/*
* Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
* All rights reserved.
*
* FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
* non-exclusive and royalty-free license to use, copy, modify and
* redistribute, solely for non-commercial and non-profit purposes, the
* computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
* conditions of this Agreement. For the avoidance of doubt, you acquire
* only a limited right to use the SOFTWARE hereunder, and FLL or any
* third party developer retains all rights, including but not limited to
* copyrights, in and to the SOFTWARE.
*
* (1) FLL does not grant you a license in any way for commercial
* purposes. You may use the SOFTWARE only for non-commercial and
* non-profit purposes only, such as academic, research and internal
* business use.
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* international copyright treaties. If you make copies of the SOFTWARE,
* with or without modification, as permitted hereunder, you shall affix
* to all such copies of the SOFTWARE the above copyright notice.
* (3) An explicit reference to this SOFTWARE and its copyright owner
* shall be made on your publication or presentation in any form of the
* results obtained by use of the SOFTWARE.
* (4) In the event that you modify the SOFTWARE, you shall notify FLL by
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* for such modification or the source code of the modified part of the
* SOFTWARE.
*
* THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
* MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
* EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
* FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
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* ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
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*
* $OpenXM: OpenXM_contrib2/asir2018/engine/PU.c,v 1.2 2018/09/28 08:20:28 noro Exp $
*/
#include "ca.h"
void reorderp(VL nvl,VL ovl,P p,P *pr)
{
DCP dc;
P x,m,s,t,c;
if ( !p )
*pr = 0;
else if ( NUM(p) )
*pr = p;
else {
MKV(VR(p),x);
for ( s = 0, dc = DC(p); dc; dc = NEXT(dc) ) {
reorderp(nvl,ovl,COEF(dc),&c);
if ( DEG(dc) ) {
pwrp(nvl,x,DEG(dc),&t); mulp(nvl,c,t,&m);
addp(nvl,m,s,&t);
} else
addp(nvl,s,c,&t);
s = t;
}
*pr = s;
}
}
void substp(VL vl,P p,V v0,P p0,P *pr)
{
P x,t,m,c,s,a;
DCP dc;
Z d;
if ( !p )
*pr = 0;
else if ( NUM(p) )
*pr = p;
else if ( VR(p) != v0 ) {
MKV(VR(p),x);
for ( c = 0, dc = DC(p); dc; dc = NEXT(dc) ) {
