_bound = 22953421
- # gives maximal length 22955664
+ length = int(parilens[i])
+ # In certain trivial cases, PARI can sometimes return longer
+ # vectors than requested.
if length < len_bound:
v = parilist[i]
sagevec = V(list(parilist[i]))
diff --git a/src/sage/rings/arith.py b/src/sage/rings/arith.py
index b9efb9f..2755682 100644
--- a/src/sage/rings/arith.py
+++ b/src/sage/rings/arith.py
@@ -2443,7 +2443,7 @@ def factor(n, proof=None, int_=False, algorithm='pari', verbose=0, **kwds):
sage: K.<i> = QuadraticField(-1)
sage: factor(122 - 454*i)
- (-1) * (-i - 4) * (-3*i - 2) * (-i - 2)^3 * (i + 1)^3
+ (-3*i - 2) * (-i - 2)^3 * (i + 1)^3 * (i + 4)
To access the data in a factorization::
@@ -4530,6 +4530,8 @@ def hilbert_symbol(a, b, p, algorithm="pari"):
b = QQ(b).numerator() * QQ(b).denominator()
if algorithm == "pari":
+ if p == -1:
+ p = 0
return ZZ(pari(a).hilbert(b,p))
elif algorithm == 'direct':
@@ -5386,7 +5388,7 @@ def dedekind_sum(p, q, algorithm='default'):
sage: dedekind_sum(3^54 - 1, 2^93 + 1, algorithm='pari')
459340694971839990630374299870/29710560942849126597578981379
- Pari uses a different definition if the inputs are not coprime::
+ We check consistency of the results::
sage: dedekind_sum(5, 7, algorithm='default')
-1/14
@@ -5399,7 +5401,7 @@ def dedekind_sum(p, q, algorithm='default'):
sage: dedekind_sum(6, 8, algorithm='flint')
-1/8
sage: dedekind_sum(6, 8, algorithm='pari')
- -1/24
+ -1/8
REFERENCES:
diff --git a/src/sage/rings/complex_double.pyx b/src/sage/rings/complex_double.pyx
index ebac16f..936044a 100644
--- a/src/sage/rings/complex_double.pyx
+++ b/src/sage/rings/complex_double.pyx
@@ -2061,8 +2061,8 @@ cdef class ComplexDoubleElement(FieldElement):
The optional argument allows us to omit the fractional part::
- sage: z.eta(omit_frac=True) # abs tol 1e-12
- 0.998129069926 - 8.12769318782e-22*I
+ sage: z.eta(omit_frac=True)
+ 0.998129069926
sage: pi = CDF(pi)
sage: prod([1-exp(2*pi*i*n*z) for n in range(1,10)]) # abs tol 1e-12
0.998129069926 + 4.59084695545e-19*I
@@ -2140,7 +2140,7 @@ cdef class ComplexDoubleElement(FieldElement):
sage: a.agm(b, algorithm='principal')
0.338175462986 - 0.0135326969565*I
sage: a.agm(b, algorithm='pari')
- 0.080689185076 + 0.239036532686*I
+ -0.371591652352 + 0.319894660207*I
Some degenerate cases::
diff --git a/src/sage/rings/complex_number.pyx b/src/sage/rings/complex_number.pyx
index 0a8ce5c..5fa15c9 100644
--- a/src/sage/rings/complex_number.pyx
+++ b/src/sage/rings/complex_number.pyx
@@ -1508,7 +1508,7 @@ cdef class ComplexNumber(sage.structure.element.FieldElement):
sage: z = 1 + i
sage: z.eta(omit_frac=True)
- 0.998129069925959 - 8.12769318...e-22*I
+ 0.998129069925959
sage: prod([1-exp(2*pi*i*n*z) for n in range(1,10)])
0.998129069925958 + 4.59099857829247e-19*I
@@ -1721,13 +1721,13 @@ cdef class ComplexNumber(sage.structure.element.FieldElement):
sage: a.agm(b, algorithm="principal")
0.338175462986180 - 0.0135326969565405*I
sage: a.agm(b, algorithm="pari")
- 0.0806891850759812 + 0.239036532685557*I
+ -0.371591652351761 + 0.319894660206830*I
sage: a.agm(b, algorithm="optimal").abs()
0.490319232466314
sage: a.agm(b, algorithm="principal").abs()
0.338446122230459
sage: a.agm(b, algorithm="pari").abs()
- 0.252287947683910
+ 0.490319232466314
TESTS:
@@ -2021,7 +2021,7 @@ cdef class ComplexNumber(sage.structure.element.FieldElement):
sage: C, i = ComplexField(30).objgen()
sage: (1+i).gamma_inc(2 + 3*i)
- 0.0020969149 - 0.059981914*I
+ 0.002096914... - 0.059981914*I
sage: (1+i).gamma_inc(5)
-0.0013781309 + 0.0065198200*I
sage: C(2).gamma_inc(1 + i)
diff --git a/src/sage/rings/fast_arith.pyx b/src/sage/rings/fast_arith.pyx
index 3a0e304..a224775 100644
--- a/src/sage/rings/fast_arith.pyx
+++ b/src/sage/rings/fast_arith.pyx
@@ -46,7 +46,7 @@ include "sage/ext/stdsage.pxi"
include "sage/libs/pari/decl.pxi"
cdef extern from "pari/pari.h":
- cdef long NEXT_PRIME_VIADIFF(long, unsigned char*)
+ cdef long NEXT_PRIME_VIADIFF(long, byteptr)
from sage.rings.integer_ring import ZZ
from sage.libs.pari.gen cimport gen as pari_gen
@@ -84,7 +84,8 @@ cpdef prime_range(start, stop=None, algorithm="pari_primes", bint py_ints=False)
- ``py_ints`` -- boolean (default False), return Python ints rather than Sage Integers (faster)
- EXAMPLES:
+ EXAMPLES::
+
sage: prime_range(10)
[2, 3, 5, 7]
sage: prime_range(7)
@@ -110,21 +111,31 @@ cpdef prime_range(start, stop=None, algorithm="pari_primes", bint py_ints=False)
sage: type(prime_range(8,algorithm="pari_isprime")[0])
<type 'sage.rings.integer.Integer'>
- TESTS:
- sage: len(prime_range(25000,2500000))
+ TESTS::
+
+ sage: prime_range(-1)
+ []
+ sage: L = prime_range(25000,2500000)
+ sage: len(L)
180310
- sage: prime_range(2500000)[-1].is_prime()
- True
+ sage: L[-10:]
+ [2499923, 2499941, 2499943, 2499947, 2499949, 2499953, 2499967, 2499983, 2499989, 2499997]
+
+ A non-trivial range without primes::
+
+ sage: prime_range(4652360, 4652400)
+ []
AUTHORS:
- - William Stein (original version)
- - Craig Citro (rewrote for massive speedup)
- - Kevin Stueve (added primes iterator option) 2010-10-16
- - Robert Bradshaw (speedup using Pari prime table, py_ints option)
+
+ - William Stein (original version)
+ - Craig Citro (rewrote for massive speedup)
+ - Kevin Stueve (added primes iterator option) 2010-10-16
+ - Robert Bradshaw (speedup using Pari prime table, py_ints option)
"""
cdef Integer z
- cdef long c_start, c_stop, p
- cdef unsigned char* pari_prime_ptr
+ cdef long c_start, c_stop, p, maxpr
+ cdef byteptr pari_prime_ptr
if algorithm == "pari_primes":
if stop is None:
# In this case, "start" is really stop
@@ -133,13 +144,18 @@ cpdef prime_range(start, stop=None, algorithm="pari_primes", bint py_ints=False)
else:
c_start = start
c_stop = stop
- if c_stop <= c_start:
- return []
if c_start < 1:
c_start = 1
+ if c_stop <= c_start:
+ return []
+
if maxprime() < c_stop:
- pari.init_primes(c_stop)
- pari_prime_ptr = <unsigned char*>diffptr
+ # Adding 1500 should be sufficient to guarantee an
+ # additional prime, given that c_stop < 2^63.
+ pari.init_primes(c_stop + 1500)
+ assert maxprime() >= c_stop
+
+ pari_prime_ptr = diffptr
p = 0
res = []
while p < c_start:
diff --git a/src/sage/rings/finite_rings/element_ext_pari.py b/src/sage/rings/finite_rings/element_ext_pari.py
index 074c2c4..cb76e70 100644
--- a/src/sage/rings/finite_rings/element_ext_pari.py
+++ b/src/sage/rings/finite_rings/element_ext_pari.py
@@ -284,20 +284,20 @@ class FiniteField_ext_pariElement(FinitePolyExtElement):
if not value:
value = [0]
try:
- # First, try the conversion directly in PARI. This
- # should cover the most common cases, like converting
- # from integers or intmods.
# Convert the list to PARI, then mod out the
- # characteristic (PARI can do this directly for lists),
- # convert to a polynomial with variable "a" and finally
- # mod out the field modulus.
- self.__value = pari(value).Mod(parent.characteristic()).Polrev("a").Mod(parent._pari_modulus())
+ # characteristic (PARI can do this directly for lists).
+ # If we get only INTMODs, we can do the conversion
+ # directly.
+ parilist = pari(value).Mod(parent.characteristic())
+ if not all(c.type() == "t_INTMOD" for c in parilist):
+ raise RuntimeError
except RuntimeError:
# That didn't work, do it in a more general but also
# slower way: first convert all list elements to the
# prime field.
GFp = parent.prime_subfield()
- self.__value = pari([GFp(c) for c in value]).Polrev("a").Mod(parent._pari_modulus())
+ parilist = pari([GFp(c) for c in value])
+ self.__value = parilist.Polrev("a").Mod(parent._pari_modulus())
elif isinstance(value, str):
raise TypeError("value must not be a string")
else:
diff --git a/src/sage/rings/finite_rings/finite_field_prime_modn.py b/src/sage/rings/finite_rings/finite_field_prime_modn.py
index a3b3044..b66b1e3 100644
--- a/src/sage/rings/finite_rings/finite_field_prime_modn.py
+++ b/src/sage/rings/finite_rings/finite_field_prime_modn.py
@@ -168,7 +168,7 @@ class FiniteField_prime_modn(FiniteField_generic, integer_mod_ring.IntegerModRin
sage: RF13 = K.residue_field(pp)
sage: RF13.hom([GF(13)(1)])
Ring morphism:
- From: Residue field of Fractional ideal (w - 18)
+ From: Residue field of Fractional ideal (-w + 18)
To: Finite Field of size 13
Defn: 1 |--> 1
"""
diff --git a/src/sage/rings/integer.pyx b/src/sage/rings/integer.pyx
index 943036d..34b5f2c 100644
--- a/src/sage/rings/integer.pyx
+++ b/src/sage/rings/integer.pyx
@@ -4746,8 +4746,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
sage: 3._bnfisnorm(QuadraticField(-1, 'i'))
(1, 3)
sage: 7._bnfisnorm(CyclotomicField(7))
- (-zeta7 + 1, 1) # 64-bit
- (-zeta7^5 + zeta7^4, 1) # 32-bit
+ (zeta7^5 - zeta7, 1)
"""
from sage.rings.rational_field import QQ
return QQ(self)._bnfisnorm(K, proof=proof, extra_primes=extra_primes)
diff --git a/src/sage/rings/number_field/class_group.py b/src/sage/rings/number_field/class_group.py
index a69a3ad..210a28c 100644
--- a/src/sage/rings/number_field/class_group.py
+++ b/src/sage/rings/number_field/class_group.py
@@ -223,7 +223,7 @@ class FractionalIdealClass(AbelianGroupWithValuesElement):
sage: k.<a> = NumberField(x^2 + 20072); G = k.class_group(); G
Class group of order 76 with structure C38 x C2
of Number Field in a with defining polynomial x^2 + 20072
- sage: I = (G.0)^35; I
+ sage: I = (G.0)^11; I
Fractional ideal class (41, 1/2*a + 5)
sage: J = G(I.ideal()^5); J
Fractional ideal class (115856201, 1/2*a + 40407883)
@@ -471,7 +471,7 @@ class ClassGroup(AbelianGroupWithValues_class):
Class group of order 68 with structure C34 x C2 of Number Field
in a with defining polynomial x^2 + x + 23899
sage: C.gens()
- (Fractional ideal class (23, a + 14), Fractional ideal class (5, a + 3))
+ (Fractional ideal class (7, a + 5), Fractional ideal class (5, a + 3))
sage: C.ngens()
2
"""
diff --git a/src/sage/rings/number_field/galois_group.py b/src/sage/rings/number_field/galois_group.py
index fbb4ab0..0189900 100644
--- a/src/sage/rings/number_field/galois_group.py
+++ b/src/sage/rings/number_field/galois_group.py
@@ -404,10 +404,12 @@ class GaloisGroup_v2(PermutationGroup_generic):
EXAMPLE::
- sage: L = CyclotomicField(7)
+ sage: L.<z> = CyclotomicField(7)
sage: G = L.galois_group()
- sage: G.complex_conjugation()
- (1,6)(2,3)(4,5)
+ sage: conj = G.complex_conjugation(); conj
+ (1,4)(2,5)(3,6)
+ sage: conj(z)
+ -z^5 - z^4 - z^3 - z^2 - z - 1
An example where the field is not CM, so complex conjugation really
depends on the choice of embedding::
diff --git a/src/sage/rings/number_field/maps.py b/src/sage/rings/number_field/maps.py
index 1f59062..d262818 100644
--- a/src/sage/rings/number_field/maps.py
+++ b/src/sage/rings/number_field/maps.py
@@ -302,12 +302,12 @@ class MapRelativeVectorSpaceToRelativeNumberField(NumberFieldIsomorphism):
# Apply to_B, so now each coefficient is in an absolute field,
# and is expressed in terms of a polynomial in y, then make
# the PARI poly in x.
- w = [pari(to_B(a).polynomial('y')) for a in w]
+ w = [to_B(a)._pari_('y') for a in w]
h = pari(w).Polrev()
# Next we write the poly in x over a poly in y in terms
# of an absolute polynomial for the rnf.
- g = self.__R(self.__rnf.rnfeltreltoabs(h))
+ g = self.__rnf.rnfeltreltoabs(h)
return self.__K._element_class(self.__K, g)
class MapRelativeNumberFieldToRelativeVectorSpace(NumberFieldIsomorphism):
diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
index 08624f0..86cba05 100644
--- a/src/sage/rings/number_field/number_field.py
+++ b/src/sage/rings/number_field/number_field.py
@@ -2632,9 +2632,9 @@ class NumberField_generic(number_field_base.NumberField):
sage: K.<a> = NumberField(x^2 + 23)
sage: d = K.ideals_of_bdd_norm(10)
sage: for n in d:
- ... print n
- ... for I in d[n]:
- ... print I
+ ....: print n
+ ....: for I in d[n]:
+ ....: print I
1
Fractional ideal (1)
2
@@ -2649,13 +2649,13 @@ class NumberField_generic(number_field_base.NumberField):
Fractional ideal (4, 1/2*a + 5/2)
5
6
- Fractional ideal (-1/2*a + 1/2)
+ Fractional ideal (1/2*a - 1/2)
Fractional ideal (6, 1/2*a + 5/2)
Fractional ideal (6, 1/2*a + 7/2)
Fractional ideal (1/2*a + 1/2)
7
8
- Fractional ideal (-1/2*a - 3/2)
+ Fractional ideal (1/2*a + 3/2)
Fractional ideal (4, a - 1)
Fractional ideal (4, a + 1)
Fractional ideal (1/2*a - 3/2)
@@ -3101,7 +3101,9 @@ class NumberField_generic(number_field_base.NumberField):
return self.__pari_nf
except AttributeError:
f = self.pari_polynomial("y")
- self.__pari_nf = pari([f, self._pari_integral_basis(important=important)]).nfinit()
+ if f.poldegree() > 1:
+ f = pari([f, self._pari_integral_basis(important=important)])
+ self.__pari_nf = f.nfinit()
return self.__pari_nf
def pari_zk(self):
@@ -3184,7 +3186,7 @@ class NumberField_generic(number_field_base.NumberField):
sage: len(k.pari_bnf())
10
sage: k.pari_bnf()[:4]
- [[;], matrix(0,7), [;], ...]
