/*
* 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.
*
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* 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
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* results obtained by use of the SOFTWARE.
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* for such modification or the source code of the modified part of the
* SOFTWARE.
*
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* MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
* EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
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* $OpenXM: OpenXM_contrib2/asir2018/engine/PD.c,v 1.2 2018/09/28 08:20:28 noro Exp $
*/
#ifndef FBASE
#define FBASE
#endif
#include "b.h"
#include "ca.h"
#include "polydiv.c"
void plisttop(P *f,V v,int n,P *gp)
{
int i;
DCP dc,dc0;
for ( i = n; (i >= 0) && !f[i]; i-- );
if ( i < 0 )
*gp = 0;
else if ( i == 0 )
*gp = f[0];
else {
for ( dc0 = 0; i >= 0; i-- ) {
if ( !f[i] )
continue;
NEXTDC(dc0,dc);
if ( i )
STOZ(i,DEG(dc));
else
DEG(dc) = 0;
COEF(dc) = f[i];
}
NEXT(dc) = 0; MKP(v,dc0,*gp);
}
}
/* for multivariate polynomials over fields */
int divtp(VL vl,P p1,P p2,P *q)
{
register int i,j;
register DCP dc1,dc2,dc;
P m,m1,s,dvr,t;
P *pq,*pr,*pd;
V v1,v2;
Z deg1,deg2;
int d1,d2,sgn;
if ( !p1 ) {
*q = 0;
return 1;
} else if ( NUM(p2) ) {
divsp(vl,p1,p2,q);
return 1;
} else if ( NUM(p1) ) {
*q = 0;
return 0;
} else if ( ( v1 = VR(p1) ) == ( v2 = VR(p2) ) ) {
dc1 = DC(p1); dc2 = DC(p2);
deg1 = DEG(dc1); deg2 = DEG(dc2);
sgn = cmpz(deg1,deg2);
if ( sgn == 0 )
if ( !divtp(vl,COEF(dc1),COEF(dc2),&m) ) {
*q = 0;
return 0;
} else {
mulp(vl,p2,m,&m1); subp(vl,p1,m1,&s);
if ( !s ) {
*q = m;
return 1;
} else {
*q = 0;
return 0;
}
}
else if ( sgn < 0 ) {
*q = 0;
return 0;
} else {
if ( !smallz(deg1) ) {
error("divtp : invalid input");
*q = 0;
return ( 0 );
}
d1 = ZTOS(deg1); d2 = ZTOS(deg2);
W_CALLOC(d1-d2,P,pq); W_CALLOC(d1,P,pr); W_CALLOC(d2,P,pd);
for ( dc = dc1; dc; dc = NEXT(dc) )
pr[ZTOS(DEG(dc))] = COEF(dc);
for ( dc = dc2; dc; dc = NEXT(dc) )
pd[ZTOS(DEG(dc))] = COEF(dc);
for ( dvr = COEF(dc2), i = d1 - d2; i >= 0; i-- )
if ( !pr[i+d2] )
continue;
else if ( !divtp(vl,pr[i+d2],dvr,&m) ) {
*q = 0;
return 0;
} else {
pq[i] = m;
for ( j = d2; j >= 0; j-- ) {
mulp(vl,pq[i],pd[j],&m);
subp(vl,pr[i + j],m,&s); pr[i + j] = s;
}
}
plisttop(pq,v1,d1 - d2,&m); plisttop(pr,v1,d1 - 1,&t);
if ( t ) {
*q = 0;
return 0;
} else {
*q = m;
return 1;
}
}
} else {
for ( ; (v1 != vl->v) && (v2 != vl->v); vl = NEXT(vl) );