substp(vl,COEF(dc),v0,p0,&t);
if ( DEG(dc) ) {
pwrp(vl,x,DEG(dc),&s); mulp(vl,s,t,&m);
addp(vl,m,c,&a);
c = a;
} else {
addp(vl,t,c,&a);
c = a;
}
}
*pr = c;
} else {
dc = DC(p);
c = COEF(dc);
for ( d = DEG(dc), dc = NEXT(dc);
dc; d = DEG(dc), dc = NEXT(dc) ) {
subz(d,DEG(dc),(Z *)&t); pwrp(vl,p0,(Z)t,&s);
mulp(vl,s,c,&m);
addp(vl,m,COEF(dc),&c);
}
if ( d ) {
pwrp(vl,p0,d,&t); mulp(vl,t,c,&m);
c = m;
}
*pr = c;
}
}
void substpp(VL vl,P p,V *vvect,P *svect,int nv,P *pr);
void substpp(VL vl,P p,V *vvect,P *svect,int nv,P *pr)
{
P x,t,m,c,s,a,p0,c1;
DCP dc;
Z d;
V v;
int i;
if ( !p )
*pr = 0;
else if ( NUM(p) )
*pr = p;
else {
v = VR(p);
for ( i = 0; i < nv; i++ ) if ( vvect[i] == v ) break;
if ( svect[i] && OID(svect[i]) < 0 ) {
MKV(VR(p),x);
for ( c = 0, dc = DC(p); dc; dc = NEXT(dc) ) {
substpp(vl,COEF(dc),vvect,svect,nv,&t);
if ( DEG(dc) ) {
pwrp(vl,x,DEG(dc),&s); mulp(vl,s,t,&m);
addp(vl,m,c,&a);
c = a;
} else {
addp(vl,t,c,&a);
c = a;
}
}
*pr = c;
} else {
p0 = svect[i];
dc = DC(p);
substpp(vl,COEF(dc),vvect,svect,nv,&c);
for ( d = DEG(dc), dc = NEXT(dc);
dc; d = DEG(dc), dc = NEXT(dc) ) {
subz(d,DEG(dc),(Z *)&t); pwrp(vl,p0,(Z)t,&s);
mulp(vl,s,c,&m);
substpp(vl,COEF(dc),vvect,svect,nv,&c1);
addp(vl,m,c1,&c);
}
if ( d ) {
pwrp(vl,p0,d,&t); mulp(vl,t,c,&m);
c = m;
}
*pr = c;
}
}
}
void detp(VL vl,P **rmat,int n,P *dp)
{
int i,j,k,l,sgn,nmin,kmin,lmin,ntmp;
P mjj,mij,t,s,u,d;
P **mat;
P *mi,*mj;
mat = (P **)almat_pointer(n,n);
for ( i = 0; i < n; i++ )
for ( j = 0; j < n; j++ )
mat[i][j] = rmat[i][j];
for ( j = 0, d = (P)ONE, sgn = 1; j < n; j++ ) {
for ( i = j; (i < n) && !mat[i][j]; i++ );
if ( i == n ) {
*dp = 0; return;
}
nmin = nmonop(mat[i][j]);
kmin=i; lmin=j;
for ( k = j; k < n; k++ )
for ( l = j; l < n; l++ )
if ( mat[k][l] && ((ntmp=nmonop(mat[k][l])) < nmin) ) {
kmin = k; lmin = l; nmin = ntmp;
}
if ( kmin != j ) {
mj = mat[j]; mat[j] = mat[kmin]; mat[kmin] = mj; sgn = -sgn;
}
if ( lmin != j ) {
for ( k = j; k < n; k++ ) {
t = mat[k][j]; mat[k][j] = mat[k][lmin]; mat[k][lmin] = t;
}
sgn = -sgn;
}
for ( i = j + 1, mj = mat[j], mjj = mj[j]; i < n; i++ )
for ( k = j + 1, mi = mat[i], mij = mi[j]; k < n; k++ ) {
mulp(vl,mi[k],mjj,&t); mulp(vl,mj[k],mij,&s);
subp(vl,t,s,&u); divsp(vl,u,d,&mi[k]);
}
d = mjj;
}
if ( sgn < 0 )
chsgnp(d,dp);
else
*dp = d;
}
void invmatp(VL vl,P **rmat,int n,P ***imatp,P *dnp)
{
int i,j,k,l,n2;
P mjj,mij,t,s,u,d;
P **mat,**imat;
P *mi,*mj,*w;
n2 = n<<1;
mat = (P **)almat_pointer(n,n2);
for ( i = 0; i < n; i++ ) {