+ [[;], matrix(0,3), [;], ...]
sage: len(k.pari_nf())
9
sage: k.<a> = NumberField(x^7 + 7); k
@@ -3545,8 +3547,8 @@ class NumberField_generic(number_field_base.NumberField):
14/13*a^2 + 267/13*a - 85/13,
7/13*a^2 + 127/13*a - 49/13,
-1,
- 1/13*a^2 + 20/13*a - 7/13,
- 1/13*a^2 - 19/13*a + 6/13],
+ 1/13*a^2 - 19/13*a + 6/13,
+ 1/13*a^2 - 19/13*a - 7/13],
[(Fractional ideal (11, a - 2), 2),
(Fractional ideal (19, 1/13*a^2 - 45/13*a - 332/13), 2)])
"""
@@ -3645,7 +3647,7 @@ class NumberField_generic(number_field_base.NumberField):
sage: K.<a> = NumberField(x^3 - 381 * x + 127)
sage: K.selmer_group(K.primes_above(13), 2)
- [-7/13*a^2 - 140/13*a + 36/13, 14/13*a^2 + 267/13*a - 85/13, 7/13*a^2 + 127/13*a - 49/13, -1, 1/13*a^2 + 20/13*a - 7/13, 1/13*a^2 - 19/13*a + 6/13, -2/13*a^2 - 53/13*a + 92/13, 10/13*a^2 + 44/13*a - 4555/13]
+ [-7/13*a^2 - 140/13*a + 36/13, 14/13*a^2 + 267/13*a - 85/13, 7/13*a^2 + 127/13*a - 49/13, -1, 1/13*a^2 - 19/13*a + 6/13, 1/13*a^2 - 19/13*a - 7/13, 2/13*a^2 + 53/13*a - 92/13, 10/13*a^2 + 44/13*a - 4555/13]
"""
units, clgp_gens = self._S_class_group_and_units(tuple(S), proof=proof)
gens = []
@@ -4197,19 +4199,19 @@ class NumberField_generic(number_field_base.NumberField):
Here are the factors::
sage: fi, fj = K.factor(17); fi,fj
- ((Fractional ideal (4*I + 1), 1), (Fractional ideal (-I - 4), 1))
+ ((Fractional ideal (I - 4), 1), (Fractional ideal (I + 4), 1))
Now we extract the reduced form of the generators::
sage: zi = fi[0].gens_reduced()[0]; zi
- 4*I + 1
+ I - 4
sage: zj = fj[0].gens_reduced()[0]; zj
- -I - 4
+ I + 4
We recover the integer that was factored in `\ZZ[i]` (up to a unit)::
sage: zi*zj
- -17*I
+ -17
One can also factor elements or ideals of the number field::
@@ -4219,15 +4221,14 @@ class NumberField_generic(number_field_base.NumberField):
sage: K.factor(1+a)
Fractional ideal (a + 1)
sage: K.factor(1+a/5)
- (Fractional ideal (-3*a - 2)) * (Fractional ideal (a + 1)) * (Fractional ideal (-a - 2))^-1 * (Fractional ideal (a - 2))^-1
+ (Fractional ideal (-3*a - 2)) * (Fractional ideal (a + 1)) * (Fractional ideal (-a - 2))^-1 * (Fractional ideal (2*a + 1))^-1
An example over a relative number field::
sage: pari('setrand(2)')
sage: L.<b> = K.extension(x^2 - 7)
sage: f = L.factor(a + 1); f
- (Fractional ideal (-1/2*a*b - a - 1/2)) * (Fractional ideal (1/2*b + 1/2*a - 1)) # 32-bit
- (Fractional ideal (1/2*a*b + a + 1/2)) * (Fractional ideal (-1/2*b - 1/2*a + 1)) # 64-bit
+ (Fractional ideal (1/2*a*b - a + 1/2)) * (Fractional ideal (-1/2*a*b - a + 1/2))
sage: f.value() == a+1
True
@@ -4553,8 +4554,7 @@ class NumberField_generic(number_field_base.NumberField):
except (AttributeError, KeyError):
f = self.pari_polynomial("y")
if len(v) > 0:
- m = self._pari_disc_factorization_matrix(v)
- B = f.nfbasis(fa = m)
+ B = f.nfbasis(fa=v)
elif self._assume_disc_small:
B = f.nfbasis(1)
elif not important:
@@ -4575,34 +4575,6 @@ class NumberField_generic(number_field_base.NumberField):
self._integral_basis_dict[v] = B
return B
- def _pari_disc_factorization_matrix(self, v):
- """
- Returns a PARI matrix representation for the partial
- factorization of the discriminant of the defining polynomial
- of self, defined by the list of primes in the Python list v.
- This function is used internally by the number fields code.
-
- EXAMPLES::
-
- sage: x = polygen(QQ,'x')
- sage: f = x^3 + 17*x + 393; f.discriminant().factor()
- -1 * 5^2 * 29 * 5779
- sage: K.<a> = NumberField(f)
- sage: fa = K._pari_disc_factorization_matrix([5,29]); fa
- [5, 2; 29, 1]
- sage: fa.type()
- 't_MAT'
- """
- f = self.pari_polynomial()
- m = pari.matrix(len(v), 2)
- d = f.poldisc()
- for i in range(len(v)):
- p = pari(ZZ(v[i]))
- m[i,0] = p
- m[i,1] = d.valuation(p)
- return m
-
-
def reduced_basis(self, prec=None):
r"""
This function returns an LLL-reduced basis for the
@@ -5299,7 +5271,14 @@ class NumberField_generic(number_field_base.NumberField):
sage: K.units(proof=True) # takes forever, not tested
...
sage: K.units(proof=False) # result not independently verified
- (a^9 + a - 1, a^16 - a^15 + a^14 - a^12 + a^11 - a^10 - a^8 + a^7 - 2*a^6 + a^4 - 3*a^3 + 2*a^2 - 2*a + 1, 2*a^16 - a^14 - a^13 + 3*a^12 - 2*a^10 + a^9 + 3*a^8 - 3*a^6 + 3*a^5 + 3*a^4 - 2*a^3 - 2*a^2 + 3*a + 4, a^15 + a^14 + 2*a^11 + a^10 - a^9 + a^8 + 2*a^7 - a^5 + 2*a^3 - a^2 - 3*a + 1, a^16 + a^15 + a^14 + a^13 + a^12 + a^11 + a^10 + a^9 + a^8 + a^7 + a^6 + a^5 + a^4 + a^3 + a^2 - 2, 2*a^16 - 3*a^15 + 3*a^14 - 3*a^13 + 3*a^12 - a^11 + a^9 - 3*a^8 + 4*a^7 - 5*a^6 + 6*a^5 - 4*a^4 + 3*a^3 - 2*a^2 - 2*a + 4, a^15 - a^12 + a^10 - a^9 - 2*a^8 + 3*a^7 + a^6 - 3*a^5 + a^4 + 4*a^3 - 3*a^2 - 2*a + 2, 2*a^16 + a^15 - a^11 - 3*a^10 - 4*a^9 - 4*a^8 - 4*a^7 - 5*a^6 - 7*a^5 - 8*a^4 - 6*a^3 - 5*a^2 - 6*a - 7)
+ (a^9 + a - 1,
+ a^15 - a^12 + a^10 - a^9 - 2*a^8 + 3*a^7 + a^6 - 3*a^5 + a^4 + 4*a^3 - 3*a^2 - 2*a + 2,
+ a^16 - a^15 + a^14 - a^12 + a^11 - a^10 - a^8 + a^7 - 2*a^6 + a^4 - 3*a^3 + 2*a^2 - 2*a + 1,
+ 2*a^16 - a^14 - a^13 + 3*a^12 - 2*a^10 + a^9 + 3*a^8 - 3*a^6 + 3*a^5 + 3*a^4 - 2*a^3 - 2*a^2 + 3*a + 4,
+ 2*a^16 - 3*a^15 + 3*a^14 - 3*a^13 + 3*a^12 - a^11 + a^9 - 3*a^8 + 4*a^7 - 5*a^6 + 6*a^5 - 4*a^4 + 3*a^3 - 2*a^2 - 2*a + 4,
+ a^16 - a^15 - 3*a^14 - 4*a^13 - 4*a^12 - 3*a^11 - a^10 + 2*a^9 + 4*a^8 + 5*a^7 + 4*a^6 + 2*a^5 - 2*a^4 - 6*a^3 - 9*a^2 - 9*a - 7,
+ a^15 + a^14 + 2*a^11 + a^10 - a^9 + a^8 + 2*a^7 - a^5 + 2*a^3 - a^2 - 3*a + 1,
+ 5*a^16 - 6*a^14 + a^13 + 7*a^12 - 2*a^11 - 7*a^10 + 4*a^9 + 7*a^8 - 6*a^7 - 7*a^6 + 8*a^5 + 6*a^4 - 11*a^3 - 5*a^2 + 13*a + 4)
"""
proof = proof_flag(proof)
@@ -5371,7 +5350,7 @@ class NumberField_generic(number_field_base.NumberField):
sage: U.gens()
(u0, u1, u2, u3, u4, u5, u6, u7, u8)
sage: U.gens_values() # result not independently verified
- [-1, a^9 + a - 1, a^16 - a^15 + a^14 - a^12 + a^11 - a^10 - a^8 + a^7 - 2*a^6 + a^4 - 3*a^3 + 2*a^2 - 2*a + 1, 2*a^16 - a^14 - a^13 + 3*a^12 - 2*a^10 + a^9 + 3*a^8 - 3*a^6 + 3*a^5 + 3*a^4 - 2*a^3 - 2*a^2 + 3*a + 4, a^15 + a^14 + 2*a^11 + a^10 - a^9 + a^8 + 2*a^7 - a^5 + 2*a^3 - a^2 - 3*a + 1, a^16 + a^15 + a^14 + a^13 + a^12 + a^11 + a^10 + a^9 + a^8 + a^7 + a^6 + a^5 + a^4 + a^3 + a^2 - 2, 2*a^16 - 3*a^15 + 3*a^14 - 3*a^13 + 3*a^12 - a^11 + a^9 - 3*a^8 + 4*a^7 - 5*a^6 + 6*a^5 - 4*a^4 + 3*a^3 - 2*a^2 - 2*a + 4, a^15 - a^12 + a^10 - a^9 - 2*a^8 + 3*a^7 + a^6 - 3*a^5 + a^4 + 4*a^3 - 3*a^2 - 2*a + 2, 2*a^16 + a^15 - a^11 - 3*a^10 - 4*a^9 - 4*a^8 - 4*a^7 - 5*a^6 - 7*a^5 - 8*a^4 - 6*a^3 - 5*a^2 - 6*a - 7]
+ [-1, a^9 + a - 1, a^15 - a^12 + a^10 - a^9 - 2*a^8 + 3*a^7 + a^6 - 3*a^5 + a^4 + 4*a^3 - 3*a^2 - 2*a + 2, a^16 - a^15 + a^14 - a^12 + a^11 - a^10 - a^8 + a^7 - 2*a^6 + a^4 - 3*a^3 + 2*a^2 - 2*a + 1, 2*a^16 - a^14 - a^13 + 3*a^12 - 2*a^10 + a^9 + 3*a^8 - 3*a^6 + 3*a^5 + 3*a^4 - 2*a^3 - 2*a^2 + 3*a + 4, 2*a^16 - 3*a^15 + 3*a^14 - 3*a^13 + 3*a^12 - a^11 + a^9 - 3*a^8 + 4*a^7 - 5*a^6 + 6*a^5 - 4*a^4 + 3*a^3 - 2*a^2 - 2*a + 4, a^16 - a^15 - 3*a^14 - 4*a^13 - 4*a^12 - 3*a^11 - a^10 + 2*a^9 + 4*a^8 + 5*a^7 + 4*a^6 + 2*a^5 - 2*a^4 - 6*a^3 - 9*a^2 - 9*a - 7, a^15 + a^14 + 2*a^11 + a^10 - a^9 + a^8 + 2*a^7 - a^5 + 2*a^3 - a^2 - 3*a + 1, 5*a^16 - 6*a^14 + a^13 + 7*a^12 - 2*a^11 - 7*a^10 + 4*a^9 + 7*a^8 - 6*a^7 - 7*a^6 + 8*a^5 + 6*a^4 - 11*a^3 - 5*a^2 + 13*a + 4]
"""
proof = proof_flag(proof)
@@ -5421,8 +5400,7 @@ class NumberField_generic(number_field_base.NumberField):
sage: U.gens()
(u0, u1, u2, u3)
sage: U.gens_values()
- [-7/275*a^3 + 1/11*a^2 - 9/11*a - 1, 6/275*a^3 - 9/55*a^2 + 14/11*a - 2, 14/275*a^3 - 21/55*a^2 + 29/11*a - 6, 1/275*a^3 + 4/55*a^2 - 5/11*a + 5] # 32-bit
- [-7/275*a^3 + 1/11*a^2 - 9/11*a - 1, 6/275*a^3 - 9/55*a^2 + 14/11*a - 2, -14/275*a^3 + 21/55*a^2 - 29/11*a + 6, 1/275*a^3 + 4/55*a^2 - 5/11*a + 5] # 64-bit
+ [-7/275*a^3 + 1/11*a^2 - 9/11*a - 1, 6/275*a^3 - 9/55*a^2 + 14/11*a - 2, -14/275*a^3 + 21/55*a^2 - 29/11*a + 6, 1/275*a^3 + 4/55*a^2 - 5/11*a + 5]
sage: U.invariants()
(10, 0, 0, 0)
sage: [u.multiplicative_order() for u in U.gens()]
@@ -5566,9 +5544,9 @@ class NumberField_generic(number_field_base.NumberField):
sage: r.<x> = QQ[]
sage: K.<b> = NumberField(x^2+1)
sage: K.zeta(4)
- -b
+ b
sage: K.zeta(4,all=True)
- [-b, b]
+ [b, -b]
sage: K.zeta(3)
Traceback (most recent call last):
...
