File: [local] / OpenXM_contrib / pari / src / basemath / Attic / base5.c (download)
Revision 1.1.1.1 (vendor branch), Sun Jan 9 17:35:30 2000 UTC (24 years, 6 months ago) by maekawa
Branch: PARI_GP
CVS Tags: maekawa-ipv6, VERSION_2_0_17_BETA, RELEASE_20000124, RELEASE_1_2_3, RELEASE_1_2_2_KNOPPIX_b, RELEASE_1_2_2_KNOPPIX, RELEASE_1_2_2, RELEASE_1_2_1, RELEASE_1_1_3, RELEASE_1_1_2 Changes since 1.1: +0 -0
lines
Import PARI/GP 2.0.17 beta.
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/*******************************************************************/
/* */
/* BASIC NF OPERATIONS */
/* (continued 2) */
/* */
/*******************************************************************/
/* $Id: base5.c,v 1.1.1.1 1999/09/16 13:47:22 karim Exp $ */
#include "pari.h"
GEN mat_to_vecpol(GEN x, long v);
GEN
matbasistoalg(GEN nf,GEN x)
{
long i,j,lx,li;
GEN p1,z;
if (typ(x)!=t_MAT)
err(talker,"argument must be a matrix in matbasistoalg");
lx=lg(x); z=cgetg(lx,t_MAT); if (lx==1) return z;
li=lg(x[1]);
for (j=1; j<lx; j++)
{
p1=cgetg(li,t_COL); z[j]=(long)p1;
for (i=1; i<li; i++) p1[i]=(long)basistoalg(nf,gcoeff(x,i,j));
}
return z;
}
GEN
matalgtobasis(GEN nf,GEN x)
{
long i,j,lx,li;
GEN p1,z;
if (typ(x)!=t_MAT)
err(talker,"argument must be a matrix in matalgtobasis");
lx=lg(x); z=cgetg(lx,t_MAT); if (lx==1) return z;
li=lg(x[1]);
for (j=1; j<lx; j++)
{
p1=cgetg(li,t_COL); z[j]=(long)p1;
for (i=1; i<li; i++) p1[i]=(long)algtobasis(nf,gcoeff(x,i,j));
}
return z;
}
static GEN
rnfmakematrices(GEN rnf)
{
long i,j,k,n,r1,r2,ru,ruk,r1rel,r2rel;
GEN nf,pol,rac,base,base1,r1r2,racnf,sig,vecmat,vecM,vecMC,vecT2,rack;
GEN M,p2,p3,MC,sigk,T2,T,p1,MD,TI,MDI;
nf=(GEN)rnf[10]; racnf=(GEN)nf[6]; pol=(GEN)rnf[1];
n=lgef(pol)-3;
base=(GEN)rnf[7]; base1=(GEN)base[1]; rac=(GEN)rnf[6]; sig=(GEN)rnf[2];
r1r2=(GEN)nf[2]; r1=itos((GEN)r1r2[1]); r2=itos((GEN)r1r2[2]); ru=r1+r2;
vecmat=cgetg(8,t_VEC);
vecM=cgetg(ru+1,t_VEC); vecmat[1]=(long)vecM;
vecMC=cgetg(ru+1,t_VEC); vecmat[2]=(long)vecMC;
vecT2=cgetg(ru+1,t_VEC); vecmat[3]=(long)vecT2;
for (k=1; k<=ru; k++)
{
rack=(GEN)rac[k]; ruk=lg(rack)-1;
M=cgetg(n+1,t_MAT); vecM[k]=(long)M;
for (j=1; j<=n; j++)
{
p2=cgetg(ruk+1,t_COL); M[j]=(long)p2; p3=lift((GEN)base1[j]);
p3=gsubst(p3,varn(nf[1]),(GEN)racnf[k]);
for (i=1; i<=ruk; i++) p2[i]=lsubst(p3,varn(rnf[1]),(GEN)rack[i]);
}
MC=gconj(gtrans(M)); vecMC[k]=(long)MC;
if (k<=r1)
{
sigk=(GEN)sig[k]; r1rel=itos((GEN)sigk[1]); r2rel=itos((GEN)sigk[2]);
if (r1rel+r2rel != lg(MC)-1) err(talker,"bug in rnfmakematrices");