for ( j = 0; j < n; j++ )
mat[i][j] = rmat[i][j];
mat[i][i+n] = (P)ONE;
}
for ( j = 0, d = (P)ONE; j < n; j++ ) {
for ( i = j; (i < n) && !mat[i][j]; i++ );
if ( i == n ) {
error("invmatp : input is singular");
}
for ( k = i; k < n; k++ )
if ( mat[k][j] && (nmonop(mat[k][j]) < nmonop(mat[i][j]) ) )
i = k;
if ( j != i ) {
mj = mat[j]; mat[j] = mat[i]; mat[i] = mj;
}
for ( i = j + 1, mj = mat[j], mjj = mj[j]; i < n; i++ )
for ( k = j + 1, mi = mat[i], mij = mi[j]; k < n2; k++ ) {
mulp(vl,mi[k],mjj,&t); mulp(vl,mj[k],mij,&s);
subp(vl,t,s,&u); divsp(vl,u,d,&mi[k]);
}
d = mjj;
}
/* backward substitution */
w = (P *)ALLOCA(n2*sizeof(P));
for ( i = n-2; i >= 0; i-- ) {
bzero(w,n2*sizeof(P));
for ( k = i+1; k < n; k++ )
for ( l = k, u = mat[i][l]; l < n2; l++ ) {
mulp(vl,mat[k][l],u,&t); addp(vl,w[l],t,&s); w[l] = s;
}
for ( j = i, u = mat[i][j]; j < n2; j++ ) {
mulp(vl,mat[i][j],d,&t); subp(vl,t,w[j],&s);
divsp(vl,s,u,&mat[i][j]);
}
}
imat = (P **)almat_pointer(n,n);
for ( i = 0; i < n; i++ )
for ( j = 0; j < n; j++ )
imat[i][j] = mat[i][j+n];
*imatp = imat;
*dnp = d;
}
void reordvar(VL vl,V v,VL *nvlp)
{
VL nvl,nvl0;
for ( NEWVL(nvl0), nvl0->v = v, nvl = nvl0;
vl; vl = NEXT(vl) )
if ( vl->v == v )
continue;
else {
NEWVL(NEXT(nvl));
nvl = NEXT(nvl);
nvl->v = vl->v;
}
NEXT(nvl) = 0;
*nvlp = nvl0;
}
void gcdprsp(VL vl,P p1,P p2,P *pr)
{
P g1,g2,gc1,gc2,gp1,gp2,g,gc,gp,gcr;
V v1,v2;
if ( !p1 )
ptozp0(p2,pr);
else if ( !p2 )
ptozp0(p1,pr);
else if ( NUM(p1) || NUM(p2) )
*pr = (P)ONE;
else {
ptozp0(p1,&g1); ptozp0(p2,&g2);
if ( ( v1 = VR(g1) ) == ( v2 = VR(g2) ) ) {
gcdcp(vl,g1,&gc1); divsp(vl,g1,gc1,&gp1);
gcdcp(vl,g2,&gc2); divsp(vl,g2,gc2,&gp2);
gcdprsp(vl,gc1,gc2,&gcr);
sprs(vl,v1,gp1,gp2,&g);
if ( VR(g) == v1 ) {
ptozp0(g,&gp);
gcdcp(vl,gp,&gc); divsp(vl,gp,gc,&gp1);
mulp(vl,gp1,gcr,pr);
} else
*pr = gcr;
} else {
while ( v1 != vl->v && v2 != vl->v )
vl = NEXT(vl);
if ( v1 == vl->v ) {
gcdcp(vl,g1,&gc1); gcdprsp(vl,gc1,g2,pr);
} else {
gcdcp(vl,g2,&gc2); gcdprsp(vl,gc2,g1,pr);
}
}
}
}
void gcdcp(VL vl,P p,P *pr)
{
P g,g1;
DCP dc;
if ( NUM(p) )
*pr = (P)ONE;
else {
dc = DC(p);
g = COEF(dc);
for ( dc = NEXT(dc); dc; dc = NEXT(dc) ) {
gcdprsp(vl,g,COEF(dc),&g1);
g = g1;
}
*pr = g;
}
}
void sprs(VL vl,V v,P p1,P p2,P *pr)
{
P q1,q2,m,m1,m2,x,h,r,g1,g2;
int d;
Z dq;
VL nvl;
reordvar(vl,v,&nvl);
reorderp(nvl,vl,p1,&q1); reorderp(nvl,vl,p2,&q2);
if ( ( VR(q1) != v ) || ( VR(q2) != v ) ) {
*pr = 0;
return;
}
if ( deg(v,q1) >= deg(v,q2) ) {
g1 = q1; g2 = q2;