@@ -5666,7 +5644,7 @@ class NumberField_generic(number_field_base.NumberField):
sage: K.<i> = NumberField(x^2+1)
sage: z = K.primitive_root_of_unity(); z
- -i
+ i
sage: z.multiplicative_order()
4
@@ -5692,11 +5670,11 @@ class NumberField_generic(number_field_base.NumberField):
sage: z.multiplicative_order()
6
- sage: K = CyclotomicField(7)
+ sage: K = CyclotomicField(3)
sage: z = K.primitive_root_of_unity(); z
- zeta7^5 + zeta7^4 + zeta7^3 + zeta7^2 + zeta7 + 1
+ zeta3 + 1
sage: z.multiplicative_order()
- 14
+ 6
TESTS:
@@ -5730,7 +5708,7 @@ class NumberField_generic(number_field_base.NumberField):
sage: K.<b> = NumberField(x^2+1)
sage: zs = K.roots_of_unity(); zs
- [-b, -1, b, 1]
+ [b, -1, -b, 1]
sage: [ z**K.number_of_roots_of_unity() for z in zs ]
[1, 1, 1, 1]
"""
@@ -7795,8 +7773,7 @@ class NumberField_absolute(NumberField_generic):
sage: K.hilbert_conductor(K(2),K(-2))
Fractional ideal (1)
sage: K.hilbert_conductor(K(2*b),K(-2))
- Fractional ideal (-b^2 - b + 2)
-
+ Fractional ideal (b^2 + b - 2)
AUTHOR:
diff --git a/src/sage/rings/number_field/number_field_element.pyx b/src/sage/rings/number_field/number_field_element.pyx
index 91c4d1b..a8dcbeb 100644
--- a/src/sage/rings/number_field/number_field_element.pyx
+++ b/src/sage/rings/number_field/number_field_element.pyx
@@ -329,9 +329,11 @@ cdef class NumberFieldElement(FieldElement):
fmod = f.mod()
for i from 0 <= i <= fmod.poldegree():
if fmod.polcoeff(i).type() in ["t_POL", "t_POLMOD"]:
- # Convert relative element to absolute
- # This returns a polynomial, not a polmod
- f = parent.pari_rnf().rnfeltreltoabs(f)
+ # Convert relative element to absolute.
+ # Sometimes the result is a polynomial,
+ # sometimed a polmod. Lift to convert to a
+ # polynomial in all cases.
+ f = parent.pari_rnf().rnfeltreltoabs(f).lift()
break
# Check that the modulus is actually the defining polynomial
# of the number field.
@@ -1188,7 +1190,7 @@ cdef class NumberFieldElement(FieldElement):
sage: Q.<X> = K[]
sage: L.<b> = NumberField(X^4 + a)
sage: t = (-a).is_norm(L, element=True); t
- (True, -b^3 + 1)
+ (True, b^3 + 1)
sage: t[1].norm(K)
-a
@@ -1289,11 +1291,11 @@ cdef class NumberFieldElement(FieldElement):
sage: Q.<X> = K[]
sage: L.<b> = NumberField(X^4 + a)
sage: t = (-a)._rnfisnorm(L); t
- (-b^3 + 1, 1)
+ (b^3 + 1, 1)
sage: t[0].norm(K)
-a
sage: t = K(3)._rnfisnorm(L); t
- ((a^2 + 1)*b^3 + b^2 - a*b + a^2 + 1, -3*a)
+ ((a^2 + 1)*b^3 - b^2 - a*b - a^2, -3*a^2 + 3*a - 3)
sage: t[0].norm(K)*t[1]
3
@@ -1323,6 +1325,9 @@ cdef class NumberFieldElement(FieldElement):
rnf_data = K.pari_rnfnorm_data(L, proof=proof)
x, q = self._pari_().rnfisnorm(rnf_data)
+
+ # Convert x to an absolute element
+ x = L.pari_rnf().rnfeltreltoabs(x)
return L(x), K(q)
def _mpfr_(self, R):
@@ -1339,7 +1344,7 @@ cdef class NumberFieldElement(FieldElement):
sage: (a^2)._mpfr_(RR)
-1.00000000000000
- Verify that :trac:`#13005` has been fixed::
+ Verify that :trac:`13005` has been fixed::
sage: K.<a> = NumberField(x^2-5)
sage: RR(K(1))
@@ -3813,12 +3818,12 @@ cdef class NumberFieldElement_relative(NumberFieldElement):
sage: K.<a> = NumberField(y^2 + y + 1)
sage: x = polygen(K)
sage: L.<b> = NumberField(x^4 + a*x + 2)
- sage: e = pari(a*b); e
- Mod(-y^4 - 2, y^8 - y^5 + 4*y^4 + y^2 - 2*y + 4)
+ sage: e = (a*b)._pari_('x'); e
+ Mod(-x^4 - 2, x^8 - x^5 + 4*x^4 + x^2 - 2*x + 4)
sage: L(e) # Conversion from PARI absolute number field element
a*b
sage: e = L.pari_rnf().rnfeltabstorel(e); e
- Mod(Mod(y, y^2 + y + 1)*x, x^4 + y*x + 2)
+ Mod(Mod(y, y^2 + y + 1)*x, x^4 + Mod(y, y^2 + y + 1)*x + 2)
sage: L(e) # Conversion from PARI relative number field element
a*b
sage: e = pari('Mod(0, x^8 + 1)'); L(e) # Wrong modulus
@@ -3832,10 +3837,12 @@ cdef class NumberFieldElement_relative(NumberFieldElement):
sage: L(e)
a*b^2 + 1
- Currently, conversions of PARI relative number fields are not checked::
+ This wrong modulus yields a PARI error::
- sage: e = pari('Mod(y*x, x^4 + y^2*x + 2)'); L(e) # Wrong modulus, but succeeds anyway
- a*b
+ sage: e = pari('Mod(y*x, x^4 + y^2*x + 2)'); L(e)
+ Traceback (most recent call last):
+ ...
+ PariError: inconsistent moduli in rnfeltreltoabs: x^4 + y^2*x + 2 != y^2 + y + 1
"""
NumberFieldElement.__init__(self, parent, f)
diff --git a/src/sage/rings/number_field/number_field_ideal.py b/src/sage/rings/number_field/number_field_ideal.py
index 51dadd8..2092543 100644
--- a/src/sage/rings/number_field/number_field_ideal.py
+++ b/src/sage/rings/number_field/number_field_ideal.py
@@ -83,14 +83,17 @@ def convert_from_idealprimedec_form(field, ideal):
sage: K_bnf = gp(K.pari_bnf())
sage: ideal = K_bnf.idealprimedec(3)[1]
sage: convert_from_idealprimedec_form(K, ideal)
+ doctest:...: DeprecationWarning: convert_from_idealprimedec_form() is deprecated
+ See http://trac.sagemath.org/15767 for details.
Fractional ideal (-a)
sage: K.factor(3)
(Fractional ideal (-a))^2
-
"""
- # This indexation is very ugly and should be dealt with in #10002
+ from sage.misc.superseded import deprecation
+ deprecation(15767, "convert_from_idealprimedec_form() is deprecated")
+
p = ZZ(ideal[1])
- alpha = field(field.pari_nf().getattr('zk') * ideal[2])
+ alpha = field(field.pari_zk() * ideal[2])
return field.ideal(p, alpha)
def convert_to_idealprimedec_form(field, ideal):
@@ -116,16 +119,13 @@ def convert_to_idealprimedec_form(field, ideal):
sage: K.<a> = NumberField(x^2 + 3)
sage: P = K.ideal(a/2-3/2)
sage: convert_to_idealprimedec_form(K, P)
- [3, [1, 2]~, 2, 1, [1, -1]~]
-
+ doctest:...: DeprecationWarning: convert_to_idealprimedec_form() is deprecated, use ideal.pari_prime() instead
+ See http://trac.sagemath.org/15767 for details.
+ [3, [1, 2]~, 2, 1, [1, 1; -1, 2]]
"""
- p = ideal.residue_field().characteristic()
- from sage.interfaces.gp import gp
- K_bnf = gp(field.pari_bnf())
- for primedecform in K_bnf.idealprimedec(p):
- if convert_from_idealprimedec_form(field, primedecform) == ideal:
- return primedecform
- raise RuntimeError
+ from sage.misc.superseded import deprecation
+ deprecation(15767, "convert_to_idealprimedec_form() is deprecated, use ideal.pari_prime() instead")
+ return field.ideal(ideal).pari_prime()
class NumberFieldIdeal(Ideal_generic):
"""
@@ -157,7 +157,7 @@ class NumberFieldIdeal(Ideal_generic):
Fractional ideal (3)
sage: F = pari(K).idealprimedec(5)
sage: K.ideal(F[0])
- Fractional ideal (i - 2)
+ Fractional ideal (2*i + 1)
TESTS:
@@ -165,7 +165,7 @@ class NumberFieldIdeal(Ideal_generic):
prime ideal::
sage: K.ideal(pari(K).idealprimedec(5)[0])._pari_prime
- [5, [-2, 1]~, 1, 1, [2, 1]~]
+ [5, [-2, 1]~, 1, 1, [2, -1; 1, 2]]
"""
if not isinstance(field, number_field.NumberField_generic):
raise TypeError("field (=%s) must be a number field."%field)
@@ -195,8 +195,8 @@ class NumberFieldIdeal(Ideal_generic):
EXAMPLES::
sage: NumberField(x^2 + 1, 'a').ideal(7).__hash__()
- -9223372036854775779 # 64-bit
- -2147483619 # 32-bit
+ 848642427 # 32-bit
+ 3643975048496365947 # 64-bit
"""
try:
return self._hash
@@ -313,7 +313,7 @@ class NumberFieldIdeal(Ideal_generic):
sage: A = K.ideal([5, 2 + I])
sage: B = K.ideal([13, 5 + 12*I])
sage: A*B
- Fractional ideal (-4*I + 7)
+ Fractional ideal (4*I - 7)
sage: (K.ideal(3 + I) * K.ideal(7 + I)).gens()
(10*I + 20,)
@@ -1060,7 +1060,7 @@ class NumberFieldIdeal(Ideal_generic):
sage: K.ideal(3).pari_prime()
[3, [3, 0]~, 1, 2, 1]
sage: K.ideal(2+i).pari_prime()
- [5, [2, 1]~, 1, 1, [-2, 1]~]
+ [5, [2, 1]~, 1, 1, [-2, -1; 1, -2]]
sage: K.ideal(2).pari_prime()
Traceback (most recent call last):
...
@@ -2238,7 +2238,7 @@ class NumberFieldFractionalIdeal(NumberFieldIdeal):
sage: I = K.ideal((3+4*i)/5); I
Fractional ideal (4/5*i + 3/5)
sage: I.denominator()
- Fractional ideal (i - 2)
+ Fractional ideal (2*i + 1)
sage: I.numerator()
Fractional ideal (-i - 2)
sage: I.numerator().is_integral() and I.denominator().is_integral()
@@ -2268,7 +2268,7 @@ class NumberFieldFractionalIdeal(NumberFieldIdeal):
sage: I = K.ideal((3+4*i)/5); I
Fractional ideal (4/5*i + 3/5)
sage: I.denominator()
- Fractional ideal (i - 2)
+ Fractional ideal (2*i + 1)
sage: I.numerator()
Fractional ideal (-i - 2)
sage: I.numerator().is_integral() and I.denominator().is_integral()
@@ -2999,15 +2999,15 @@ class NumberFieldFractionalIdeal(NumberFieldIdeal):
An example of reduction maps to the residue field: these are
defined on the whole valuation ring, i.e. the subring of the
number field consisting of elements with non-negative
- valuation. This shows that the issue raised in trac \#1951
+ valuation. This shows that the issue raised in :trac:`1951`
has been fixed::
sage: K.<i> = NumberField(x^2 + 1)
sage: P1, P2 = [g[0] for g in K.factor(5)]; (P1,P2)
- (Fractional ideal (-i - 2), Fractional ideal (i - 2))
+ (Fractional ideal (-i - 2), Fractional ideal (2*i + 1))
sage: a = 1/(1+2*i)
sage: F1, F2 = [g.residue_field() for g in [P1,P2]]; (F1,F2)
- (Residue field of Fractional ideal (-i - 2), Residue field of Fractional ideal (i - 2))
+ (Residue field of Fractional ideal (-i - 2), Residue field of Fractional ideal (2*i + 1))
sage: a.valuation(P1)
0
sage: F1(i/7)
@@ -3018,7 +3018,7 @@ class NumberFieldFractionalIdeal(NumberFieldIdeal):
-1
sage: F2(a)
Traceback (most recent call last):
- ZeroDivisionError: Cannot reduce field element -2/5*i + 1/5 modulo Fractional ideal (i - 2): it has negative valuation
+ ZeroDivisionError: Cannot reduce field element -2/5*i + 1/5 modulo Fractional ideal (2*i + 1): it has negative valuation
An example with a relative number field::
@@ -3058,7 +3058,7 @@ class NumberFieldFractionalIdeal(NumberFieldIdeal):
sage: K.<a> = NumberField(x^5 + 2); K
Number Field in a with defining polynomial x^5 + 2
sage: f = K.factor(19); f
- (Fractional ideal (a^2 + a - 3)) * (Fractional ideal (-2*a^4 - a^2 + 2*a - 1)) * (Fractional ideal (-a^2 - a + 1))
+ (Fractional ideal (a^2 + a - 3)) * (Fractional ideal (-2*a^4 - a^2 + 2*a - 1)) * (Fractional ideal (a^2 + a - 1))
sage: [i.residue_class_degree() for i, _ in f]
[2, 2, 1]
"""
diff --git a/src/sage/rings/number_field/number_field_ideal_rel.py b/src/sage/rings/number_field/number_field_ideal_rel.py
index ba6fab5..6f50855 100644
--- a/src/sage/rings/number_field/number_field_ideal_rel.py
+++ b/src/sage/rings/number_field/number_field_ideal_rel.py
@@ -114,12 +114,12 @@ class NumberFieldFractionalIdeal_rel(NumberFieldFractionalIdeal):
sage: K.<a, b> = NumberField([x^2 + 23, x^2 - 7])
sage: I = K.ideal(2, (a + 2*b + 3)/2)
sage: I.pari_rhnf()
- [[1, -2; 0, 1], [[2, 1; 0, 1], [1/2, 0; 0, 1/2]]]
+ [[1, -2; 0, 1], [[2, 1; 0, 1], 1/2]]
"""
try:
return self.__pari_rhnf
except AttributeError:
- nfzk = self.number_field().absolute_field('a').pari_zk()
+ nfzk = self.number_field().pari_nf().nf_subst('x').nf_get_zk()
rnf = self.number_field().pari_rnf()
L_hnf = self.absolute_ideal().pari_hnf()
self.__pari_rhnf = rnf.rnfidealabstorel(nfzk * L_hnf)
@@ -485,7 +485,7 @@ class NumberFieldFractionalIdeal_rel(NumberFieldFractionalIdeal):
sage: K.<c> = F.extension(Y^2 - (1 + a)*(a + b)*a*b)
sage: I = K.ideal(3, c)
sage: J = I.ideal_below(); J
- Fractional ideal (-b)
+ Fractional ideal (b)
sage: J.number_field() == F
True
"""
diff --git a/src/sage/rings/number_field/number_field_rel.py b/src/sage/rings/number_field/number_field_rel.py
index 3fb70f7..98435fe 100644
--- a/src/sage/rings/number_field/number_field_rel.py
+++ b/src/sage/rings/number_field/number_field_rel.py
@@ -207,7 +207,7 @@ class NumberField_relative(NumberField_generic):
sage: b
Traceback (most recent call last):
...