for (j=r1rel+1; j<=r1rel+r2rel; j++) MC[j]=lmul2n((GEN)MC[j],1);
}
T2=gmul(MC,M); vecT2[k]=(long)T2;
}
T=cgetg(n+1,t_MAT); vecmat[4]=(long)T;
for (j=1; j<=n; j++)
{
p1=cgetg(n+1,t_COL); T[j]=(long)p1;
for (i=1; i<=n; i++)
p1[i]=ltrace(gmodulcp(gmul((GEN)base1[i],(GEN)base1[j]),pol));
}
MD=cgetg(1,t_MAT); vecmat[5]=(long)MD; /* matrice de la differente */
TI=cgetg(1,t_MAT); vecmat[6]=(long)TI; /* matrice .... ? */
MDI=cgetg(1,t_MAT); vecmat[7]=(long)MDI; /* matrice .... ? */
return vecmat;
}
GEN
rnfinitalg(GEN nf,GEN pol,long prec)
{
long av=avma,tetpil,m,n,r1,r2,vnf,i,j,k,vpol,v1,r1j,r2j,lfac,degabs;
GEN RES,sig,r1r2,rac,p1,p2,liftpol,delta,RAC,ro,p3,bas;
GEN f,f2,fac,fac1,fac2,id,p4,p5;
if (typ(pol)!=t_POL) err(notpoler,"rnfinitalg");
nf=checknf(nf); n=lgef(pol)-3; vpol=varn(pol);
vnf=0;
for (i=0; i<=n; i++)
{
long tp1;
p1=(GEN)pol[i+2];
tp1=typ(p1);
if (! is_const_t(tp1))
{
if (tp1!=t_POLMOD) err(typeer,"rnfinitalg");
if (!gegal((GEN)p1[1],(GEN)nf[1]))
err(talker,"incompatible number fields in rnfinitalg");
p1=(GEN)p1[2];
if (! is_const_t(typ(p1)))
{
v1=varn(p1);
if (vnf && vnf!=v1) err(talker,"different variables in rnfinitalg");
if (!vnf) vnf=v1;
}
}
}
if (!vnf) vnf=varn(nf[1]);
if (vpol>=vnf)
err(talker,"main variable must be of higher priority in rnfinitalg");
RES=cgetg(12,t_VEC);
RES[1]=(long)pol;
m=lgef(nf[1])-3; degabs=n*m;
r1r2=(GEN)nf[2]; r1=itos((GEN)r1r2[1]); r2=itos((GEN)r1r2[2]);
sig=cgetg(r1+r2+1,t_VEC); RES[2]=(long)sig;
rac=(GEN)nf[6]; liftpol=lift(pol);
RAC=cgetg(r1+r2+1,t_VEC); RES[6]=(long)RAC;
for (j=1; j<=r1; j++)
{
p1=gsubst(liftpol,vnf,(GEN)rac[j]);
ro=roots(p1,prec);
r1j=0;
while (r1j<n && gcmp0(gimag((GEN)ro[r1j+1]))) r1j++;
p2=cgetg(3,t_VEC); p2[1]=lstoi(r1j); p2[2]=lstoi(r2j=((n-r1j)>>1));
sig[j]=(long)p2;
p3=cgetg(r1j+r2j+1,t_VEC);
for (i=1; i<=r1j; i++) p3[i]=lreal((GEN)ro[i]);
for (; i<=r1j+r2j; i++) p3[i]=(long)ro[(i<<1)-r1j];
RAC[j]=(long)p3;
}
for (; j<=r1+r2; j++)
{
p2=cgetg(3,t_VEC); p2[1]=zero; p2[2]=lstoi(n); sig[j]=(long)p2;
p1=gsubst(liftpol,vnf,(GEN)rac[j]);
RAC[j]=(long)roots(p1,prec);
}
p1 = rnfpseudobasis(nf,pol);
delta = cgetg(3,t_VEC);
delta[1]=p1[3];
delta[2]=p1[4];
RES[3]=(long)delta;
p2 = matbasistoalg(nf,(GEN)p1[1]);
bas = cgetg(3,t_VEC);
bas[1]=(long)mat_to_vecpol(p2,vpol);
bas[2]=(long)p1[2];
RES[7]=(long)bas;
RES[8]=linvmat(p2);
f2=idealdiv(nf,discsr(pol),(GEN)p1[3]);
fac=idealfactor(nf,f2);
fac1=(GEN)fac[1]; fac2=(GEN)fac[2]; lfac=lg(fac1)-1;
f=idmat(m);
for (i=1; i<=lfac; i++)