if ( v2 == vl->v ) {
*q = 0;
return 0;
} else
return divtdcp(vl,p1,p2,q);
}
}
int divtdcp(VL vl,P p1,P p2,P *q)
{
P m;
register DCP dc,dcr,dcr0;
for ( dc = DC(p1), dcr0 = 0; dc; dc = NEXT(dc) )
if ( !divtp(vl,COEF(dc),p2,&m) ) {
*q = 0;
return 0;
} else {
NEXTDC(dcr0,dcr); DEG(dcr) = DEG(dc); COEF(dcr) = m; NEXT(dcr) = 0;
}
MKP(VR(p1),dcr0,*q);
return 1;
}
int divtpz(VL vl,P p1,P p2,P *q)
{
register int i,j;
register DCP dc1,dc2,dc;
P m,m1,s,dvr,t;
P *pq,*pr,*pd;
V v1,v2;
Z deg1,deg2;
int d1,d2,sgn;
if ( !p1 ) {
*q = 0;
return ( 1 );
} else if ( NUM(p2) )
if ( NUM(p1) ) {
divq((Q)p1,(Q)p2,(Q *)&s);
if ( INT((Q)s) ) {
*q = s;
return ( 1 );
} else {
*q = 0;
return ( 0 );
}
} else
return ( divtdcpz(vl,p1,p2,q) );
else if ( NUM(p1) ) {
*q = 0;
return ( 0 );
} else if ( ( v1 = VR(p1) ) == ( v2 = VR(p2) ) ) {
Q csum1,csum2;
csump(vl,p1,&csum1); csump(vl,p2,&csum2);
if ( csum2 && !divtpz(vl,(P)csum1,(P)csum2,&t) ) {
*q = 0;
return 0;
}
dc1 = DC(p1); dc2 = DC(p2);
deg1 = DEG(dc1); deg2 = DEG(dc2);
sgn = cmpz(deg1,deg2);
if ( sgn == 0 )
if ( !divtpz(vl,COEF(dc1),COEF(dc2),&m) ) {
*q = 0;
return ( 0 );
} else {
mulp(vl,p2,m,&m1); subp(vl,p1,m1,&s);
if ( !s ) {
*q = m;
return ( 1 );
} else {
*q = 0;
return ( 0 );
}
}
else if ( sgn < 0 ) {
*q = 0;
return ( 0 );
} else {
if ( !smallz(deg1) ) {
error("divtpz : invalid input");
*q = 0;
return ( 0 );
}
d1 = ZTOS(deg1); d2 = ZTOS(deg2);
W_CALLOC(d1-d2,P,pq); W_CALLOC(d1,P,pr); W_CALLOC(d2,P,pd);
for ( dc = dc1; dc; dc = NEXT(dc) )
pr[ZTOS(DEG(dc))] = COEF(dc);
for ( dc = dc2; dc; dc = NEXT(dc) )
pd[ZTOS(DEG(dc))] = COEF(dc);
for ( dvr = COEF(dc2), i = d1 - d2; i >= 0; i-- )
if ( !pr[i+d2] )
continue;
else if ( !divtpz(vl,pr[i+d2],dvr,&m) ) {
*q = 0;
return ( 0 );
} else {
pq[i] = m;
for ( j = d2; j >= 0; j-- ) {
mulp(vl,pq[i],pd[j],&m);
subp(vl,pr[i + j],m,&s); pr[i + j] = s;
}
}
plisttop(pq,v1,d1 - d2,&m); plisttop(pr,v1,d1 - 1,&t);
if ( t ) {
*q = 0;
return ( 0 );
} else {
*q = m;
return ( 1 );
}
}
} else {
for ( ; (v1 != vl->v) && (v2 != vl->v); vl = NEXT(vl) );
if ( v2 == vl->v ) {
*q = 0;
return ( 0 );
} else
return ( divtdcpz(vl,p1,p2,q) ) ;
}
}
int divtdcpz(VL vl,P p1,P p2,P *q)
{
P m;
register DCP dc,dcr,dcr0;
for ( dc = DC(p1), dcr0 = 0; dc; dc = NEXT(dc) )
if ( !divtpz(vl,COEF(dc),p2,&m) ) {
*q = 0;
return ( 0 );
} else {
NEXTDC(dcr0,dcr); DEG(dcr) = DEG(dc); COEF(dcr) = m; NEXT(dcr) = 0;
}
MKP(VR(p1),dcr0,*q);
return ( 1 );
}
void udivpz(P f1,P f2,P *fqp,P *frp)
{
int n1,n2,i,j,sgn;
Z *pq,*pr,*pd,d,m,s;
DCP dc;
Z qn,rn,q;
if ( !f2 )
error("udivpz: division by 0");
else if ( !f1 ) {