- PariError: incorrect type in core2partial
+ PariError: incorrect type in core2partial (t_FRAC)
However, if the polynomial is linear, rational coefficients should work::
@@ -1060,7 +1060,7 @@ class NumberField_relative(NumberField_generic):
pol = element.polynomial('y')
t2 = pol(a).lift()
if check:
- t1 = self.pari_rnf().rnfeltreltoabs(pol._pari_())
+ t1 = self.pari_rnf().rnfeltreltoabs(pol).lift()
assert t1 == t2
return t2
@@ -1145,7 +1145,7 @@ class NumberField_relative(NumberField_generic):
sage: k.<a> = NumberField([x^3 + 2, x^2 + 2])
sage: k._pari_base_bnf()
- [[;], matrix(0,9), [;], ... 0]
+ [[;], matrix(0,3), [;], ...]
"""
abs_base, from_abs_base, to_abs_base = self.absolute_base_field()
return abs_base.pari_bnf(proof, units)
@@ -1283,10 +1283,10 @@ class NumberField_relative(NumberField_generic):
Galois conjugate::
sage: for g in G:
- ... if L1.is_isomorphic_relative(L2, g.as_hom()):
- ... print g.as_hom()
+ ....: if L1.is_isomorphic_relative(L2, g.as_hom()):
+ ....: print g.as_hom()
Ring endomorphism of Number Field in z9 with defining polynomial x^6 + x^3 + 1
- Defn: z9 |--> -z9^4 - z9
+ Defn: z9 |--> z9^4
"""
if is_RelativeNumberField(other):
s_base_field = self.base_field()
@@ -1575,7 +1575,7 @@ class NumberField_relative(NumberField_generic):
sage: k.<a> = NumberField([x^4 + 3, x^2 + 2])
sage: k.pari_rnf()
- [x^4 + 3, [], [[108, 0; 0, 108], 3], [8, 0; 0, 8], [], [], [[1, x - 1, x^2 - 1, x^3 - x^2 - x - 3], ..., 0]
+ [x^4 + 3, [[364, -10*x^7 - 87*x^5 - 370*x^3 - 41*x], 1/364], [[108, 0; 0, 108], 3], ...]
"""
return self._pari_base_nf().rnfinit(self.pari_relative_polynomial())
@@ -2317,7 +2317,7 @@ class NumberField_relative(NumberField_generic):
...
ValueError: The element b is not in the base field
"""
- polmodmod_xy = self.pari_rnf().rnfeltabstorel( self(element)._pari_() )
+ polmodmod_xy = self.pari_rnf().rnfeltabstorel( self(element)._pari_('x') )
# polmodmod_xy is a POLMOD with POLMOD coefficients in general.
# These POLMOD coefficients represent elements of the base field K.
# We do two lifts so we get a polynomial. We need the simplify() to
diff --git a/src/sage/rings/number_field/order.py b/src/sage/rings/number_field/order.py
index 99fe015..43d2e25 100644
--- a/src/sage/rings/number_field/order.py
+++ b/src/sage/rings/number_field/order.py
@@ -245,7 +245,7 @@ class Order(IntegralDomain):
sage: k.<a> = NumberField(x^2 + 5077); G = k.class_group(); G
Class group of order 22 with structure C22 of Number Field in a with defining polynomial x^2 + 5077
- sage: G.0
+ sage: G.0 ^ -9
Fractional ideal class (11, a + 7)
sage: Ok = k.maximal_order(); Ok
Maximal Order in Number Field in a with defining polynomial x^2 + 5077
diff --git a/src/sage/rings/number_field/unit_group.py b/src/sage/rings/number_field/unit_group.py
index 6029b83..a8fcc15 100644
--- a/src/sage/rings/number_field/unit_group.py
+++ b/src/sage/rings/number_field/unit_group.py
@@ -173,18 +173,10 @@ class UnitGroup(AbelianGroupWithValues_class):
sage: UK = K.unit_group()
sage: UK.ngens()
6
- sage: UK.gen(0) # random
- -z^11
- sage: UK.gen(1) # random
- z^5 + z^3
- sage: UK.gen(2) # random
- z^6 + z^5
- sage: UK.gen(3) # random
- z^9 + z^7 + z^5
- sage: UK.gen(4) # random
- z^9 + z^5 + z^4 + 1
- sage: UK.gen(5) # random
- z^5 + z
+ sage: UK.gen(5)
+ u5
+ sage: UK.gen(5).value()
+ z^6 + z^4
An S-unit group::
@@ -195,7 +187,7 @@ class UnitGroup(AbelianGroupWithValues_class):
sage: SUK.zeta_order()
26
sage: SUK.log(21*z)
- (6, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1)
+ (13, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1)
"""
# This structure is not a parent in the usual sense. The
# "elements" are NumberFieldElement_absolute. Instead, they should
@@ -427,7 +419,7 @@ class UnitGroup(AbelianGroupWithValues_class):
sage: K.<b> = NumberField(x^2+1)
sage: U = UnitGroup(K)
sage: zs = U.roots_of_unity(); zs
- [-b, -1, b, 1]
+ [b, -1, -b, 1]
sage: [ z**U.zeta_order() for z in zs ]
[1, 1, 1, 1]
"""
@@ -493,9 +485,9 @@ class UnitGroup(AbelianGroupWithValues_class):
sage: K.<b> = NumberField(x^2+1)
sage: U = UnitGroup(K)
sage: U.zeta(4)
- -b
+ b
sage: U.zeta(4,all=True)
- [-b, b]
+ [b, -b]
sage: U.zeta(3)
Traceback (most recent call last):
...
@@ -599,7 +591,7 @@ class UnitGroup(AbelianGroupWithValues_class):
sage: SUK = UnitGroup(K,S=2)
sage: v = (3,1,4,1,5,9,2)
sage: u = SUK.exp(v); u
- -997204*z^11 - 2419728*z^10 - 413812*z^9 - 413812*z^8 - 2419728*z^7 - 997204*z^6 - 2129888*z^4 - 1616524*z^3 + 149364*z^2 - 1616524*z - 2129888
+ 180*z^10 - 280*z^9 + 580*z^8 - 720*z^7 + 948*z^6 - 924*z^5 + 948*z^4 - 720*z^3 + 580*z^2 - 280*z + 180
sage: SUK.log(u)
(3, 1, 4, 1, 5, 9, 2)
sage: SUK.log(u) == v
@@ -645,7 +637,7 @@ class UnitGroup(AbelianGroupWithValues_class):
sage: SUK = UnitGroup(K,S=2)
sage: v = (3,1,4,1,5,9,2)
sage: u = SUK.exp(v); u
- -997204*z^11 - 2419728*z^10 - 413812*z^9 - 413812*z^8 - 2419728*z^7 - 997204*z^6 - 2129888*z^4 - 1616524*z^3 + 149364*z^2 - 1616524*z - 2129888
+ 180*z^10 - 280*z^9 + 580*z^8 - 720*z^7 + 948*z^6 - 924*z^5 + 948*z^4 - 720*z^3 + 580*z^2 - 280*z + 180
sage: SUK.log(u)
(3, 1, 4, 1, 5, 9, 2)
sage: SUK.log(u) == v
diff --git a/src/sage/rings/polynomial/cyclotomic.pyx b/src/sage/rings/polynomial/cyclotomic.pyx
index 8c5adb8..571c9d2 100644
--- a/src/sage/rings/polynomial/cyclotomic.pyx
+++ b/src/sage/rings/polynomial/cyclotomic.pyx
@@ -247,13 +247,16 @@ def cyclotomic_value(n, x):
TESTS::
- sage: K.<i> = NumberField(polygen(QQ)^2 + 1)
sage: R.<x> = QQ[]
- sage: for y in [-1, 0, 1, 2, 1/2, mod(3, 8), GF(9,'a').gen(), Zp(3)(54), i, x^2+2]:
- ... for n in range(1, 61):
- ... val1 = cyclotomic_value(n, y)
- ... val2 = cyclotomic_polynomial(n)(y)
- ... assert val1 == val2 and val1.parent() is val2.parent()
+ sage: K.<i> = NumberField(x^2 + 1)
+ sage: for y in [-1, 0, 1, 2, 1/2, Mod(3, 8), Mod(3,11), GF(9,'a').gen(), Zp(3)(54), i, x^2+2]:
+ ....: for n in [1..60]:
+ ....: val1 = cyclotomic_value(n, y)
+ ....: val2 = cyclotomic_polynomial(n)(y)
+ ....: if val1 != val2:
+ ....: print "Wrong value for cyclotomic_value(%s, %s) in %s"%(n,y,parent(y))
+ ....: if val1.parent() is not val2.parent():
+ ....: print "Wrong parent for cyclotomic_value(%s, %s) in %s"%(n,y,parent(y))
sage: cyclotomic_value(20, I)
5
@@ -275,15 +278,25 @@ def cyclotomic_value(n, x):
1
"""
n = int(n)
- if n == 1:
- return x - 1
- if n <= 0:
- raise ValueError, "n must be positive"
+ if n < 3:
+ if n == 1:
+ return x - 1
+ if n == 2:
+ return x + 1
+ raise ValueError("n must be positive")
+
try:
- return x.parent()(pari.polcyclo_eval(n, x._pari_()))
+ return x.parent()(pari.polcyclo_eval(n, x))
except Exception:
pass
- # The following is modeled on the implementation in Pari
+
+ # The following is modeled on the implementation in PARI and is
+ # used for cases for which PARI doesn't work. These are in
+ # particular:
+ # - n does not fit in a C long;
+ # - x is some Sage type which cannot be converted to PARI;
+ # - PARI's algorithm encounters a zero-divisor which is not zero.
+
factors = factor(n)
cdef Py_ssize_t i, j, ti, L, root_of_unity = -1
primes = [p for p, e in factors]
diff --git a/src/sage/rings/polynomial/padics/polynomial_padic.py b/src/sage/rings/polynomial/padics/polynomial_padic.py
index c8cae05..c99fe1e 100644
--- a/src/sage/rings/polynomial/padics/polynomial_padic.py
+++ b/src/sage/rings/polynomial/padics/polynomial_padic.py
@@ -86,7 +86,7 @@ class Polynomial_padic(Polynomial):
1 (1 + O(3^3))*t + (-1 + O(3^3))
1 (1 + O(3^3))*t^2 + (5 + O(3^3))*t + (-1 + O(3^3))
1 (1 + O(3^3))*t^2 + (-5 + O(3^3))*t + (-1 + O(3^3))
- 1 (1 + O(3^3))*t^2 + (1 + O(3^3))
+ 1 (1 + O(3^3))*t^2 + (0 + O(3^3))*t + (1 + O(3^3))
sage: R.<t> = PolynomialRing(Qp(5,6,print_mode='terse',print_pos=False))
sage: pol = 100 * (5*t - 1) * (t - 5)
sage: pol
diff --git a/src/sage/rings/polynomial/polynomial_element.pyx b/src/sage/rings/polynomial/polynomial_element.pyx
index b81a919..14173df 100644
--- a/src/sage/rings/polynomial/polynomial_element.pyx
+++ b/src/sage/rings/polynomial/polynomial_element.pyx
@@ -3244,9 +3244,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
sage: K.<a> = QuadraticField(p*q)
sage: R.<x> = PolynomialRing(K)
sage: K.pari_polynomial('a').nffactor("x^2+1")
- Traceback (most recent call last):
- ...
- PariError: precision too low in floorr (precision loss in truncation)
+ Mat([x^2 + 1, 1])
sage: factor(x^2 + 1)
x^2 + 1
sage: factor( (x - a) * (x + 2*a) )
@@ -4614,7 +4612,7 @@ cdef class Polynomial(CommutativeAlgebraElement):
sage: pari(f)
Traceback (most recent call last):
...