{
if (mpodd((GEN)fac2[i])) err(bugparier,"rnfinitalg (odd exponent)");
f=idealmul(nf,f,idealpow(nf,(GEN)fac1[i],gmul2n((GEN)fac2[i],-1)));
}
RES[4]=(long)f;
RES[10]=(long)nf;
RES[5]=(long)rnfmakematrices(RES);
if (DEBUGLEVEL>1) msgtimer("matrices");
RES[9]=lgetg(1,t_VEC); /* table de multiplication */
p2=cgetg(6,t_VEC); RES[11]=(long)p2;
p1=rnfequation2(nf,pol); for (i=1; i<=3; i++) p2[i]=p1[i];
p4=cgetg(degabs+1,t_MAT);
for (i=1; i<=n; i++)
{ /* removing denominators speeds up multiplication */
GEN cop3,com, om = rnfelementreltoabs(RES,gmael(bas,1,i));
if (DEBUGLEVEL>1) msgtimer("i = %ld",i);
com = content(om); om = gdiv(om,com);
id=gmael(bas,2,i);
for (j=1; j<=m; j++)
{
p5=cgetg(degabs+1,t_COL); p4[(i-1)*m+j]=(long)p5;
p1=gmul((GEN)nf[7],(GEN)id[j]);
p3 = gsubst(p1,varn(nf[1]), (GEN)p2[2]);
cop3 = content(p3); p3 = gdiv(p3,cop3);
p3 = gmul(gmul(com,cop3), lift_intern(gmul(om,p3)));
for (k=1; k<lgef(p3)-1; k++) p5[k]=p3[k+1];
for ( ; k<=degabs; k++) p5[k]=zero;
}
}
if (DEBUGLEVEL>1) msgtimer("p4");
p3=denom(p4); if (gcmp1(p3)) p3=NULL; else p4=gmul(p3,p4);
p4=hnfmod(p4,detint(p4));
if (DEBUGLEVEL>1) msgtimer("hnfmod");
for (j=degabs-1; j>0; j--)
if (cmpis(gcoeff(p4,j,j),2) > 0)
{
p1=shifti(gcoeff(p4,j,j),-1);
for (k=j+1; k<=degabs; k++)
if (cmpii(gcoeff(p4,j,k),p1) > 0)
for (i=1; i<=j; i++)
coeff(p4,i,k)=lsubii(gcoeff(p4,i,k),gcoeff(p4,i,j));
}
if (p3) p4=gdiv(p4,p3);
p2[4]=(long)mat_to_vecpol(p4,vpol);
p2[5]=linvmat(p4);
tetpil=avma; return gerepile(av,tetpil,gcopy(RES));
}
GEN
rnfbasistoalg(GEN rnf,GEN x)
{
long tx=typ(x),lx=lg(x),av=avma,tetpil,i,n;
GEN p1,z,nf;
checkrnf(rnf); nf=(GEN)rnf[10];
switch(tx)
{
case t_VEC:
x=gtrans(x); /* fall through */
case t_COL:
n=lg(x)-1; p1=cgetg(n+1,t_COL);
for (i=1; i<=n; i++)
{
if (typ(x[i])==t_COL) p1[i]=(long)basistoalg(nf,(GEN)x[i]);
else p1[i]=x[i];
}
p1=gmul(gmael(rnf,7,1),p1); tetpil=avma;
return gerepile(av,tetpil,gmodulcp(p1,(GEN)rnf[1]));
case t_MAT:
z=cgetg(lx,tx);
for (i=1; i<lx; i++) z[i]=(long)rnfbasistoalg(rnf,(GEN)x[i]);
return z;
case t_POLMOD:
return gcopy(x);
default:
z=cgetg(3,t_POLMOD); z[1]=lcopy((GEN)rnf[1]);
z[2]=lmul(x,polun[varn(rnf[1])]); return z;
}
}
long polegal_spec(GEN x, GEN y);
/* assuem x is a t_POLMOD */
GEN
lift_to_pol(GEN x)
{
GEN y = (GEN)x[2];
return (typ(y) != t_POL)? gtopoly(y,varn(x[1])): y;
}
GEN
rnfalgtobasis(GEN rnf,GEN x)
{
long av=avma,tetpil,tx=typ(x),lx=lg(x),i,N;
GEN z;
checkrnf(rnf);
switch(tx)
{
case t_VEC: case t_COL: case t_MAT:
z=cgetg(lx,tx);