} else {
g2 = q1; g1 = q2;
}
for ( h = (P)ONE, x = (P)ONE; ; ) {
if ( !deg(v,g2) )
break;
premp(nvl,g1,g2,&r);
if ( !r )
break;
d = deg(v,g1) - deg(v,g2); STOZ(d,dq);
pwrp(nvl,h,dq,&m); mulp(nvl,m,x,&m1); g1 = g2;
divsp(nvl,r,m1,&g2); x = LC(g1); /* g1 is not const w.r.t v */
pwrp(nvl,x,dq,&m1); mulp(nvl,m1,h,&m2);
divsp(nvl,m2,m,&h);
}
*pr = g2;
}
void resultp(VL vl,V v,P p1,P p2,P *pr)
{
P q1,q2,m,m1,m2,lc,q,r,t,g1,g2,adj;
int d,d1,d2,j,k;
VL nvl;
Z dq;
if ( !p1 || !p2 ) {
*pr = 0; return;
}
reordvar(vl,v,&nvl);
reorderp(nvl,vl,p1,&q1); reorderp(nvl,vl,p2,&q2);
if ( VR(q1) != v )
if ( VR(q2) != v ) {
*pr = 0;
return;
} else {
d = deg(v,q2); STOZ(d,dq);
pwrp(vl,q1,dq,pr);
return;
}
else if ( VR(q2) != v ) {
d = deg(v,q1); STOZ(d,dq);
pwrp(vl,q2,dq,pr);
return;
}
if ( ( VR(q1) != v ) || ( VR(q2) != v ) ) {
*pr = 0;
return;
}
d1 = deg(v,q1); d2 = deg(v,q2);
if ( d1 > d2 ) {
g1 = q1; g2 = q2; adj = (P)ONE;
} else if ( d1 < d2 ) {
g2 = q1; g1 = q2;
if ( (d1 % 2) && (d2 % 2) ) {
STOZ(-1,dq); adj = (P)dq;
} else
adj = (P)ONE;
} else {
premp(nvl,q1,q2,&t);
d = deg(v,t); STOZ(d,dq); pwrp(nvl,LC(q2),dq,&adj);
g1 = q2; g2 = t;
if ( d1 % 2 ) {
chsgnp(adj,&t); adj = t;
}
}
d1 = deg(v,g1); j = d1 - 1;
for ( lc = (P)ONE; ; ) {
if ( ( k = deg(v,g2) ) < 0 ) {
*pr = 0;
return;
}
if ( k == j )
if ( !k ) {
divsp(nvl,g2,adj,pr);
return;
} else {
premp(nvl,g1,g2,&r); mulp(nvl,lc,lc,&m);
divsp(nvl,r,m,&q);
g1 = g2; g2 = q;
lc = LC(g1); /* g1 is not const */
j = k - 1;
}
else {
d = j - k; STOZ(d,dq);
pwrp(nvl,(VR(g2)==v?LC(g2):g2),dq,&m);
mulp(nvl,g2,m,&m1);
pwrp(nvl,lc,dq,&m); divsp(nvl,m1,m,&t);
if ( k == 0 ) {
divsp(nvl,t,adj,pr);
return;
} else {
premp(nvl,g1,g2,&r);
mulp(nvl,lc,lc,&m1); mulp(nvl,m,m1,&m2);
divsp(nvl,r,m2,&q);
g1 = t; g2 = q;
if ( d % 2 ) {
chsgnp(g2,&t); g2 = t;
}
lc = LC(g1); /* g1 is not const */
j = k - 1;
}
}
}
}
void srch2(VL vl,V v,P p1,P p2,P *pr)
{
P q1,q2,m,m1,m2,lc,q,r,t,s,g1,g2,adj;
int d,d1,d2,j,k;
VL nvl;
Z dq;
reordvar(vl,v,&nvl);
reorderp(nvl,vl,p1,&q1); reorderp(nvl,vl,p2,&q2);
if ( VR(q1) != v )
if ( VR(q2) != v ) {
*pr = 0;
return;
} else {
d = deg(v,q2); STOZ(d,dq);
pwrp(vl,q1,dq,pr);
return;
}
else if ( VR(q2) != v ) {
d = deg(v,q1); STOZ(d,dq);
pwrp(vl,q2,dq,pr);
return;
}
if ( ( VR(q1) != v ) || ( VR(q2) != v ) ) {
*pr = 0;
return;
}
if ( deg(v,q1) >= deg(v,q2) ) {
g1 = q1; g2 = q2;
} else {
g2 = q1; g1 = q2;
}
if ( ( d1 = deg(v,g1) ) > ( d2 = deg(v,g2) ) ) {
j = d1 - 1;
adj = (P)ONE;
} else {
premp(nvl,g1,g2,&t);