- PariError: variable must have higher priority in gtopoly
+ PariError: incorrect priority in gtopoly: variable x <= a
Stacked polynomial rings, first with a univariate ring on the
bottom::
diff --git a/src/sage/rings/polynomial/polynomial_quotient_ring.py b/src/sage/rings/polynomial/polynomial_quotient_ring.py
index 8d9975d..99bec5a 100644
--- a/src/sage/rings/polynomial/polynomial_quotient_ring.py
+++ b/src/sage/rings/polynomial/polynomial_quotient_ring.py
@@ -1234,11 +1234,11 @@ class PolynomialQuotientRing_generic(sage.rings.commutative_ring.CommutativeRing
sage: L.<b> = K['y'].quotient(y^3 + 5); L
Univariate Quotient Polynomial Ring in b over Number Field in a with defining polynomial x^2 + 3 with modulus y^3 + 5
sage: L.S_units([])
- [(-1/2*a + 1/2, 6), ((-1/3*a + 1)*b^2 - 4/3*a*b - 4/3*a - 3, +Infinity), (2/3*a*b^2 + (2/3*a + 2)*b - 4/3*a + 3, +Infinity)]
+ [(-1/2*a + 1/2, 6), ((1/3*a - 1)*b^2 + 4/3*a*b + 5/6*a + 7/2, +Infinity), ((-1/3*a + 1)*b^2 + (2/3*a - 2)*b - 5/6*a + 7/2, +Infinity)]
sage: L.S_units([K.ideal(1/2*a - 3/2)])
- [((-1/6*a - 1/2)*b^2 + (1/3*a + 1)*b - 2/3*a - 2, +Infinity), (-1/2*a + 1/2, 6), ((-1/3*a + 1)*b^2 - 4/3*a*b - 4/3*a - 3, +Infinity), (2/3*a*b^2 + (2/3*a + 2)*b - 4/3*a + 3, +Infinity)]
+ [((-1/6*a - 1/2)*b^2 + (1/3*a - 1)*b + 4/3*a, +Infinity), (-1/2*a + 1/2, 6), ((1/3*a - 1)*b^2 + 4/3*a*b + 5/6*a + 7/2, +Infinity), ((-1/3*a + 1)*b^2 + (2/3*a - 2)*b - 5/6*a + 7/2, +Infinity)]
sage: L.S_units([K.ideal(2)])
- [((1/6*a + 1/2)*b^2 + (-1/3*a - 1)*b + 2/3*a + 1, +Infinity), ((-1/6*a - 1/2)*b^2 + (1/3*a + 1)*b - 1/6*a - 3/2, +Infinity), ((-1/2*a + 1/2)*b^2 + (a - 1)*b - 3/2*a + 3/2, +Infinity), (-1/2*a + 1/2, 6), ((-1/3*a + 1)*b^2 - 4/3*a*b - 4/3*a - 3, +Infinity), (2/3*a*b^2 + (2/3*a + 2)*b - 4/3*a + 3, +Infinity)]
+ [((-1/2*a + 1/2)*b^2 + (-a - 1)*b - 3, +Infinity), ((-1/6*a - 1/2)*b^2 + (1/3*a - 1)*b + 5/6*a - 1/2, +Infinity), ((1/6*a + 1/2)*b^2 + (-1/3*a + 1)*b - 5/6*a - 1/2, +Infinity), (-1/2*a + 1/2, 6), ((1/3*a - 1)*b^2 + 4/3*a*b + 5/6*a + 7/2, +Infinity), ((-1/3*a + 1)*b^2 + (2/3*a - 2)*b - 5/6*a + 7/2, +Infinity)]
Note that all the returned values live where we expect them to::
@@ -1314,14 +1314,14 @@ class PolynomialQuotientRing_generic(sage.rings.commutative_ring.CommutativeRing
sage: L.<b> = K['y'].quotient(y^3 + 5); L
Univariate Quotient Polynomial Ring in b over Number Field in a with defining polynomial x^2 + 3 with modulus y^3 + 5
sage: L.units()
- [(-1/2*a + 1/2, 6), ((-1/3*a + 1)*b^2 - 4/3*a*b - 4/3*a - 3, +Infinity), (2/3*a*b^2 + (2/3*a + 2)*b - 4/3*a + 3, +Infinity)]
+ [(-1/2*a + 1/2, 6), ((1/3*a - 1)*b^2 + 4/3*a*b + 5/6*a + 7/2, +Infinity), ((-1/3*a + 1)*b^2 + (2/3*a - 2)*b - 5/6*a + 7/2, +Infinity)]
sage: L.<b> = K.extension(y^3 + 5)
sage: L.unit_group()
Unit group with structure C6 x Z x Z of Number Field in b with defining polynomial x^3 + 5 over its base field
sage: L.unit_group().gens() # abstract generators
(u0, u1, u2)
sage: L.unit_group().gens_values()
- [-1/2*a + 1/2, (-1/3*a + 1)*b^2 - 4/3*a*b - 4/3*a - 3, 2/3*a*b^2 + (2/3*a + 2)*b - 4/3*a + 3]
+ [-1/2*a + 1/2, (1/3*a - 1)*b^2 + 4/3*a*b + 5/6*a + 7/2, (-1/3*a + 1)*b^2 + (2/3*a - 2)*b - 5/6*a + 7/2]
Note that all the returned values live where we expect them to::
diff --git a/src/sage/rings/polynomial/polynomial_rational_flint.pyx b/src/sage/rings/polynomial/polynomial_rational_flint.pyx
index 0c13ffe..e84e148 100644
--- a/src/sage/rings/polynomial/polynomial_rational_flint.pyx
+++ b/src/sage/rings/polynomial/polynomial_rational_flint.pyx
@@ -1568,9 +1568,9 @@ cdef class Polynomial_rational_flint(Polynomial):
sage: R.<x> = QQ[]
sage: f = x^3 - 2
sage: f.factor_padic(2)
- (1 + O(2^10))*x^3 + (2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + 2^9 + O(2^10))
+ (1 + O(2^10))*x^3 + (O(2^10))*x^2 + (O(2^10))*x + (2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 + 2^9 + O(2^10))
sage: f.factor_padic(3)
- (1 + O(3^10))*x^3 + (1 + 2*3 + 2*3^2 + 2*3^3 + 2*3^4 + 2*3^5 + 2*3^6 + 2*3^7 + 2*3^8 + 2*3^9 + O(3^10))
+ (1 + O(3^10))*x^3 + (O(3^10))*x^2 + (O(3^10))*x + (1 + 2*3 + 2*3^2 + 2*3^3 + 2*3^4 + 2*3^5 + 2*3^6 + 2*3^7 + 2*3^8 + 2*3^9 + O(3^10))
sage: f.factor_padic(5)
((1 + O(5^10))*x + (2 + 4*5 + 2*5^2 + 2*5^3 + 5^4 + 3*5^5 + 4*5^7 + 2*5^8 + 5^9 + O(5^10))) * ((1 + O(5^10))*x^2 + (3 + 2*5^2 + 2*5^3 + 3*5^4 + 5^5 + 4*5^6 + 2*5^8 + 3*5^9 + O(5^10))*x + (4 + 5 + 2*5^2 + 4*5^3 + 4*5^4 + 3*5^5 + 3*5^6 + 4*5^7 + 4*5^9 + O(5^10)))
diff --git a/src/sage/rings/qqbar.py b/src/sage/rings/qqbar.py
index 7f5653e..1038bcb 100644
--- a/src/sage/rings/qqbar.py
+++ b/src/sage/rings/qqbar.py
@@ -1635,7 +1635,7 @@ def do_polred(poly):
sage: do_polred(x^2 - x - 11)
(1/3*x + 1/3, 3*x - 1, x^2 - x - 1)
sage: do_polred(x^3 + 123456)
- (-1/4*x, -4*x, x^3 - 1929)
+ (1/4*x, 4*x, x^3 + 1929)
This shows that :trac:`13054` has been fixed::
@@ -1887,11 +1887,11 @@ def number_field_elements_from_algebraics(numbers, minimal=False):
elements, and then mapping them back into ``QQbar``::
sage: (fld,nums,hom) = number_field_elements_from_algebraics((rt2, rt3, qqI, z3))
- sage: fld,nums,hom
- (Number Field in a with defining polynomial y^8 - y^4 + 1, [-a^5 + a^3 + a, a^6 - 2*a^2, -a^6, a^4 - 1], Ring morphism:
- From: Number Field in a with defining polynomial y^8 - y^4 + 1
- To: Algebraic Field
- Defn: a |--> -0.2588190451025208? + 0.9659258262890683?*I)
+ sage: fld,nums,hom # random
+ (Number Field in a with defining polynomial y^8 - y^4 + 1, [-a^5 + a^3 + a, a^6 - 2*a^2, a^6, -a^4], Ring morphism:
+ From: Number Field in a with defining polynomial y^8 - y^4 + 1
+ To: Algebraic Field
+ Defn: a |--> -0.2588190451025208? - 0.9659258262890683?*I)
sage: (nfrt2, nfrt3, nfI, nfz3) = nums
sage: hom(nfrt2)
1.414213562373095? + 0.?e-18*I
@@ -1904,7 +1904,8 @@ def number_field_elements_from_algebraics(numbers, minimal=False):
sage: nfI^2
-1
sage: sum = nfrt2 + nfrt3 + nfI + nfz3; sum
- -a^5 + a^4 + a^3 - 2*a^2 + a - 1
+ -a^5 + a^4 + a^3 - 2*a^2 + a - 1 # 32-bit
+ 2*a^6 - a^5 - a^4 + a^3 - 2*a^2 + a # 64-bit
sage: hom(sum)
2.646264369941973? + 1.866025403784439?*I
sage: hom(sum) == rt2 + rt3 + qqI + z3
diff --git a/src/sage/rings/rational.pyx b/src/sage/rings/rational.pyx
index d4e65c8..51ca79a 100644
--- a/src/sage/rings/rational.pyx
+++ b/src/sage/rings/rational.pyx
@@ -1193,7 +1193,7 @@ cdef class Rational(sage.structure.element.FieldElement):
sage: 0.is_norm(K)
True
sage: (1/7).is_norm(K, element=True)
- (True, -1/7*beta - 3/7)
+ (True, 1/7*beta + 3/7)
sage: (1/10).is_norm(K, element=True)
(False, None)
sage: (1/691).is_norm(QQ, element=True)
diff --git a/src/sage/rings/residue_field.pyx b/src/sage/rings/residue_field.pyx
index 828b638..884ff93 100644
--- a/src/sage/rings/residue_field.pyx
+++ b/src/sage/rings/residue_field.pyx
@@ -19,13 +19,13 @@ monogenic (i.e., 2 is an essential discriminant divisor)::
sage: K.<a> = NumberField(x^3 + x^2 - 2*x + 8)
sage: F = K.factor(2); F
- (Fractional ideal (-1/2*a^2 + 1/2*a - 1)) * (Fractional ideal (-a^2 + 2*a - 3)) * (Fractional ideal (3/2*a^2 - 5/2*a + 4))
+ (Fractional ideal (1/2*a^2 - 1/2*a + 1)) * (Fractional ideal (-a^2 + 2*a - 3)) * (Fractional ideal (-3/2*a^2 + 5/2*a - 4))
sage: F[0][0].residue_field()
- Residue field of Fractional ideal (-1/2*a^2 + 1/2*a - 1)
+ Residue field of Fractional ideal (1/2*a^2 - 1/2*a + 1)
sage: F[1][0].residue_field()
Residue field of Fractional ideal (-a^2 + 2*a - 3)
sage: F[2][0].residue_field()
- Residue field of Fractional ideal (3/2*a^2 - 5/2*a + 4)
+ Residue field of Fractional ideal (-3/2*a^2 + 5/2*a - 4)
We can also form residue fields from `\ZZ`::
@@ -254,9 +254,9 @@ class ResidueFieldFactory(UniqueFactory):
the index of ``ZZ[a]`` in the maximal order for all ``a``::
sage: K.<a> = NumberField(x^3 + x^2 - 2*x + 8); P = K.ideal(2).factor()[0][0]; P
- Fractional ideal (-1/2*a^2 + 1/2*a - 1)
+ Fractional ideal (1/2*a^2 - 1/2*a + 1)
sage: F = K.residue_field(P); F
- Residue field of Fractional ideal (-1/2*a^2 + 1/2*a - 1)
+ Residue field of Fractional ideal (1/2*a^2 - 1/2*a + 1)
sage: F(a)
0
sage: B = K.maximal_order().basis(); B
@@ -266,7 +266,7 @@ class ResidueFieldFactory(UniqueFactory):
sage: F(B[2])
0
sage: F
- Residue field of Fractional ideal (-1/2*a^2 + 1/2*a - 1)
+ Residue field of Fractional ideal (1/2*a^2 - 1/2*a + 1)
sage: F.degree()
1
@@ -692,15 +692,15 @@ class ResidueField_generic(Field):
EXAMPLES::
sage: I = QQ[3^(1/3)].factor(5)[1][0]; I
- Fractional ideal (a - 2)
+ Fractional ideal (-a + 2)
sage: k = I.residue_field(); k
- Residue field of Fractional ideal (a - 2)
+ Residue field of Fractional ideal (-a + 2)
sage: f = k.lift_map(); f
Lifting map:
- From: Residue field of Fractional ideal (a - 2)
+ From: Residue field of Fractional ideal (-a + 2)
To: Maximal Order in Number Field in a with defining polynomial x^3 - 3
sage: f.domain()
- Residue field of Fractional ideal (a - 2)
+ Residue field of Fractional ideal (-a + 2)
sage: f.codomain()
Maximal Order in Number Field in a with defining polynomial x^3 - 3
sage: f(k.0)
@@ -728,7 +728,7 @@ class ResidueField_generic(Field):
sage: K.<a> = NumberField(x^3-11)
sage: F = K.ideal(37).factor(); F
- (Fractional ideal (37, a + 12)) * (Fractional ideal (-2*a + 5)) * (Fractional ideal (37, a + 9))
+ (Fractional ideal (37, a + 12)) * (Fractional ideal (2*a - 5)) * (Fractional ideal (37, a + 9))
sage: k = K.residue_field(F[0][0])
sage: l = K.residue_field(F[1][0])
sage: k == l
@@ -805,7 +805,7 @@ cdef class ReductionMap(Map):
sage: F.reduction_map()
Partially defined reduction map:
From: Number Field in a with defining polynomial x^3 + x^2 - 2*x + 8
- To: Residue field of Fractional ideal (-1/2*a^2 + 1/2*a - 1)
+ To: Residue field of Fractional ideal (1/2*a^2 - 1/2*a + 1)
sage: K.<theta_5> = CyclotomicField(5)
sage: F = K.factor(7)[0][0].residue_field()
@@ -933,10 +933,10 @@ cdef class ReductionMap(Map):
sage: K.<i> = NumberField(x^2 + 1)
sage: P1, P2 = [g[0] for g in K.factor(5)]; (P1,P2)
- (Fractional ideal (-i - 2), Fractional ideal (i - 2))
+ (Fractional ideal (-i - 2), Fractional ideal (2*i + 1))
sage: a = 1/(1+2*i)
sage: F1, F2 = [g.residue_field() for g in [P1,P2]]; (F1,F2)
- (Residue field of Fractional ideal (-i - 2), Residue field of Fractional ideal (i - 2))
+ (Residue field of Fractional ideal (-i - 2), Residue field of Fractional ideal (2*i + 1))
sage: a.valuation(P1)
0
sage: F1(i/7)
@@ -948,7 +948,7 @@ cdef class ReductionMap(Map):
sage: F2(a)
Traceback (most recent call last):
...