for (i=1; i<lx; i++) z[i]=(long)rnfalgtobasis(rnf,(GEN)x[i]);
return z;
case t_POLMOD:
if (!polegal_spec((GEN)rnf[1],(GEN)x[1]))
err(talker,"not the same number field in rnfalgtobasis");
x=lift_to_pol(x); /* fall through */
case t_POL:
N=lgef(rnf[1])-3;
if (tx==t_POL && lgef(x)-3 >= N) x=gmod(x,(GEN)rnf[1]);
z=cgetg(N+1,t_COL); for (i=1; i<=N; i++) z[i]=(long)truecoeff(x,i-1);
tetpil=avma; return gerepile(av,tetpil,gmul((GEN)rnf[8],z));
}
return gscalcol(x, lgef(rnf[1])-3);
}
/* x doit etre un polymod ou un polynome ou un vecteur de tels objets... */
GEN
rnfelementreltoabs(GEN rnf,GEN x)
{
long av=avma,tx,i,lx,va,tp3;
GEN z,p1,p2,p3,polabs,teta,alpha,s,k;
checkrnf(rnf); tx=typ(x); lx=lg(x); va=varn((GEN)rnf[1]);
switch(tx)
{
case t_VEC: case t_COL: case t_MAT:
z=cgetg(lx,tx);
for (i=1; i<lx; i++) z[i]=(long)rnfelementreltoabs(rnf,(GEN)x[i]);
return z;
case t_POLMOD:
x=lift_to_pol(x); /* fall through */
case t_POL:
if (gvar(x) > va)
{
if (gcmp0(x)) {x=cgetg(2,t_POL); x[1]=evalvarn(va) | evallgef(2);}
else
{
p1=cgetg(3,t_POL); p1[1]=evalvarn(va) | evallgef(3) | evalsigne(1);
p1[2]=(long)x; x=p1;
}
}
p1=(GEN)rnf[11]; polabs=(GEN)p1[1]; alpha=(GEN)p1[2]; k=(GEN)p1[3];
teta=gmodulcp(gsub(polx[va],gmul(k,(GEN)alpha[2])),polabs);
s=gzero;
for (i=lgef(x)-1; i>1; i--)
{
p3=(GEN)x[i]; tp3=typ(p3);
if (is_const_t(tp3)) p2 = p3;
else
switch(tp3)
{
case t_POLMOD:
p3 = (GEN)p3[2]; /* fall through */
case t_POL:
p2 = poleval(p3,alpha);
}
s=gadd(p2,gmul(teta,s));
}
return gerepileupto(av,s);
default: return gcopy(x);
}
}
GEN
rnfelementabstorel(GEN rnf,GEN x)
{
long av=avma,tx,i,lx;
GEN z,p1,s,tetap,k,nf;
checkrnf(rnf); tx=typ(x); lx=lg(x);
switch(tx)
{
case t_VEC: case t_COL: case t_MAT:
z=cgetg(lx,tx);
for (i=1; i<lx; i++) z[i]=(long)rnfelementabstorel(rnf,(GEN)x[i]);
return z;
case t_POLMOD:
x=lift_to_pol(x); /* fall through */
case t_POL:
p1=(GEN)rnf[11]; k=(GEN)p1[3]; nf=(GEN)rnf[10];
tetap=gmodulcp(gadd(polx[varn(rnf[1])],
gmul(k,gmodulcp(polx[varn(nf[1])],(GEN)nf[1]))),(GEN)rnf[1]);
s=gzero;
for (i=lgef(x)-1; i>1; i--) s=gadd((GEN)x[i],gmul(tetap,s));
return gerepileupto(av,s);
default: return gcopy(x);
}
}
/* x doit etre un polymod ou un polynome ou un vecteur de tels objets... */
GEN
rnfelementup(GEN rnf,GEN x)
{
long i,lx,tx;
GEN z;
checkrnf(rnf); tx=typ(x); lx=lg(x);
switch(tx)
{
case t_VEC: case t_COL: case t_MAT:
z=cgetg(lx,tx);
for (i=1; i<lx; i++) z[i]=(long)rnfelementup(rnf,(GEN)x[i]);
return z;
case t_POLMOD:
x=(GEN)x[2]; /* fall through */
case t_POL:
