File: [local] / OpenXM_contrib2 / asir2000 / engine / PD.c (download)
Revision 1.6, Wed Aug 18 00:17:02 2004 UTC (20 years, 1 month ago) by noro
Branch: MAIN
CVS Tags: R_1_3_1-2, RELEASE_1_3_1_13b, RELEASE_1_2_3_12, RELEASE_1_2_3, KNOPPIX_2006, DEB_REL_1_2_3-9 Changes since 1.5: +2 -116
lines
Added support of Laurent polynomial (experimental).
'ctrl("allow_laurent",1)' is necessary for activating this feature.
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/*
* 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.
* (2) The SOFTWARE is protected by the Copyright Law of Japan and
* 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
* e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
* 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'
* RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
* MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
* UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
* OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
* DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
* DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
* ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
* FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
* DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
* SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
* OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
* DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
* PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
*
* $OpenXM: OpenXM_contrib2/asir2000/engine/PD.c,v 1.6 2004/08/18 00:17:02 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 )
STOQ(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;
Q 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 = cmpq(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 ( (PL(NM(deg1)) > 1) ) {
error("divtp : invalid input");
*q = 0;
return ( 0 );
}
d1 = QTOS(deg1); d2 = QTOS(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[QTOS(DEG(dc))] = COEF(dc);
for ( dc = dc2; dc; dc = NEXT(dc) )
pd[QTOS(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;
Q 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 = cmpq(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 ( (PL(NM(deg1)) > 1) ) {
error("divtpz : invalid input");
*q = 0;
return ( 0 );
}
d1 = QTOS(deg1); d2 = QTOS(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[QTOS(DEG(dc))] = COEF(dc);
for ( dc = dc2; dc; dc = NEXT(dc) )
pd[QTOS(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)
{
register int n1,n2,i,j;
Q *pq,*pr,*pd,d,m,s,q;
DCP dc;
N qn,rn;
if ( !f2 )
error("udivpz: division by 0");
else if ( !f1 ) {
*fqp = *frp = 0;
return;
} else if ( NUM(f1) )
if ( NUM(f2) ) {
divn(NM((Q)f1),NM((Q)f2),&qn,&rn);
if ( rn ) {
*fqp = *frp = 0;
} else {
NTOQ(qn,SGN((Q)f1)*SGN((Q)f2),q),*fqp = (P)q; *frp = 0;
}
return;
} else {
*fqp = 0; *frp = f1;
return;
}
else if ( NUM(f2) ) {
n1 = UDEG(f1); W_CALLOC(n1,Q,pq);
for ( dc = DC(f1); dc; dc = NEXT(dc) ) {
divn(NM((Q)COEF(dc)),NM((Q)f2),&qn,&rn);
if ( rn ) {
*fqp = *frp = 0;
return;
} else {
NTOQ(qn,SGN((Q)COEF(dc))*SGN((Q)f2),s); pq[QTOS(DEG(dc))] = s;
}
}
plisttop((P *)pq,VR(f1),n1,fqp);
return;
}
n1 = UDEG(f1); n2 = UDEG(f2);
if ( n1 < n2 ) {
*fqp = NULL; *frp = f1;
return;
}
W_CALLOC(n1-n2,Q,pq); W_CALLOC(n1,Q,pr); W_CALLOC(n2,Q,pd);
for ( dc = DC(f1); dc; dc = NEXT(dc) )
pr[QTOS(DEG(dc))] = (Q)COEF(dc);
for ( dc = DC(f2); dc; dc = NEXT(dc) )
pd[QTOS(DEG(dc))] = (Q)COEF(dc);
for ( d = (Q)UCOEF(f2), i = n1 - n2; i >= 0; i-- ) {
if ( !pr[i+n2] )
continue;
divn(NM(pr[i+n2]),NM(d),&qn,&rn);
if ( rn ) {
*fqp = *frp = 0;
return;
}
NTOQ(qn,SGN(pr[i+n2])*SGN(d),pq[i]);
for ( j = n2; j >= 0; j-- ) {
mulq(pq[i],pd[j],&m); subq(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);
}
void udivpwm(Q mod,P p1,P p2,P *q,P *r)
{
P s,t,u,tq,tr;
invl((Q)UCOEF(p2),mod,(Q *)&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(Q mod,P f1,P f2,P *fqp,P *frp)
{
register int n1,n2,i,j;
Q *pq,*pr,*pd,d,m,s,q;
DCP dc;
N qn,rn;
if ( !f2 )
error("udivpz: division by 0");
else if ( !f1 ) {
*fqp = *frp = 0;
return;
} else if ( NUM(f1) )
if ( NUM(f2) ) {
divn(NM((Q)f1),NM((Q)f2),&qn,&rn);
if ( rn ) {
*fqp = *frp = 0;
} else {
NTOQ(qn,SGN((Q)f1)*SGN((Q)f2),q),*fqp = (P)q; *frp = 0;
}
return;
} else {
*fqp = 0; *frp = f1;
return;
}
else if ( NUM(f2) ) {
n1 = UDEG(f1); W_CALLOC(n1,Q,pq);
for ( dc = DC(f1); dc; dc = NEXT(dc) ) {
divn(NM((Q)COEF(dc)),NM((Q)f2),&qn,&rn);
if ( rn ) {
*fqp = *frp = 0;
return;
} else {
NTOQ(qn,SGN((Q)COEF(dc))*SGN((Q)f2),s); pq[QTOS(DEG(dc))] = s;
}
}
plisttop((P *)pq,VR(f1),n1,fqp);
return;
}
n1 = UDEG(f1); n2 = UDEG(f2);
if ( n1 < n2 ) {
*fqp = NULL; *frp = f1;
return;
}
W_CALLOC(n1-n2,Q,pq); W_CALLOC(n1,Q,pr); W_CALLOC(n2,Q,pd);
for ( dc = DC(f1); dc; dc = NEXT(dc) )
pr[QTOS(DEG(dc))] = (Q)COEF(dc);
for ( dc = DC(f2); dc; dc = NEXT(dc) )
pd[QTOS(DEG(dc))] = (Q)COEF(dc);
for ( d = (Q)UCOEF(f2), i = n1 - n2; i >= 0; i-- ) {
if ( !pr[i+n2] )
continue;
divn(NM(pr[i+n2]),NM(d),&qn,&rn);
if ( rn ) {
*fqp = *frp = 0;
return;
}
NTOQ(qn,SGN(pr[i+n2])*SGN(d),pq[i]);
for ( j = n2; j >= 0; j-- ) {
mulq(pq[i],pd[j],&m); remq(m,mod,&s);
subq(pr[i+j],s,&m); remq(m,mod,&s); pr[i+j] = s;
}
}
plisttop((P *)pq,VR(f1),n1-n2,fqp); plisttop((P *)pr,VR(f1),n2-1,frp);
}