- ZeroDivisionError: Cannot reduce field element -2/5*i + 1/5 modulo Fractional ideal (i - 2): it has negative valuation
+ ZeroDivisionError: Cannot reduce field element -2/5*i + 1/5 modulo Fractional ideal (2*i + 1): it has negative valuation
"""
# The reduction map is just x |--> F(to_vs(x) * (PB**(-1))) if
# either x is integral or the denominator of x is coprime to
@@ -1012,7 +1012,7 @@ cdef class ReductionMap(Map):
sage: f = k.convert_map_from(K)
sage: s = f.section(); s
Lifting map:
- From: Residue field in abar of Fractional ideal (-14*a^4 + 24*a^3 + 26*a^2 - 58*a + 15)
+ From: Residue field in abar of Fractional ideal (14*a^4 - 24*a^3 - 26*a^2 + 58*a - 15)
To: Number Field in a with defining polynomial x^5 - 5*x + 2
sage: s(k.gen())
a
@@ -1223,7 +1223,7 @@ cdef class ResidueFieldHomomorphism_global(RingHomomorphism):
sage: f = k.coerce_map_from(K.ring_of_integers())
sage: s = f.section(); s
Lifting map:
- From: Residue field in abar of Fractional ideal (-14*a^4 + 24*a^3 + 26*a^2 - 58*a + 15)
+ From: Residue field in abar of Fractional ideal (14*a^4 - 24*a^3 - 26*a^2 + 58*a - 15)
To: Maximal Order in Number Field in a with defining polynomial x^5 - 5*x + 2
sage: s(k.gen())
a
diff --git a/src/sage/schemes/elliptic_curves/ell_generic.py b/src/sage/schemes/elliptic_curves/ell_generic.py
index 1c3b2bb..be2fd62 100644
--- a/src/sage/schemes/elliptic_curves/ell_generic.py
+++ b/src/sage/schemes/elliptic_curves/ell_generic.py
@@ -565,7 +565,7 @@ class EllipticCurve_generic(plane_curve.ProjectiveCurve_generic):
sage: E = EllipticCurve([0,0,0,-49,0])
sage: T = E.torsion_subgroup()
sage: [E(t) for t in T]
- [(0 : 1 : 0), (7 : 0 : 1), (0 : 0 : 1), (-7 : 0 : 1)]
+ [(0 : 1 : 0), (-7 : 0 : 1), (0 : 0 : 1), (7 : 0 : 1)]
::
@@ -2923,26 +2923,24 @@ class EllipticCurve_generic(plane_curve.ProjectiveCurve_generic):
Over a finite field::
sage: EllipticCurve(GF(41),[2,5]).pari_curve()
- [Mod(0, 41), Mod(0, 41), Mod(0, 41), Mod(2, 41), Mod(5, 41), Mod(0, 41), Mod(4, 41), Mod(20, 41), Mod(37, 41), Mod(27, 41), Mod(26, 41), Mod(4, 41), Mod(11, 41), 0, 0, 0, 0, 0, 0]
+ [Mod(0, 41), Mod(0, 41), Mod(0, 41), Mod(2, 41), Mod(5, 41), Mod(0, 41), Mod(4, 41), Mod(20, 41), Mod(37, 41), Mod(27, 41), Mod(26, 41), Mod(4, 41), Mod(11, 41), Vecsmall([3]), [41, [9, 31, [6, 0, 0, 0]]], [0, 0, 0, 0]]
Over a `p`-adic field::
sage: Qp = pAdicField(5, prec=3)
sage: E = EllipticCurve(Qp,[3, 4])
sage: E.pari_curve()
- [O(5^3), O(5^3), O(5^3), 3 + O(5^3), 4 + O(5^3), O(5^3), 1 + 5 + O(5^3), 1 + 3*5 + O(5^3), 1 + 3*5 + 4*5^2 + O(5^3), 1 + 5 + 4*5^2 + O(5^3), 4 + 3*5 + 5^2 + O(5^3), 2*5 + 4*5^2 + O(5^3), 3*5^-1 + O(5), [4 + 4*5 + 4*5^2 + O(5^3)], 1 + 2*5 + 4*5^2 + O(5^3), 1 + 5 + 4*5^2 + O(5^3), 2*5 + 4*5^2 + O(5^3), 3 + 3*5 + 3*5^2 + O(5^3), 0]
+ [0, 0, 0, 3, 4, 0, 6, 16, -9, -144, -3456, -8640, 1728/5, Vecsmall([2]), [O(5^3)], [0, 0]]
sage: E.j_invariant()
3*5^-1 + O(5)
- The `j`-invariant must have negative `p`-adic valuation::
+ PARI no longer requires that the `j`-invariant has negative `p`-adic valuation::
sage: E = EllipticCurve(Qp,[1, 1])
sage: E.j_invariant() # the j-invariant is a p-adic integer
2 + 4*5^2 + O(5^3)
sage: E.pari_curve()
- Traceback (most recent call last):
- ...
- PariError: valuation of j must be negative in p-adic ellinit
+ [0, 0, 0, 1, 1, 0, 2, 4, -1, -48, -864, -496, 6912/31, Vecsmall([2]), [O(5^3)], [0, 0]]
"""
try:
return self._pari_curve
@@ -2965,13 +2963,11 @@ class EllipticCurve_generic(plane_curve.ProjectiveCurve_generic):
sage: E = EllipticCurve('11a1')
sage: pari(E)
- [0, -1, 1, -10, -20, -4, -20, -79, -21, 496, 20008, -161051, -122023936/161051, [4.34630815820539, -1.67315407910270 + 1.32084892226908*I, -1.67315407910270 - 1.32084892226908*I]~, ...]
- sage: E.pari_curve(prec=64)
- [0, -1, 1, -10, -20, -4, -20, -79, -21, 496, 20008, -161051, -122023936/161051, [4.34630815820539, -1.67315407910270 + 1.32084892226908*I, -1.67315407910270 - 1.32084892226908*I]~, ...]
+ [0, -1, 1, -10, -20, -4, -20, -79, -21, 496, 20008, -161051, -122023936/161051, Vecsmall([1]), [Vecsmall([64, -1])], [0, 0, 0, 0, 0, 0, 0, 0]]
Over a finite field::
sage: EllipticCurve(GF(2), [0,0,1,1,1])._pari_()
- [Mod(0, 2), Mod(0, 2), Mod(1, 2), Mod(1, 2), Mod(1, 2), Mod(0, 2), Mod(0, 2), Mod(1, 2), Mod(1, 2), Mod(0, 2), Mod(0, 2), Mod(1, 2), Mod(0, 2), 0, 0, 0, 0, 0, 0]
+ [0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, Vecsmall([4]), [1, [[Vecsmall([0, 1]), Vecsmall([0, 1]), Vecsmall([0, 1])], Vecsmall([0, 1]), [Vecsmall([0, 1]), Vecsmall([0]), Vecsmall([0]), Vecsmall([0])]]], [0, 0, 0, 0]]
"""
return self.pari_curve()
diff --git a/src/sage/schemes/elliptic_curves/ell_number_field.py b/src/sage/schemes/elliptic_curves/ell_number_field.py
index eff2c0a..c8a23be 100644
--- a/src/sage/schemes/elliptic_curves/ell_number_field.py
+++ b/src/sage/schemes/elliptic_curves/ell_number_field.py
@@ -281,8 +281,10 @@ class EllipticCurve_number_field(EllipticCurve_field):
A = 0
B = Mod(1, y^2 + 7)
C = Mod(y, y^2 + 7)
+ <BLANKLINE>
Computing L(S,2)
- L(S,2) = [Mod(Mod(-1, y^2 + 7)*x^2 + Mod(-1/2*y + 1/2, y^2 + 7)*x + 1, x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(Mod(-1, y^2 + 7)*x^2 + Mod(-1/2*y - 1/2, y^2 + 7)*x + 1, x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(-1, x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(Mod(1/2*y - 1/2, y^2 + 7)*x + Mod(1/2*y - 3/2, y^2 + 7), x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(Mod(1, y^2 + 7)*x + Mod(1/2*y + 3/2, y^2 + 7), x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(Mod(-1, y^2 + 7)*x + Mod(-1/2*y + 3/2, y^2 + 7), x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7))]
+ L(S,2) = [Mod(Mod(-1, y^2 + 7)*x^2 + Mod(-1/2*y + 1/2, y^2 + 7)*x + 1, x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(Mod(-1, y^2 + 7)*x^2 + Mod(-1/2*y - 1/2, y^2 + 7)*x + 1, x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(-1, x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(x^2 + 2, x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(Mod(1, y^2 + 7)*x + Mod(1/2*y + 3/2, y^2 + 7), x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(Mod(1, y^2 + 7)*x + Mod(1/2*y - 3/2, y^2 + 7), x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7))]
+ <BLANKLINE>
Computing the Selmer group
#LS2gen = 2
LS2gen = [Mod(Mod(-5, y^2 + 7)*x^2 + Mod(-3*y, y^2 + 7)*x + Mod(8, y^2 + 7), x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7)), Mod(Mod(1, y^2 + 7)*x^2 + Mod(1/2*y - 1/2, y^2 + 7)*x - 1, x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7))]
@@ -296,7 +298,7 @@ class EllipticCurve_number_field(EllipticCurve_field):
zc*z1^2 = Mod(Mod(2*y - 2, y^2 + 7)*x + Mod(2*y + 10, y^2 + 7), x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7))
quartic: (-1/2*y + 1/2)*Y^2 = x^4 + (-3*y - 15)*x^2 + (-8*y - 16)*x + (-11/2*y - 15/2)
reduced: Y^2 = (-1/2*y + 1/2)*x^4 - 4*x^3 + (-3*y + 3)*x^2 + (2*y - 2)*x + (1/2*y + 3/2)
- not ELS at [2, [0, 1]~, 1, 1, [1, 1]~]
+ not ELS at [2, [0, 1]~, 1, 1, [1, -2; 1, 0]]
zc = Mod(Mod(1, y^2 + 7)*x^2 + Mod(1/2*y + 1/2, y^2 + 7)*x + Mod(-1, y^2 + 7), x^3 + Mod(1, y^2 + 7)*x + Mod(y, y^2 + 7))
comes from the trivial point [Mod(1/2*y + 3/2, y^2 + 7), Mod(-y - 2, y^2 + 7)]
m1 = 1
@@ -336,8 +338,7 @@ class EllipticCurve_number_field(EllipticCurve_field):
sage: K = CyclotomicField(43).subfields(3)[0][0]
sage: E = EllipticCurve(K, '37')
sage: E.simon_two_descent() # long time (4s on sage.math, 2013)
- (3, 3, [(0 : 0 : 1), (1/2*zeta43_0^2 + 3/2*zeta43_0 - 2 : -zeta43_0^2 - 4*zeta43_0 + 3 : 1)])
-
+ (3, 3, [(0 : 0 : 1), (-1/4*zeta43_0^2 - 1/2*zeta43_0 + 3 : -3/8*zeta43_0^2 - 3/4*zeta43_0 + 4 : 1)])
"""
verbose = int(verbose)
if known_points is None:
@@ -380,7 +381,7 @@ class EllipticCurve_number_field(EllipticCurve_field):
- ``map`` -- (default: ``False``) also return an embedding of
the :meth:`base_field` into the resulting field.
- - ``kwds`` -- additional keywords passed to
+ - ``kwds`` -- additional keywords passed to
:func:`sage.rings.number_field.splitting_field.splitting_field`.
OUTPUT:
@@ -840,7 +841,7 @@ class EllipticCurve_number_field(EllipticCurve_field):
sage: K.<v> = NumberField(x^2 + 161*x - 150)
sage: E = EllipticCurve([25105/216*v - 3839/36, 634768555/7776*v - 98002625/1296, 634768555/7776*v - 98002625/1296, 0, 0])
sage: E.global_integral_model()
- Elliptic Curve defined by y^2 + (-502639783*v+465618899)*x*y + (-6603604211463489399460860*v+6117229527723443603191500)*y = x^3 + (1526887622075335620*v-1414427901517840500)*x^2 over Number Field in v with defining polynomial x^2 + 161*x - 150
+ Elliptic Curve defined by y^2 + (2094779518028859*v-1940492905300351)*x*y + (477997268472544193101178234454165304071127500*v-442791377441346852919930773849502871958097500)*y = x^3 + (26519784690047674853185542622500*v-24566525306469707225840460652500)*x^2 over Number Field in v with defining polynomial x^2 + 161*x - 150
:trac:`14476`::
@@ -970,7 +971,7 @@ class EllipticCurve_number_field(EllipticCurve_field):
sage: K.<i> = NumberField(x^2+1)
sage: E = EllipticCurve([1 + i, 0, 1, 0, 0])
sage: E.local_data()
- [Local data at Fractional ideal (i - 2):
+ [Local data at Fractional ideal (2*i + 1):
Reduction type: bad non-split multiplicative
Local minimal model: Elliptic Curve defined by y^2 + (i+1)*x*y + y = x^3 over Number Field in i with defining polynomial x^2 + 1
Minimal discriminant valuation: 1
@@ -1530,7 +1531,7 @@ class EllipticCurve_number_field(EllipticCurve_field):
Fractional ideal (21*i - 3)
sage: K.<a>=NumberField(x^2-x+3)
sage: EllipticCurve([1 + a , -1 + a , 1 + a , -11 + a , 5 -9*a ]).conductor()
- Fractional ideal (6*a)
+ Fractional ideal (-6*a)
A not so well known curve with everywhere good reduction::
@@ -2139,7 +2140,7 @@ class EllipticCurve_number_field(EllipticCurve_field):
sage: E.gens(lim1=1, lim3=1)
[]
sage: E.rank(), E.gens() # long time (about 3 s)
- (1, [(-369/25*y^3 + 539/25*y^2 - 1178/25*y + 1718/25 : -27193/125*y^3 + 39683/125*y^2 - 86816/125*y + 126696/125 : 1)])
+ (1, [(9/25*y^2 + 26/25 : -229/125*y^3 - 67/25*y^2 - 731/125*y - 213/25 : 1)])
Here is a curve of rank 2, yet the list contains many points::
@@ -2315,10 +2316,10 @@ class EllipticCurve_number_field(EllipticCurve_field):
sage: K.<i> = QuadraticField(-1)
sage: E1 = EllipticCurve([i + 1, 0, 1, -240*i - 400, -2869*i - 2627])
sage: E1.conductor()
- Fractional ideal (4*i + 7)
+ Fractional ideal (-4*i - 7)
sage: E2 = EllipticCurve([1+i,0,1,0,0])
sage: E2.conductor()
- Fractional ideal (4*i + 7)
+ Fractional ideal (-4*i - 7)
sage: E1.is_isogenous(E2) # long time (2s on sage.math, 2014)
Traceback (most recent call last):
...
diff --git a/src/sage/schemes/elliptic_curves/ell_point.py b/src/sage/schemes/elliptic_curves/ell_point.py
index 78b99fa..33fc802 100644
--- a/src/sage/schemes/elliptic_curves/ell_point.py
+++ b/src/sage/schemes/elliptic_curves/ell_point.py
@@ -2266,7 +2266,7 @@ class EllipticCurvePoint_number_field(EllipticCurvePoint_field):
sage: E.discriminant().support()
[Fractional ideal (i + 1),
Fractional ideal (-i - 2),
- Fractional ideal (i - 2),
+ Fractional ideal (2*i + 1),
Fractional ideal (3)]
sage: [E.tamagawa_exponent(p) for p in E.discriminant().support()]
[1, 4, 4, 4]
@@ -2651,7 +2651,7 @@ class EllipticCurvePoint_number_field(EllipticCurvePoint_field):
Emin = E.minimal_model()
iso = E.isomorphism_to(Emin)
P = iso(self)
- h = Emin.pari_curve(prec=precision).ellheight(P, precision=precision)
+ h = Emin.pari_curve().ellheight(P, precision=precision)
height = rings.RealField(precision)(h)
else:
height = (self.non_archimedean_local_height(prec=precision)
@@ -3192,7 +3192,7 @@ class EllipticCurvePoint_number_field(EllipticCurvePoint_field):
E_work = EllipticCurve(ai) # defined over RR
pt_pari = pari([emb(x), emb(y)])
working_prec = precision
- E_pari = E_work.pari_curve(prec=working_prec)
+ E_pari = E_work.pari_curve()
log_pari = E_pari.ellpointtoz(pt_pari, precision=working_prec)
while prec_words_to_bits(log_pari.precision()) < precision:
@@ -3206,7 +3206,7 @@ class EllipticCurvePoint_number_field(EllipticCurvePoint_field):
ai = [emb(a) for a in E.a_invariants()]
E_work = EllipticCurve(ai) # defined over RR
pt_pari = pari([emb(x), emb(y)])
- E_pari = E_work.pari_curve(prec=working_prec)
+ E_pari = E_work.pari_curve()
log_pari = E_pari.ellpointtoz(pt_pari, precision=working_prec)
# normalization step
diff --git a/src/sage/schemes/elliptic_curves/ell_rational_field.py b/src/sage/schemes/elliptic_curves/ell_rational_field.py
index c831c7f..913d408 100644
--- a/src/sage/schemes/elliptic_curves/ell_rational_field.py
+++ b/src/sage/schemes/elliptic_curves/ell_rational_field.py
@@ -592,17 +592,9 @@ class EllipticCurve_rational_field(EllipticCurve_number_field):
INPUT:
+ - ``prec`` -- Deprecated
- - ``prec`` - The precision of quantities calculated for the
- returned curve, in bits. If None, defaults to factor
- multiplied by the precision of the largest cached curve (or
- a small default precision depending on the curve if none yet
- computed).