return poleval(x,gmael(rnf,11,2));
default: return gcopy(x);
}
}
/* x doit etre un polymod ou un polynome ou un vecteur de tels objets..*/
GEN
rnfelementdown(GEN rnf,GEN x)
{
long av=avma,tetpil,i,lx,tx;
GEN p1,z;
checkrnf(rnf); tx=typ(x); lx=lg(x);
switch(tx)
{
case t_VEC: case t_COL: case t_MAT:
z=cgetg(lx,tx);
for (i=1; i<lx; i++) z[i]=(long)rnfelementdown(rnf,(GEN)x[i]);
return z;
case t_POLMOD:
x=(GEN)x[2]; /* fall through */
case t_POL:
if (gcmp0(x)) return gzero;
p1=rnfelementabstorel(rnf,x);
if (typ(p1)==t_POLMOD && varn(p1[1])==varn(rnf[1])) p1=(GEN)p1[2];
if (gvar(p1)>varn(rnf[1]))
{
tetpil=avma;
return gerepile(av,tetpil,gcopy(p1));
}
if (lgef(p1)==3)
{
tetpil=avma;
return gerepile(av,tetpil,gcopy((GEN)p1[2]));
}
err(talker,"element is not in the base field in rnfelementdown");
default: return gcopy(x);
}
}
/* x est exprime sur la base relative */
static GEN
rnfprincipaltohermite(GEN rnf,GEN x)
{
long av=avma,tetpil;
GEN nf,bas,bas1,p1,z;
x=rnfbasistoalg(rnf,x); nf=(GEN)rnf[10];
bas=(GEN)rnf[7]; bas1=(GEN)bas[1];
p1=rnfalgtobasis(rnf,gmul(x,gmodulcp(bas1,(GEN)rnf[1])));
z=cgetg(3,t_VEC); z[2]=bas[2];
settyp(p1,t_MAT); z[1]=(long)matalgtobasis(nf,p1);
tetpil=avma;
return gerepile(av,tetpil,nfhermite(nf,z));
}
GEN
rnfidealhermite(GEN rnf,GEN x)
{
long tx=typ(x),lx=lg(x),av=avma,tetpil,i,j,n,m;
GEN z,p1,p2,x1,x2,x1j,nf,bas,unnf,zeronf;
checkrnf(rnf);
n=lgef(rnf[1])-3; nf=(GEN)rnf[10]; bas=(GEN)rnf[7];
switch(tx)
{
case t_INT: case t_FRAC: case t_FRACN: z=cgetg(3,t_VEC);
m=lgef(nf[1])-3; zeronf=gscalcol_i(gzero,m); unnf=gscalcol_i(gun,m);
p1=cgetg(n+1,t_MAT); z[1]=(long)p1;
for (j=1; j<=n; j++)
{
p2=cgetg(n+1,t_COL); p1[j]=(long)p2;
for (i=1; i<=n; i++) p2[i]=(i==j)?(long)unnf:(long)zeronf;
}
z[2]=lmul(x,(GEN)bas[2]); return z;
case t_POLMOD: case t_POL:
p1=rnfalgtobasis(rnf,x); tetpil=avma;
return gerepile(av,tetpil,rnfprincipaltohermite(rnf,p1));
case t_VEC:
switch(lx)
{
case 3:
x1=(GEN)x[1];
if (typ(x1)!=t_MAT || lg(x1) < n+1 || lg(x1[1]) != n+1)
err(talker,"incorrect type in rnfidealhermite");
p1=cgetg(n+1,t_MAT);
for (j=1; j<=n; j++)
{
p2=cgetg(n+1,t_COL); p1[j]=(long)p2; x1j=(GEN)x1[j];
for (i=1; i<=n; i++)
{
tx = typ(x1j[i]);
if (is_const_t(tx)) p2[i] = x1j[i];
else
switch(tx)
{
case t_POLMOD: case t_POL:
p2[i]=(long)algtobasis(nf,(GEN)x1j[i]); break;
case t_COL:
p2[i]=x1j[i]; break;
default: err(talker,"incorrect type in rnfidealhermite");
}
}
}
x2=(GEN)x[2];
if (typ(x2)!=t_VEC || lg(x2)!=lg(x1))
err(talker,"incorrect type in rnfidealhermite");