d = deg(v,t); STOZ(d,dq);
pwrp(nvl,LC(g2),dq,&adj);
g1 = g2; g2 = t;
j = deg(v,g1) - 1;
}
for ( lc = (P)ONE; ; ) {
if ( ( k = deg(v,g2) ) < 0 ) {
*pr = 0;
return;
}
ptozp(g1,1,(Q *)&t,&s); g1 = s; ptozp(g2,1,(Q *)&t,&s); g2 = s;
if ( k == j )
if ( !k ) {
divsp(nvl,g2,adj,pr);
return;
} else {
premp(nvl,g1,g2,&r); mulp(nvl,lc,lc,&m);
divsp(nvl,r,m,&q);
g1 = g2; g2 = q;
lc = LC(g1); /* g1 is not const */
j = k - 1;
}
else {
d = j - k; STOZ(d,dq);
pwrp(nvl,(VR(g2)==v?LC(g2):g2),dq,&m);
mulp(nvl,g2,m,&m1);
pwrp(nvl,lc,dq,&m); divsp(nvl,m1,m,&t);
if ( k == 0 ) {
divsp(nvl,t,adj,pr);
return;
} else {
premp(nvl,g1,g2,&r);
mulp(nvl,lc,lc,&m1); mulp(nvl,m,m1,&m2);
divsp(nvl,r,m2,&q);
g1 = t; g2 = q;
if ( d % 2 ) {
chsgnp(g2,&t); g2 = t;
}
lc = LC(g1); /* g1 is not const */
j = k - 1;
}
}
}
}
void srcr(VL vl,V v,P p1,P p2,P *pr)
{
P q1,q2,c,c1;
P tg,tg1,tg2,resg;
int index,mod;
Q a,b,f,q,s,u,w;
Z n,m,t;
VL nvl;
reordvar(vl,v,&nvl);
reorderp(nvl,vl,p1,&q1); reorderp(nvl,vl,p2,&q2);
if ( ( VR(q1) != v ) && ( VR(q2) != v ) ) {
*pr = 0;
return;
}
if ( VR(q1) != v ) {
pwrp(vl,q1,DEG(DC(q2)),pr);
return;
}
if ( VR(q2) != v ) {
pwrp(vl,q2,DEG(DC(q1)),pr);
return;
}
norm1c(q1,&a); norm1c(q2,&b);
n = DEG(DC(q1)); m = DEG(DC(q2));
pwrq(a,(Q)m,&w); pwrq(b,(Q)n,&s); mulq(w,s,&u);
factorialz(ZTOS(n)+ZTOS(m),&t);
mulq(u,(Q)t,&s); addq(s,s,&f);
for ( index = 0, q = (Q)ONE, c = 0; cmpq(f,q) >= 0; ) {
mod = get_lprime(index++);
ptomp(mod,LC(q1),&tg);
if ( !tg )
continue;
ptomp(mod,LC(q2),&tg);
if ( !tg )
continue;
ptomp(mod,q1,&tg1); ptomp(mod,q2,&tg2);
srchmp(nvl,mod,v,tg1,tg2,&resg);
chnremp(nvl,mod,c,(Z)q,resg,&c1); c = c1;
STOZ(mod,t); mulq(q,(Q)t,&s); q = s;
}
*pr = c;
}
void res_ch_det(VL vl,V v,P p1,P p2,P *pr)
{
P q1,q2,c,c1;
P tg,tg1,tg2,resg;
int index,mod;
Q a,b,f,q,s,u,w;
Z n,m,t;
VL nvl;
reordvar(vl,v,&nvl);
reorderp(nvl,vl,p1,&q1); reorderp(nvl,vl,p2,&q2);
if ( ( VR(q1) != v ) && ( VR(q2) != v ) ) {
*pr = 0;
return;
}
if ( VR(q1) != v ) {
pwrp(vl,q1,DEG(DC(q2)),pr);
return;
}
if ( VR(q2) != v ) {
pwrp(vl,q2,DEG(DC(q1)),pr);
return;
}
norm1c(q1,&a); norm1c(q2,&b);
n = DEG(DC(q1)); m = DEG(DC(q2));
pwrq(a,(Q)m,&w); pwrq(b,(Q)n,&s); mulq(w,s,&u);
factorialz(ZTOS(n)+ZTOS(m),&t);
mulq(u,(Q)t,&s); addq(s,s,&f);
for ( index = 0, q = (Q)ONE, c = 0; cmpq(f,q) >= 0; ) {
mod = get_lprime(index++);
ptomp(mod,LC(q1),&tg);
if ( !tg )
continue;
ptomp(mod,LC(q2),&tg);
if ( !tg )
continue;
ptomp(mod,q1,&tg1); ptomp(mod,q2,&tg2);
res_detmp(nvl,mod,v,tg1,tg2,&resg);