-
- - ``factor`` - The factor by which to increase the
- precision over the maximum previously computed precision. Only used
- if prec (which gives an explicit precision) is None.
-
+ - ``factor`` -- Deprecated
EXAMPLES::
@@ -618,84 +610,57 @@ class EllipticCurve_rational_field(EllipticCurve_number_field):
::
sage: E = EllipticCurve(RationalField(), ['1/3', '2/3'])
- sage: e = E.pari_curve(prec=100)
- sage: 100 in E._pari_curve
- True
- sage: e.type()
- 't_VEC'
+ sage: e = E.pari_curve()
sage: e[:5]
[0, 0, 0, 1/3, 2/3]
- This shows that the bug uncovered by trac:`3954` is fixed::
-
- sage: 100 in E._pari_curve
- True
-
- ::
+ When doing certain computations, PARI caches the results::
sage: E = EllipticCurve('37a1')
sage: Epari = E.pari_curve()
- sage: Epari[14].python().prec()
- 64
- sage: [a.precision() for a in Epari]
- [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4] # 32-bit
- [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3] # 64-bit
- sage: Epari = E.pari_curve(factor=2)
- sage: Epari[14].python().prec()
- 128
+ sage: Epari
+ [0, 0, 1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, Vecsmall([1]), [Vecsmall([64, 1])], [0, 0, 0, 0, 0, 0, 0, 0]]
+ sage: Epari.omega()
+ [2.99345864623196, -2.45138938198679*I]
+ sage: Epari
+ [0, 0, 1, -1, 0, 0, -2, 1, -1, 48, -216, 37, 110592/37, Vecsmall([1]), [Vecsmall([64, 1])], [[2.99345864623196, -2.45138938198679*I], 0, [0.837565435283323, 0.269594436405445, -1.10715987168877]~, 0, 0, 0, 0, 0]]
- This shows that the bug uncovered by trac`4715` is fixed::
+ This shows that the bug uncovered by :trac:`4715` is fixed::
sage: Ep = EllipticCurve('903b3').pari_curve()
- When the curve coefficients are large, a larger precision is
- required (see :trac:`13163`)::
+ This still works, even When the curve coefficients are large
+ (see :trac:`13163`)::
sage: E = EllipticCurve([4382696457564794691603442338788106497, 28, 3992, 16777216, 298])
- sage: E.pari_curve(prec=64)
- Traceback (most recent call last):
- ...
- PariError: precision too low in ellinit
- sage: E.pari_curve() # automatically choose the right precision
+ sage: E.pari_curve()
[4382696457564794691603442338788106497, 28, 3992, 16777216, 298, ...]
sage: E.minimal_model()
Elliptic Curve defined by y^2 + x*y + y = x^3 + x^2 - 7686423934083797390675981169229171907674183588326184511391146727143672423167091484392497987721106542488224058921302964259990799229848935835464702*x + 8202280443553761483773108648734271851215988504820214784899752662100459663011709992446860978259617135893103951840830254045837355547141096270521198994389833928471736723050112419004202643591202131091441454709193394358885 over Rational Field
- """
- try:
- # if the PARI curve has already been computed to this
- # precision, returned the cached copy
- return self._pari_curve[prec]
- except AttributeError:
- self._pari_curve = {}
- except KeyError:
- pass
- # Double the precision if needed?
- retry_prec = False
+ The arguments ``prec`` and ``factor`` are deprecated::
- if prec is None:
- if len(self._pari_curve) == 0:
- # No curves computed yet
- prec = 64
- retry_prec = True
- else:
- # Take largest cached precision
- prec = max(self._pari_curve.keys())
- if factor == 1:
- return self._pari_curve[prec]
- prec = int(prec * factor)
+ sage: E.pari_curve(prec=128)
+ doctest:...: DeprecationWarning: The prec argument to pari_curve() is deprecated and no longer used
+ See http://trac.sagemath.org/15767 for details.
+ [4382696457564794691603442338788106497, 28, 3992, 16777216, 298, ...]
+ sage: E.pari_curve(factor=2)
+ doctest:...: DeprecationWarning: The factor argument to pari_curve() is deprecated and no longer used
+ See http://trac.sagemath.org/15767 for details.
+ [4382696457564794691603442338788106497, 28, 3992, 16777216, 298, ...]
+ """
+ if prec is not None:
+ from sage.misc.superseded import deprecation
+ deprecation(15767, 'The prec argument to pari_curve() is deprecated and no longer used')
+ if factor != 1:
+ from sage.misc.superseded import deprecation
+ deprecation(15767, 'The factor argument to pari_curve() is deprecated and no longer used')
- pari_invariants = pari(self.a_invariants())
- while True:
- try:
- self._pari_curve[prec] = pari_invariants.ellinit(precision=prec)
- return self._pari_curve[prec]
- except PariError as e:
- if retry_prec and 'precision too low' in str(e):
- # Retry with double precision
- prec *= 2
- else:
- raise
+ try:
+ return self._pari_curve
+ except AttributeError:
+ self._pari_curve = pari(self.a_invariants()).ellinit()
+ return self._pari_curve
def pari_mincurve(self, prec=None, factor=1):
"""
@@ -704,16 +669,9 @@ class EllipticCurve_rational_field(EllipticCurve_number_field):
INPUT:
+ - ``prec`` -- Deprecated
- - ``prec`` - The precision of quantities calculated for the
- returned curve, in bits. If None, defaults to factor
- multiplied by the precision of the largest cached curve (or
- the default real precision if none yet computed).
-
- - ``factor`` - The factor by which to increase the
- precision over the maximum previously computed precision. Only used
- if prec (which gives an explicit precision) is None.
-
+ - ``factor`` -- Deprecated
EXAMPLES::
@@ -724,29 +682,21 @@ class EllipticCurve_rational_field(EllipticCurve_number_field):
sage: E.conductor()
47232
sage: e.ellglobalred()
- [47232, [1, 0, 0, 0], 2]
+ [47232, [1, 0, 0, 0], 2, [2, 7; 3, 2; 41, 1], [[7, 2, 0, 1], [2, -3, 0, 2], [1, 5, 0, 1]]]
"""
+ if prec is not None:
+ from sage.misc.superseded import deprecation
+ deprecation(15767, 'The prec argument to pari_mincurve() is deprecated and no longer used')
+ if factor != 1:
+ from sage.misc.superseded import deprecation
+ deprecation(15767, 'The factor argument to pari_mincurve() is deprecated and no longer used')
+
try:
- # if the PARI curve has already been computed to this
- # precision, returned the cached copy
- return self._pari_mincurve[prec]
+ return self._pari_mincurve
except AttributeError:
- # no PARI curves have been computed for this elliptic curve
- self._pari_mincurve = {}
- except KeyError:
- # PARI curves are cached for this elliptic curve, but they
- # are not of the requested precision (or prec = None)
- if prec is None:
- L = sorted(self._pari_mincurve.keys())
- if factor == 1:
- return self._pari_mincurve[L[-1]]
- else:
- prec = int(factor * L[-1])
- e = self.pari_curve(prec)
- mc, change = e.ellminimalmodel()
- self._pari_mincurve[prec] = mc
- # self.__min_transform = change
- return mc
+ mc, change = self.pari_curve().ellminimalmodel()
+ self._pari_mincurve = mc
+ return self._pari_mincurve
def database_curve(self):
"""
@@ -3705,12 +3655,12 @@ class EllipticCurve_rational_field(EllipticCurve_number_field):
Torsion Subgroup isomorphic to Z/2 + Z/8 associated to the Elliptic
Curve defined by y^2 = x^3 - 1386747*x + 368636886 over
Rational Field
- sage: G.0
+ sage: G.0*3 + G.1
(1227 : 22680 : 1)
sage: G.1
(282 : 0 : 1)
sage: list(G)
- [(0 : 1 : 0), (1227 : 22680 : 1), (2307 : -97200 : 1), (8787 : 816480 : 1), (1011 : 0 : 1), (8787 : -816480 : 1), (2307 : 97200 : 1), (1227 : -22680 : 1), (282 : 0 : 1), (-933 : 29160 : 1), (-285 : -27216 : 1), (147 : 12960 : 1), (-1293 : 0 : 1), (147 : -12960 : 1), (-285 : 27216 : 1), (-933 : -29160 : 1)]
+ [(0 : 1 : 0), (147 : 12960 : 1), (2307 : 97200 : 1), (-933 : 29160 : 1), (1011 : 0 : 1), (-933 : -29160 : 1), (2307 : -97200 : 1), (147 : -12960 : 1), (282 : 0 : 1), (8787 : 816480 : 1), (-285 : 27216 : 1), (1227 : 22680 : 1), (-1293 : 0 : 1), (1227 : -22680 : 1), (-285 : -27216 : 1), (8787 : -816480 : 1)]
"""
try:
return self.__torsion_subgroup
@@ -3745,10 +3695,10 @@ class EllipticCurve_rational_field(EllipticCurve_number_field):
sage: EllipticCurve('37b').torsion_points()
[(0 : 1 : 0), (8 : -19 : 1), (8 : 18 : 1)]
- ::
+ Some curves with large torsion groups::
- sage: E=EllipticCurve([-1386747,368636886])
- sage: T=E.torsion_subgroup(); T
+ sage: E = EllipticCurve([-1386747,368636886])
+ sage: T = E.torsion_subgroup(); T
Torsion Subgroup isomorphic to Z/2 + Z/8 associated to the Elliptic Curve defined by y^2 = x^3 - 1386747*x + 368636886 over Rational Field
sage: T == E.torsion_subgroup(algorithm="doud")
True
@@ -3756,33 +3706,54 @@ class EllipticCurve_rational_field(EllipticCurve_number_field):
True
sage: E.torsion_points()
[(-1293 : 0 : 1),
- (-933 : -29160 : 1),
- (-933 : 29160 : 1),
- (-285 : -27216 : 1),
- (-285 : 27216 : 1),
- (0 : 1 : 0),
- (147 : -12960 : 1),
- (147 : 12960 : 1),
- (282 : 0 : 1),
- (1011 : 0 : 1),
- (1227 : -22680 : 1),
- (1227 : 22680 : 1),
- (2307 : -97200 : 1),
- (2307 : 97200 : 1),
- (8787 : -816480 : 1),
- (8787 : 816480 : 1)]
+ (-933 : -29160 : 1),
+ (-933 : 29160 : 1),
+ (-285 : -27216 : 1),
+ (-285 : 27216 : 1),
+ (0 : 1 : 0),
+ (147 : -12960 : 1),
+ (147 : 12960 : 1),
+ (282 : 0 : 1),
+ (1011 : 0 : 1),
+ (1227 : -22680 : 1),
+ (1227 : 22680 : 1),
+ (2307 : -97200 : 1),
+ (2307 : 97200 : 1),
+ (8787 : -816480 : 1),
+ (8787 : 816480 : 1)]
+ sage: EllipticCurve('210b5').torsion_points()
+ [(-41/4 : 37/8 : 1),
+ (-5 : -103 : 1),
+ (-5 : 107 : 1),
+ (0 : 1 : 0),
+ (10 : -208 : 1),
+ (10 : 197 : 1),
+ (37 : -397 : 1),
+ (37 : 359 : 1),
+ (100 : -1153 : 1),
+ (100 : 1052 : 1),
+ (415 : -8713 : 1),
+ (415 : 8297 : 1)]
+ sage: EllipticCurve('210e2').torsion_points()
+ [(-36 : 18 : 1),
+ (-26 : -122 : 1),
+ (-26 : 148 : 1),
+ (-8 : -122 : 1),
+ (-8 : 130 : 1),
+ (0 : 1 : 0),
+ (4 : -62 : 1),
+ (4 : 58 : 1),
+ (31/4 : -31/8 : 1),
+ (28 : -14 : 1),
+ (34 : -122 : 1),
+ (34 : 88 : 1),
+ (64 : -482 : 1),
+ (64 : 418 : 1),
+ (244 : -3902 : 1),
+ (244 : 3658 : 1)]
"""
return sorted(self.torsion_subgroup(algorithm).points())
- ## def newform_eval(self, z, prec):
-## """
-## The value of the newform attached to this elliptic curve at
-## the point z in the complex upper half plane, computed using
-## prec terms of the power series expansion. Note that the power
-## series need not converge well near the real axis.