tetpil=avma; z=cgetg(3,t_VEC); z[1]=lcopy(p1); z[2]=lcopy(x2);
z=gerepile(av,tetpil,nfhermite(nf,z));
if (lg(z[1]) != n+1)
err(talker,"not an ideal in rnfidealhermite");
return z;
case 6:
err(impl,"rnfidealhermite for prime ideals");
default:
err(typeer,"rnfidealhermite");
}
case t_COL:
if (lx!=(n+1)) err(typeer,"rnfidealhermite");
return rnfprincipaltohermite(rnf,x);
case t_MAT:
return rnfidealabstorel(rnf,x);
}
err(typeer,"rnfidealhermite");
return NULL; /* not reached */
}
GEN
rnfidealnormrel(GEN rnf,GEN id)
{
long av=avma,i,n;
GEN z,id2,nf;
checkrnf(rnf);
id=rnfidealhermite(rnf,id); id2=(GEN)id[2];
n=lgef(rnf[1])-3; nf=(GEN)rnf[10];
if (n==1) { avma=av; return idmat(lgef(nf[1]-3)); }
z=(GEN)id2[1]; for (i=2; i<=n; i++) z=idealmul(nf,z,(GEN)id2[i]);
return gerepileupto(av,z);
}
GEN
rnfidealnormabs(GEN rnf,GEN id)
{
long av=avma,i,n;
GEN z,id2;
checkrnf(rnf);
id=rnfidealhermite(rnf,id); id2=(GEN)id[2];
n=lgef(rnf[1])-3;
z=gun; for (i=1; i<=n; i++) z=gmul(z,dethnf((GEN)id2[i]));
return gerepileupto(av,z);
}
GEN
rnfidealreltoabs(GEN rnf,GEN x)
{
long av=avma,tetpil,i,j,k,n,m;
GEN nf,basinv,om,id,p1,p2,p3,p4,p5;
checkrnf(rnf);
x=rnfidealhermite(rnf,x);
n=lgef(rnf[1])-3; nf=(GEN)rnf[10]; m=lgef(nf[1])-3;
basinv=(GEN)((GEN)rnf[11])[5];
p3=cgetg(n*m+1,t_MAT); p2=gmael(rnf,11,2);
for (i=1; i<=n; i++)
{
om=rnfbasistoalg(rnf,gmael(x,1,i)); id=gmael(x,2,i);
om=rnfelementreltoabs(rnf,om);
for (j=1; j<=m; j++)
{
p1=gmul((GEN)nf[7],(GEN)id[j]);
p4=lift_intern(gmul(om,gsubst(p1,varn(nf[1]),p2)));
p5=cgetg(n*m+1,t_COL);
for (k=0; k<n*m; k++) p5[k+1]=(long)truecoeff(p4,k);
p3[(i-1)*m+j]=(long)p5;
}
}
p1=gmul(basinv,p3); p2=detint(p1);
tetpil=avma; return gerepile(av,tetpil,hnfmod(p1,p2));
}
GEN
rnfidealabstorel(GEN rnf,GEN x)
{
long av=avma,tetpil,n,m,j,k;
GEN nf,basabs,ma,xj,p1,p2,id;
checkrnf(rnf); n=lgef(rnf[1])-3; nf=(GEN)rnf[10]; m=lgef(nf[1])-3;
if (typ(x)!=t_MAT || lg(x)!=(n*m+1) || lg(x[1])!=(n*m+1))
err(impl,"rnfidealabstorel for an ideal not in HNF");
basabs=gmael(rnf,11,4); ma=cgetg(n*m+1,t_MAT);
for (j=1; j<=n*m; j++)
{
p2=cgetg(n+1,t_COL); ma[j]=(long)p2;
xj=gmul(basabs,(GEN)x[j]);
xj=lift_intern(rnfelementabstorel(rnf,xj));
for (k=0; k<n; k++)
p2[k+1]=(long)truecoeff(xj,k);
}
ma=gmul((GEN)rnf[8],ma);
ma=matalgtobasis(nf,ma);
p1=cgetg(n*m+1,t_VEC); id=idmat(m);
for (j=1; j<=n*m; j++) p1[j]=(long)id;
p2=cgetg(3,t_VEC); p2[1]=(long)ma; p2[2]=(long)p1;
tetpil=avma; return gerepile(av,tetpil,nfhermite(nf,p2));
}
GEN
rnfidealdown(GEN rnf,GEN x)
{
long av=avma,tetpil;