chnremp(nvl,mod,c,(Z)q,resg,&c1); c = c1;
STOZ(mod,t); mulq(q,(Q)t,&s); q = s;
}
*pr = c;
}
void res_detmp(VL vl,int mod,V v,P p1,P p2,P *dp)
{
int n1,n2,n,sgn;
int i,j,k;
P mjj,mij,t,s,u,d;
P **mat;
P *mi,*mj;
DCP dc;
n1 = UDEG(p1); n2 = UDEG(p2); n = n1+n2;
mat = (P **)almat_pointer(n,n);
for ( dc = DC(p1); dc; dc = NEXT(dc) )
mat[0][n1-ZTOS(DEG(dc))] = COEF(dc);
for ( i = 1; i < n2; i++ )
for ( j = 0; j <= n1; j++ )
mat[i][i+j] = mat[0][j];
for ( dc = DC(p2); dc; dc = NEXT(dc) )
mat[n2][n2-ZTOS(DEG(dc))] = COEF(dc);
for ( i = 1; i < n1; i++ )
for ( j = 0; j <= n2; j++ )
mat[i+n2][i+j] = mat[n2][j];
for ( j = 0, d = (P)ONEM, sgn = 1; j < n; j++ ) {
for ( i = j; (i < n) && !mat[i][j]; i++ );
if ( i == n ) {
*dp = 0; return;
}
for ( k = i; k < n; k++ )
if ( mat[k][j] && (nmonop(mat[k][j]) < nmonop(mat[i][j]) ) )
i = k;
if ( j != i ) {
mj = mat[j]; mat[j] = mat[i]; mat[i] = mj; sgn = -sgn;
}
for ( i = j + 1, mj = mat[j], mjj = mj[j]; i < n; i++ )
for ( k = j + 1, mi = mat[i], mij = mi[j]; k < n; k++ ) {
mulmp(vl,mod,mi[k],mjj,&t); mulmp(vl,mod,mj[k],mij,&s);
submp(vl,mod,t,s,&u); divsmp(vl,mod,u,d,&mi[k]);
}
d = mjj;
}
if ( sgn > 0 )
*dp = d;
else
chsgnmp(mod,d,dp);
}
#if 0
showmat(VL vl,P **mat,int n)
{
int i,j;
P t;
for ( i = 0; i < n; i++ ) {
for ( j = 0; j < n; j++ ) {
mptop(mat[i][j],&t); asir_printp(vl,t); fprintf(out," ");
}
fprintf(out,"\n");
}
fflush(out);
}
showmp(VL vl,P p)
{
P t;
mptop(p,&t); asir_printp(vl,t); fprintf(out,"\n");
}
#endif
void premp(VL vl,P p1,P p2,P *pr)
{
P m,m1,m2;
P *pw;
DCP dc;
V v1,v2;
register int i,j;
int n1,n2,d;
if ( NUM(p1) )
if ( NUM(p2) )
*pr = 0;
else
*pr = p1;
else if ( NUM(p2) )
*pr = 0;
else if ( ( v1 = VR(p1) ) == ( v2 = VR(p2) ) ) {
n1 = deg(v1,p1); n2 = deg(v1,p2);
if ( n1 < n2 ) {
*pr = p1;
return;
}
pw = (P *)ALLOCA((n1+1)*sizeof(P));
bzero((char *)pw,(int)((n1+1)*sizeof(P)));
for ( dc = DC(p1); dc; dc = NEXT(dc) )
pw[ZTOS(DEG(dc))] = COEF(dc);
for ( i = n1; i >= n2; i-- ) {
if ( pw[i] ) {
m = pw[i];
for ( j = i; j >= 0; j-- ) {
mulp(vl,pw[j],LC(p2),&m1); pw[j] = m1;
}
for ( dc = DC(p2), d = i - n2; dc; dc = NEXT(dc) ) {
mulp(vl,COEF(dc),m,&m1);
subp(vl,pw[ZTOS(DEG(dc))+d],m1,&m2);
pw[ZTOS(DEG(dc))+d] = m2;
}
} else
for ( j = i; j >= 0; j-- )
if ( pw[j] ) {
mulp(vl,pw[j],LC(p2),&m1); pw[j] = m1;
}
}
plisttop(pw,v1,n2-1,pr);
} else {
while ( v1 != vl->v && v2 != vl->v )
vl = NEXT(vl);
if ( v1 == vl->v )
*pr = 0;
else
*pr = p1;
}
}
void ptozp0(P p,P *pr)
{
Q c;
if ( qpcheck((Obj)p) )
ptozp(p,1,&c,pr);
else
*pr = p;