-## """
-## raise NotImplementedError
-
@cached_method
def root_number(self, p=None):
"""
diff --git a/src/sage/schemes/elliptic_curves/ell_torsion.py b/src/sage/schemes/elliptic_curves/ell_torsion.py
index 050b7fa..6cac604 100644
--- a/src/sage/schemes/elliptic_curves/ell_torsion.py
+++ b/src/sage/schemes/elliptic_curves/ell_torsion.py
@@ -44,7 +44,7 @@ class EllipticCurveTorsionSubgroup(groups.AdditiveAbelianGroupWrapper):
sage: G.order()
4
sage: G.gen(0)
- (2 : 0 : 1)
+ (-2 : 0 : 1)
sage: G.gen(1)
(0 : 0 : 1)
sage: G.ngens()
@@ -81,7 +81,7 @@ class EllipticCurveTorsionSubgroup(groups.AdditiveAbelianGroupWrapper):
sage: E = EllipticCurve([0,0,0,-49,0])
sage: T = E.torsion_subgroup()
sage: [E(t) for t in T]
- [(0 : 1 : 0), (7 : 0 : 1), (0 : 0 : 1), (-7 : 0 : 1)]
+ [(0 : 1 : 0), (-7 : 0 : 1), (0 : 0 : 1), (7 : 0 : 1)]
An example where the torsion subgroup is trivial::
@@ -166,23 +166,15 @@ class EllipticCurveTorsionSubgroup(groups.AdditiveAbelianGroupWrapper):
if self.__K is RationalField() and algorithm in pari_torsion_algorithms:
flag = pari_torsion_algorithms.index(algorithm)
- G = None
- loop = 0
- while G is None and loop < 3:
- loop += 1
- try:
- G = self.__E.pari_curve(prec = 400).elltors(flag) # pari_curve will return the curve of maximum known precision
- except RuntimeError:
- self.__E.pari_curve(factor = 2) # caches a curve of twice the precision
- if G is not None:
- order = G[0].python()
- structure = G[1].python()
- gens = G[2].python()
-
- self.__torsion_gens = [ self.__E(P) for P in gens ]
- from sage.groups.additive_abelian.additive_abelian_group import cover_and_relations_from_invariants
- groups.AdditiveAbelianGroupWrapper.__init__(self, self.__E(0).parent(), self.__torsion_gens, structure)
- return
+ G = self.__E.pari_curve().elltors(flag)
+ order = G[0].python()
+ structure = G[1].python()
+ gens = G[2].python()
+
+ self.__torsion_gens = [ self.__E(P) for P in gens ]
+ from sage.groups.additive_abelian.additive_abelian_group import cover_and_relations_from_invariants
+ groups.AdditiveAbelianGroupWrapper.__init__(self, self.__E(0).parent(), self.__torsion_gens, structure)
+ return
T1 = E(0) # these will be the two generators
T2 = E(0)
diff --git a/src/sage/schemes/elliptic_curves/heegner.py b/src/sage/schemes/elliptic_curves/heegner.py
index d1a114d..5af7988 100644
--- a/src/sage/schemes/elliptic_curves/heegner.py
+++ b/src/sage/schemes/elliptic_curves/heegner.py
@@ -22,7 +22,7 @@ EXAMPLES::
1
sage: K.<a> = QuadraticField(-8)
sage: K.factor(3)
- (Fractional ideal (1/2*a + 1)) * (Fractional ideal (1/2*a - 1))
+ (Fractional ideal (1/2*a + 1)) * (Fractional ideal (-1/2*a + 1))
Next try an inert prime::
diff --git a/src/sage/schemes/elliptic_curves/lseries_ell.py b/src/sage/schemes/elliptic_curves/lseries_ell.py
index 1f4905d..02b1358 100644
--- a/src/sage/schemes/elliptic_curves/lseries_ell.py
+++ b/src/sage/schemes/elliptic_curves/lseries_ell.py
@@ -67,8 +67,8 @@ class Lseries_ell(SageObject):
sage: E = EllipticCurve('389a')
sage: L = E.lseries()
sage: L.taylor_series(series_prec=3)
- -1.28158145675273e-23 + (7.26268290541182e-24)*z + 0.759316500288427*z^2 + O(z^3) # 32-bit
- -2.69129566562797e-23 + (1.52514901968783e-23)*z + 0.759316500288427*z^2 + O(z^3) # 64-bit
+ -1.27685190980159e-23 + (7.23588070754027e-24)*z + 0.759316500288427*z^2 + O(z^3) # 32-bit
+ -2.72911738151096e-23 + (1.54658247036311e-23)*z + 0.759316500288427*z^2 + O(z^3) # 64-bit
sage: L.taylor_series(series_prec=3)[2:]
0.000000000000000 + 0.000000000000000*z + 0.759316500288427*z^2 + O(z^3)
"""
@@ -602,7 +602,7 @@ class Lseries_ell(SageObject):
sage: E.lseries().deriv_at1()
(-0.00010911444, 0.142428)
sage: E.lseries().deriv_at1(4000)
- (6.9902290...e-50, 1.31318e-43)
+ (6.990...e-50, 1.31318e-43)
"""
sqrtN = sqrt(self.__E.conductor())
if k:
diff --git a/src/sage/schemes/elliptic_curves/modular_parametrization.py b/src/sage/schemes/elliptic_curves/modular_parametrization.py
index 91833f8..a5ea060 100644
--- a/src/sage/schemes/elliptic_curves/modular_parametrization.py
+++ b/src/sage/schemes/elliptic_curves/modular_parametrization.py
@@ -245,9 +245,9 @@ class ModularParameterization:
EXAMPLES::
- sage: E=EllipticCurve('389a1')
+ sage: E = EllipticCurve('389a1')
sage: phi = E.modular_parametrization()
- sage: X,Y = phi.power_series(prec = 10)
+ sage: X,Y = phi.power_series(prec=10)
sage: X
q^-2 + 2*q^-1 + 4 + 7*q + 13*q^2 + 18*q^3 + 31*q^4 + 49*q^5 + 74*q^6 + 111*q^7 + O(q^8)
sage: Y
@@ -264,21 +264,16 @@ class ModularParameterization:
sage: E.defining_polynomial()(X,Y,1) + O(q^11) == 0
True
- Note that below we have to change variable from x to q::
+ Note that below we have to change variable from `x` to `q`::
- sage: a1,_,a3,_,_=E.a_invariants()
- sage: f=E.q_expansion(17)
- sage: q=f.parent().gen()
+ sage: a1,_,a3,_,_ = E.a_invariants()
+ sage: f = E.q_expansion(17)
+ sage: q = f.parent().gen()
sage: f/q == (X.derivative()/(2*Y+a1*X+a3))
True
"""
R = LaurentSeriesRing(RationalField(),'q')
if not self._E.is_minimal():
- raise NotImplementedError("Only implemented for minimal curves.")
- from sage.libs.all import pari
- old_prec = pari.get_series_precision()
- pari.set_series_precision(prec-1)
- XY = self._E.pari_mincurve().elltaniyama()
- pari.set_series_precision(old_prec)
+ raise NotImplementedError("only implemented for minimal curves")
+ XY = self._E.pari_mincurve().elltaniyama(prec-1)
return R(XY[0]),R(XY[1])
-
diff --git a/src/sage/schemes/elliptic_curves/period_lattice.py b/src/sage/schemes/elliptic_curves/period_lattice.py
index 227b32f..ef66865 100644
--- a/src/sage/schemes/elliptic_curves/period_lattice.py
+++ b/src/sage/schemes/elliptic_curves/period_lattice.py
@@ -530,12 +530,12 @@ class PeriodLattice_ell(PeriodLattice):
if algorithm=='pari':
if self.E.base_field() is QQ:
- periods = self.E.pari_curve(prec).omega().python()
+ periods = self.E.pari_curve().omega(prec).python()
return (R(periods[0]), C(periods[1]))
from sage.libs.pari.all import pari
- E_pari = pari([R(self.embedding(ai).real()) for ai in self.E.a_invariants()]).ellinit(precision=prec)
- periods = E_pari.omega().python()
+ E_pari = pari([R(self.embedding(ai).real()) for ai in self.E.a_invariants()]).ellinit()
+ periods = E_pari.omega(prec).python()
return (R(periods[0]), C(periods[1]))
if algorithm!='sage':
@@ -937,9 +937,9 @@ class PeriodLattice_ell(PeriodLattice):
if prec is None:
prec = RealField().precision()
try:
- return self.E.pari_curve(prec).ellsigma(z, flag)
+ return self.E.pari_curve().ellsigma(z, flag, precision=prec)
except AttributeError:
- raise NotImplementedError("sigma function not yet implemented for period lattices of curves not defined over Q.")
+ raise NotImplementedError("sigma function not yet implemented for period lattices of curves not defined over Q")
def curve(self):
r"""
diff --git a/src/sage/schemes/plane_conics/con_number_field.py b/src/sage/schemes/plane_conics/con_number_field.py
index 4ae48d8..b241d81 100644
--- a/src/sage/schemes/plane_conics/con_number_field.py
+++ b/src/sage/schemes/plane_conics/con_number_field.py
@@ -124,7 +124,7 @@ class ProjectiveConic_number_field(ProjectiveConic_field):
sage: C.has_rational_point(algorithm = 'local', read_cache = False)
True
- Examples over number fields ::
+ Examples over number fields::
sage: K.<i> = QuadraticField(-1)
sage: C = Conic(K, [1, 3, -5])
diff --git a/src/sage/symbolic/constants.py b/src/sage/symbolic/constants.py
index 6f76834..a91c008 100644
--- a/src/sage/symbolic/constants.py
+++ b/src/sage/symbolic/constants.py
@@ -851,7 +851,7 @@ class Log2(Constant):
.6931471805599453
sage: gp(log2)
0.6931471805599453094172321215 # 32-bit
- 0.69314718055994530941723212145817656808 # 64-bit
+ 0.69314718055994530941723212145817656807 # 64-bit
sage: RealField(150)(2).log()
0.69314718055994530941723212145817656807550013
"""
diff --git a/src/sage/symbolic/integration/integral.py b/src/sage/symbolic/integration/integral.py
index d092529..901acf0 100644
--- a/src/sage/symbolic/integration/integral.py
+++ b/src/sage/symbolic/integration/integral.py
@@ -677,7 +677,7 @@ def integrate(expression, v=None, a=None, b=None, algorithm=None):
Check that :trac:`11737` is fixed::
sage: N(integrate(sin(x^2)/(x^2), x, 1, infinity))
- 0.285736646322858
+ 0.285736646322853
"""
expression, v, a, b = _normalize_integral_input(expression, v, a, b)
diff --git a/src/sage/tests/parigp.py b/src/sage/tests/parigp.py
index e58d427..6077db3 100644
--- a/src/sage/tests/parigp.py
+++ b/src/sage/tests/parigp.py
@@ -6,7 +6,7 @@ Check that :trac:`9876` has been fixed, this test comes from PARI's
self-test "rnfkummer"::
sage: pari('setrand(1); lift(rnfkummer(bnrinit(bnfinit(y^4-52*y^2+26,1),3,1),Mat(5)))') # long time (4s on sage.math, 2011)
- x^5 + (-12490585381661544359255403301035053110061910*y^3 + 8875378520404561472503422910872004290197460*y^2 + 643203912732761873050292808675549433737179610*y - 457038484130159980782436350930533714409061170)*x^3 + (-134027514281645340620300162483056350640850689292892267066826165512*y^3 + 95235243030030469814112992330493778292557062830362488860799262053*y^2 + 6901759924725033375901003506523314713919218011682438894990413482822*y - 4904148131739972327284545793455166015180538153351582525198684659988)*x^2 + (-47397957557570888155708856849994683849365520972511563824369572802678417823703951003630*y^3 + 33679323468496441220407209890566679520252152888549909181980050360738580514765560899830*y^2 + 2440762448949326006691055037485233408803108189791110990339027554592708168372793653934980*y - 1734320048033240933678067521047553381449799255523887315704756124974424249211251806055445)*x + (88847913213212543643724914281374137431466584547137800780754135469698376356168903046151157223082894732483818/5*y^3 - 63132205749445286461822170095386361952302057584137825393349862937480952856334509099209369622841067534904427/5*y^2 - 4575231959624371057665356018310756876851369587901000773265750996233180145132238920504044583057371848969400608/5*y + 3250999094748458040342075570309205473235256099747294466325048378505864671503910959921397017511503388596960342/5)
+ x^5 + (677308732982301944730030845266716201702837696162187325328/5*y^3 + 481271319660811460139352501916644558975058261230836596652/5*y^2 - 34878079733048511269299413306183851642254427026365686673888/5*y - 24783137893632185532697291886880720222932490781434136563942/5)*x^3 + (3121825424585613564828729670704559492032765858876683224121119983801219547643890505070*y^3 + 2218259473949490736667831079912338956828105689590705243343986337391928943383709808005*y^2 - 160758704836112475349193472119432636971334139776148581364333958289434482806877560648970*y - 114229487928172801039731551289054638597376141715926648946031483976252167029243247022480)*x^2 + (-166692999053535356002572927874917139211874871730209960830468398970597547702137238176414705764356470658863661934844/5*y^3 - 118446188915971905087412803032726595730394344242831753676734791550346393669679117451359918013807557809143042588696/5*y^2 + 8583872250159852857479162156889677342550132950704205078118190632176525884150800135006242479797595396229858998666474/5*y + 6099398054781102460046012340322433264871600802691098946100231203424708988718659688581036467351459717869466864403491/5)*x + (-3761942859516698460017771578887550299728643548425212623644925442305118051299870709569967640457662697840860989973276516003636843449764721490044/5*y^3 - 2673104432455463952284352656647109245231103663592899118247897745294025980581570350460813923435311458682114748384710825808171997155877533243621/5*y^2 + 193721614595917576607166927238849546114076202473503220710707213556396586084964322202670927424345172110316287310450443586757567876756951302594424/5*y + 137651773558650909762864388498297831958827163349141150095186154867116600261791580542516653158613689676015829782898702530873665348851222173825666/5)
Check that :trac:`10195` (PARI bug 1153) has been fixed::
@@ -48,7 +48,7 @@ Check that the optional PARI databases work::
[x^212 + (-y^7 + 5207*y^6 - 10241606*y^5 + 9430560101*y^4 - 4074860204015*y^3 + 718868274900397*y^2 - 34897101275826114*y + 104096378056356968)*x^211...
The following requires the modular polynomials up to degree 223, while
-only those up to degree 199 come standard in Sage:
+only those up to degree 199 come standard in Sage::
sage: p = next_prime(2^328)
sage: E = EllipticCurve(GF(p), [6,1])
@@ -56,7 +56,7 @@ only those up to degree 199 come standard in Sage:
546812681195752981093125556779405341338292357723293496548601032930284335897180749997402596957976244
Create a number field with Galois group `A4`. Group `A4` corresponds to
-transitive group `(12,3)` in GAP.
+transitive group `(12,3)` in GAP::
sage: R.<x> = PolynomialRing(ZZ)
sage: pol = pari("galoisgetpol(12,3)[1]") # optional -- database_pari
--
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