checkrnf(rnf); x=rnfidealhermite(rnf,x);
tetpil=avma; return gerepile(av,tetpil,gcopy(gmael(x,2,1)));
}
/* lift ideal x to the relative extension, returns a Z-basis */
GEN
rnfidealup(GEN rnf,GEN x)
{
long av=avma,tetpil,i,n,m;
GEN nf,bas,bas2,p1,p2,zeronf,unnf;
checkrnf(rnf);
bas=(GEN)rnf[7]; bas2=(GEN)bas[2];
n=lg(bas2)-1; nf=(GEN)rnf[10]; m=lgef((GEN)nf[1])-3;
zeronf=zerocol(m); unnf=gscalcol_i(gun,m);
p2=cgetg(3,t_VEC); p1=cgetg(n+1,t_VEC);
p2[1]=(long)idmat_intern(n,unnf,zeronf);
p2[2]=(long)p1;
for (i=1; i<=n; i++) p1[i]=(long)idealmul(nf,x,(GEN)bas2[i]);
tetpil=avma; return gerepile(av,tetpil,rnfidealreltoabs(rnf,p2));
}
/* x a relative HNF ---> vector of 2 generators (relative polymods) */
GEN
rnfidealtwoelement(GEN rnf,GEN x)
{
long av=avma,tetpil,j;
GEN p1,p2,p3,res,polabs,nfabs,z;
res=(GEN)rnf[11]; polabs=(GEN)res[1];
nfabs=cgetg(10,t_VEC); nfabs[1]=(long)polabs;
for (j=2; j<=9; j++) nfabs[j]=zero;
nfabs[7]=(long)lift((GEN)res[4]); nfabs[8]=res[5];
p1=rnfidealreltoabs(rnf,x);
p2=ideal_two_elt(nfabs,p1);
p3=rnfelementabstorel(rnf,gmul((GEN)res[4],(GEN)p2[2]));
tetpil=avma; z=cgetg(3,t_VEC); z[1]=lcopy((GEN)p2[1]);
z[2]=(long)rnfalgtobasis(rnf,p3);
return gerepile(av,tetpil,z);
}
GEN
rnfidealmul(GEN rnf,GEN x,GEN y) /* x et y sous HNF relative uniquement */
{
long av=avma,tetpil,i,j,n;
GEN z,nf,x1,x2,p1,p2,p3,p4,p5,res;
z=rnfidealtwoelement(rnf,y);
nf=(GEN)rnf[10]; n=lgef(rnf[1])-3;
x=rnfidealhermite(rnf,x);
x1=gmodulcp(gmul(gmael(rnf,7,1),matbasistoalg(nf,(GEN)x[1])),(GEN) rnf[1]);
x2=(GEN)x[2]; p1=gmul((GEN)z[1],(GEN)x[1]);
p2=lift_intern(gmul(rnfbasistoalg(rnf,(GEN)z[2]),x1));
p3=cgetg(n+1,t_MAT);
for (j=1; j<=n; j++)
{
p4=cgetg(n+1,t_COL); p3[j]=(long)p4; p5=(GEN)p2[j];
for (i=1; i<=n; i++)
p4[i]=(long)algtobasis(nf,truecoeff((GEN)p5,i-1));
}
res=cgetg(3,t_VEC);
res[1]=(long)concatsp(p1,p3);
res[2]=(long)concatsp(x2,x2);
tetpil=avma; return gerepile(av,tetpil,nfhermite(nf,res));
}
/*********************************************************************/
/** **/
/** LIBRARY FOR POLYNOMIALS WITH COEFFS. IN Z_K/P **/
/** An element in Z_K/P is a t_COL with degree(nf[1]) components. **/
/** These are integers modulo the prime p under prime ideal P **/
/** (only f(P/p) elements are non zero). These components are **/
/** given on the integer basis of K. **/
/** **/
/*********************************************************************/
/* K.B: What follows is not meant to work (yet?) */
GEN
polnfmulscal(GEN nf,GEN s,GEN x)
{
long i,lx=lgef(x);