}
void mindegp(VL vl,P p,VL *mvlp,P *pr)
{
P t;
VL nvl,tvl,avl;
V v;
int n,d;
clctv(vl,p,&nvl); v = nvl->v; d = getdeg(nvl->v,p);
for ( avl = NEXT(nvl); avl; avl = NEXT(avl) ) {
n = getdeg(avl->v,p);
if ( n < d ) {
v = avl->v; d = n;
}
}
if ( v != nvl->v ) {
reordvar(nvl,v,&tvl); reorderp(tvl,nvl,p,&t);
*pr = t; *mvlp = tvl;
} else {
*pr = p; *mvlp = nvl;
}
}
void maxdegp(VL vl,P p,VL *mvlp,P *pr)
{
P t;
VL nvl,tvl,avl;
V v;
int n,d;
clctv(vl,p,&nvl); v = nvl->v; d = getdeg(nvl->v,p);
for ( avl = NEXT(nvl); avl; avl = NEXT(avl) ) {
n = getdeg(avl->v,p);
if ( n > d ) {
v = avl->v; d = n;
}
}
if ( v != nvl->v ) {
reordvar(nvl,v,&tvl); reorderp(tvl,nvl,p,&t);
*pr = t; *mvlp = tvl;
} else {
*pr = p; *mvlp = nvl;
}
}
void min_common_vars_in_coefp(VL vl,P p,VL *mvlp,P *pr)
{
P u,p0;
VL tvl,cvl,svl,uvl,avl,vl0;
int n,n0,d,d0;
DCP dc;
clctv(vl,p,&tvl); vl = tvl;
for ( tvl = vl, n0 = 0; tvl; tvl = NEXT(tvl), n0++ );
for ( avl = vl; avl; avl = NEXT(avl) ) {
if ( VR(p) != avl->v ) {
reordvar(vl,avl->v,&uvl); reorderp(uvl,vl,p,&u);
} else {
uvl = vl; u = p;
}
for ( cvl = NEXT(uvl), dc = DC(u); dc && cvl; dc = NEXT(dc) ) {
clctv(uvl,COEF(dc),&tvl); intersectv(cvl,tvl,&svl); cvl = svl;
}
if ( !cvl ) {
*mvlp = uvl; *pr = u; return;
} else {
for ( tvl = cvl, n = 0; tvl; tvl = NEXT(tvl), n++ );
if ( n < n0 ) {
vl0 = uvl; p0 = u; n0 = n; d0 = getdeg(uvl->v,u);
} else if ( (n == n0) && ((d = getdeg(uvl->v,u)) < d0) ) {
vl0 = uvl; p0 = u; n0 = n; d0 = d;
}
}
}
*pr = p0; *mvlp = vl0;
}
void minlcdegp(VL vl,P p,VL *mvlp,P *pr)
{
P u,p0;
VL tvl,uvl,avl,vl0;
int d,d0;
clctv(vl,p,&tvl); vl = tvl;
vl0 = vl; p0 = p; d0 = homdeg(COEF(DC(p)));
for ( avl = NEXT(vl); avl; avl = NEXT(avl) ) {
reordvar(vl,avl->v,&uvl); reorderp(uvl,vl,p,&u);
d = homdeg(COEF(DC(u)));
if ( d < d0 ) {
vl0 = uvl; p0 = u; d0 = d;
}
}
*pr = p0; *mvlp = vl0;
}
void sort_by_deg(int n,P *p,P *pr)
{
int j,k,d,k0;
V v;
for ( j = 0; j < n; j++ ) {
for ( k0 = k = j, d = deg(v = VR(p[0]),p[j]);
k < n; k++ )
if ( deg(v,p[k]) < d ) {
k0 = k;
d = deg(v,p[k]);
}
pr[j] = p[k0];
if ( j != k0 )
p[k0] = p[j];
}
}
void sort_by_deg_rev(int n,P *p,P *pr)
{
int j,k,d,k0;
V v;
for ( j = 0; j < n; j++ ) {
for ( k0 = k = j, d = deg(v = VR(p[0]),p[j]);
k < n; k++ )
if ( deg(v,p[k]) > d ) {
k0 = k;
d = deg(v,p[k]);
}
pr[j] = p[k0];
if ( j != k0 )
p[k0] = p[j];
}
}
void getmindeg(V v,P p,Z *dp)
{
Z dt,d;
DCP dc;
if ( !p || NUM(p) )
*dp = 0;
else if ( v == VR(p) ) {
for ( dc = DC(p); NEXT(dc); dc = NEXT(dc) );
*dp = DEG(dc);