*fqp = *frp = 0;
return;
} else if ( NUM(f1) ) {
if ( NUM(f2) ) {
divqrz((Z)f1,(Z)f2,&qn,&rn);
if ( rn ) {
*fqp = *frp = 0;
} else {
*fqp = (P)qn; *frp = 0;
}
return;
} else {
*fqp = 0; *frp = f1;
return;
}
} else if ( NUM(f2) ) {
n1 = UDEG(f1); W_CALLOC(n1,Z,pq);
for ( dc = DC(f1); dc; dc = NEXT(dc) ) {
divqrz((Z)COEF(dc),(Z)f2,&qn,&rn);
if ( rn ) {
*fqp = *frp = 0;
return;
} else {
pq[ZTOS(DEG(dc))] = qn;
}
}
plisttop((P *)pq,VR(f1),n1,fqp);
*frp = 0;
return;
}
n1 = UDEG(f1); n2 = UDEG(f2);
if ( n1 < n2 ) {
*fqp = NULL; *frp = f1;
return;
}
W_CALLOC(n1-n2,Z,pq); W_CALLOC(n1,Z,pr); W_CALLOC(n2,Z,pd);
for ( dc = DC(f1); dc; dc = NEXT(dc) )
pr[ZTOS(DEG(dc))] = (Z)COEF(dc);
for ( dc = DC(f2); dc; dc = NEXT(dc) )
pd[ZTOS(DEG(dc))] = (Z)COEF(dc);
for ( d = (Z)UCOEF(f2), i = n1 - n2; i >= 0; i-- ) {
if ( !pr[i+n2] )
continue;
divqrz(pr[i+n2],d,&qn,&rn);
if ( rn ) {
*fqp = *frp = 0;
return;
}
pq[i] = qn;
for ( j = n2; j >= 0; j-- ) {
mulz(pq[i],pd[j],&m); subz(pr[i+j],m,&s); pr[i+j] = s;
}
}
plisttop((P *)pq,VR(f1),n1-n2,fqp); plisttop((P *)pr,VR(f1),n2-1,frp);
}
/* YYY */
void udivpwm(Z mod,P p1,P p2,P *q,P *r)
{
P s,t,u,tq,tr;
invz((Z)UCOEF(p2),mod,(Z *)&t); mulpq(p2,t,&s); cmp(mod,s,&u);
udivpzwm(mod,p1,u,&tq,&tr);
cmp(mod,tr,r); mulpq(tq,t,&s); cmp(mod,s,q);
}
void udivpzwm(Z mod,P f1,P f2,P *fqp,P *frp)
{
int n1,n2,i,j;
Z *pq,*pr,*pd,d,m,s;
DCP dc;
Z qn,rn,q;
if ( !f2 )
error("udivpz: division by 0");
else if ( !f1 ) {
*fqp = *frp = 0;
return;
} else if ( NUM(f1) ) {
if ( NUM(f2) ) {
divqrz((Z)f1,(Z)f2,&qn,&rn);
if ( rn ) {
*fqp = *frp = 0;
} else {
*fqp = (P)qn; *frp = 0;
}
return;
} else {
*fqp = 0; *frp = f1;
return;
}
} else if ( NUM(f2) ) {
n1 = UDEG(f1); W_CALLOC(n1,Z,pq);
for ( dc = DC(f1); dc; dc = NEXT(dc) ) {
divqrz((Z)COEF(dc),(Z)f2,&qn,&rn);
if ( rn ) {
*fqp = *frp = 0;
return;
} else {
pq[ZTOS(DEG(dc))] = qn;
}
}
plisttop((P *)pq,VR(f1),n1,fqp);
*frp = 0;
return;
}
n1 = UDEG(f1); n2 = UDEG(f2);
if ( n1 < n2 ) {
*fqp = NULL; *frp = f1;
return;
}
W_CALLOC(n1-n2,Z,pq); W_CALLOC(n1,Z,pr); W_CALLOC(n2,Z,pd);
for ( dc = DC(f1); dc; dc = NEXT(dc) )
pr[ZTOS(DEG(dc))] = (Z)COEF(dc);
for ( dc = DC(f2); dc; dc = NEXT(dc) )
pd[ZTOS(DEG(dc))] = (Z)COEF(dc);
for ( d = (Z)UCOEF(f2), i = n1 - n2; i >= 0; i-- ) {
if ( !pr[i+n2] )
continue;
divqrz(pr[i+n2],d,&qn,&rn);
if ( rn ) {
*fqp = *frp = 0;
return;
} else
pq[i] = qn;
for ( j = n2; j >= 0; j-- ) {
mulz(pq[i],pd[j],&m); remz(m,mod,&s);
subz(pr[i+j],s,&m); remz(m,mod,&s); pr[i+j] = s;
}
}
plisttop((P *)pq,VR(f1),n1-n2,fqp); plisttop((P *)pr,VR(f1),n2-1,frp);
}