GEN z;
if (lx<3) return gcopy(x);
if (gcmp0(s))
{
z=cgetg(2,t_POL); z[1]=evallgef(2) | evalvarn(varn(x));
return z;
}
z=cgetg(lx,t_POL); z[1]=x[1];
for (i=2; i<lx; i++) z[i]=(long)element_mul(nf,s,(GEN)x[i]);
return z;
}
GEN
polnfmul(GEN nf, GEN x, GEN y)
{
long av,tetpil,m,i,d,imin,imax,lx,ly,lz;
GEN p1,z,zeronf;
if (gcmp0(x)||gcmp0(y))
{
z=cgetg(2,t_POL); z[1]=evallgef(2) | evalvarn(varn(x));
return z;
}
m=lgef(nf[1])-3; av=avma;
lx=lgef(x)-3; ly=lgef(y)-3; lz=lx+ly;
zeronf=gscalcol_i(gzero,m);
z=cgetg(lz+3,t_POL);
z[1] = evallgef(lz+3) | evalvarn(x) | evalsigne(1);
for (d=0; d<=lz; d++)
{
p1=zeronf; imin=max(0,d-ly); imax=min(d,lx);
for (i=imin; i<=imax; i++)
p1=gadd(p1,element_mul(nf,(GEN)x[i+2],(GEN)y[d-i+2]));
z[d+2]=(long)p1;
}
tetpil=avma; return gerepile(av,tetpil,gcopy(z));
}
/* division euclidienne */
GEN
polnfdeuc(GEN nf, GEN x, GEN y, GEN *ptr)
{
long av=avma,m,i,d,tx,lx,ly,lz,fl;
GEN z,unnf,lcy,r;
GEN *gptr[2];
if (gcmp0(y)) err(talker,"division by zero in polnfdiv");
lx=lgef(x); ly=lgef(y); lz=lx-ly;
if (gcmp0(x) || lz<0) { *ptr=gcopy(x); return zeropol(varn(x)); }
m=lgef(nf[1])-3; unnf=gscalcol_i(gun,m);
x=dummycopy(x); y=dummycopy(y);
for (i=2; i<lx; i++)
{
tx=typ(x[i]);
if (is_intreal_t(tx) || tx == t_INTMOD || is_frac_t(tx))
x[i]=lmul((GEN)x[i],unnf);
}
for (i=2; i<ly; i++)
{
tx=typ(y[i]);
if (is_intreal_t(tx) || tx == t_INTMOD || is_frac_t(tx))
y[i]=lmul((GEN)y[i],unnf);
}
lz += 3;
z=cgetg(lz,t_POL); z[1]=evallgef(lz) | evalvarn(x) | evalsigne(1);
lcy=(GEN)y[ly-1];
if (gegal(lift(lcy),unnf)) fl=0;
else
{
fl=1; y=polnfmulscal(nf,element_inv(nf,lcy),y);
}
for (d=lz-1; d>=2; d--)
{
z[d]=x[d+ly-3];
for (i=d; i<d+ly-3; i++)
x[i]=lsub((GEN)x[i],element_mul(nf,(GEN)z[d],(GEN)y[i-d-2]));
}
if (fl) z=polnfmulscal(nf,lcy,z);
for(;;)
{
if (!gcmp0((GEN)x[d]))
{
r=cgetg(d,t_POL);
r[1] = evallgef(d) | evalvarn(varn(x)) | evalsigne(1);
for (i=2; i<d; i++) r[i]=x[i];
break;
}
if (d==2) { r = zeropol(varn(x)); break; }
d--;
}
*ptr=r; gptr[0]=ptr; gptr[1]=&z;
gerepilemany(av,gptr,2); return z;
}
GEN
polnfpow(GEN nf,GEN x,GEN k)
{
long s,av=avma,m;
GEN y,z;
m=lgef(nf[1])-3;
if (typ(k)!=t_INT) err(talker,"not an integer exponent in nfpow");
s=signe(k); if (s<0) err(impl,"polnfpow for negative exponents");
z=x; y=cgetg(3,t_POL);
y[1] = evallgef(3) | evalvarn(varn(x)) | evalsigne(1);
y[2] = (long)gscalcol_i(gun,m);
for(;;)
{
if (mpodd(k)) y=polnfmul(nf,z,y);
k=shifti(k,-1);
if (!signe(k)) { cgiv(k); return gerepileupto(av,y); }
z=polnfmul(nf,z,z);
}
}