} else {
dc = DC(p);
getmindeg(v,COEF(dc),&d);
for ( dc = NEXT(dc); dc; dc = NEXT(dc) ) {
getmindeg(v,COEF(dc),&dt);
if ( cmpz(dt,d) < 0 )
d = dt;
}
*dp = d;
}
}
void minchdegp(VL vl,P p,VL *mvlp,P *pr)
{
P t;
VL tvl,nvl,avl;
int n,d,z;
V v;
if ( NUM(p) ) {
*mvlp = vl;
*pr = p;
return;
}
clctv(vl,p,&nvl);
v = nvl->v;
d = getchomdeg(v,p) + getlchomdeg(v,p,&z);
for ( avl = NEXT(nvl); avl; avl = NEXT(avl) ) {
n = getchomdeg(avl->v,p) + getlchomdeg(avl->v,p,&z);
if ( n < d ) {
v = avl->v; d = n;
}
}
if ( v != nvl->v ) {
reordvar(nvl,v,&tvl); reorderp(tvl,nvl,p,&t);
*pr = t; *mvlp = tvl;
} else {
*pr = p; *mvlp = nvl;
}
}
int getchomdeg(V v,P p)
{
int m,m1;
DCP dc;
if ( !p || NUM(p) )
return ( 0 );
else if ( VR(p) == v )
return ( dbound(v,p) );
else {
for ( dc = DC(p), m = 0; dc; dc = NEXT(dc) ) {
m1 = getchomdeg(v,COEF(dc))+ZTOS(DEG(dc));
m = MAX(m,m1);
}
return ( m );
}
}
int getlchomdeg(V v,P p,int *d)
{
int m0,m1,d0,d1;
DCP dc;
if ( !p || NUM(p) ) {
*d = 0;
return ( 0 );
} else if ( VR(p) == v ) {
*d = ZTOS(DEG(DC(p)));
return ( homdeg(LC(p)) );
} else {
for ( dc = DC(p), m0 = 0, d0 = 0; dc; dc = NEXT(dc) ) {
m1 = getlchomdeg(v,COEF(dc),&d1)+ZTOS(DEG(dc));
if ( d1 > d0 ) {
m0 = m1;
d0 = d1;
} else if ( d1 == d0 )
m0 = MAX(m0,m1);
}
*d = d0;
return ( m0 );
}
}
int nmonop(P p)
{
int s;
DCP dc;
if ( !p )
return 0;
else
switch ( OID(p) ) {
case O_N:
return 1; break;
case O_P:
for ( dc = DC((P)p), s = 0; dc; dc = NEXT(dc) )
s += nmonop(COEF(dc));
return s; break;
default:
return 0;
}
}
int qpcheck(Obj p)
{
DCP dc;
if ( !p )
return 1;
else
switch ( OID(p) ) {
case O_N:
return RATN((Num)p)?1:0;
case O_P:
for ( dc = DC((P)p); dc; dc = NEXT(dc) )
if ( !qpcheck((Obj)COEF(dc)) )
return 0;
return 1;
default:
return 0;
}
}
/* check if p is univariate and all coeffs are INT or LM */
int uzpcheck(Obj p)
{
DCP dc;
P c;
if ( !p )
return 1;
else
switch ( OID(p) ) {
case O_N:
return (RATN((Num)p)&&INT(p))||(NID((Num)p)==N_LM);
case O_P:
for ( dc = DC((P)p); dc; dc = NEXT(dc) ) {
c = COEF(dc);
if ( !NUM(c) || !uzpcheck((Obj)c) )
return 0;
}
return 1;
default:
return 0;
}
}
int p_mag(P p)
{
int s;
DCP dc;
if ( !p )
return 0;
else if ( OID(p) == O_N )
return z_bits((Q)p);
else {
for ( dc = DC(p), s = 0; dc; dc = NEXT(dc) )
s += p_mag(COEF(dc));
return s;
}
}
int maxblenp(P p)
{
int s,t;
DCP dc;
if ( !p )
return 0;
else if ( OID(p) == O_N )
return z_bits((Q)p);
else {
for ( dc = DC(p), s = 0; dc; dc = NEXT(dc) ) {
t = maxblenp(COEF(dc));
s = MAX(t,s);
}
return s;
}
}