File: [local] / OpenXM_contrib2 / asir2000 / engine / NEZ.c (download)
Revision 1.7, Thu Mar 29 01:32:51 2018 UTC (6 years, 6 months ago) by noro
Branch: MAIN
CVS Tags: HEAD Changes since 1.6: +372 -372
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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/NEZ.c,v 1.7 2018/03/29 01:32:51 noro Exp $
*/
#include "ca.h"
void nezgcdnpz(vl,ps,m,pr)
VL vl;
P *ps,*pr;
int m;
{
P t,s,mg;
VL tvl,svl,avl,nvl;
int i,j,k;
N c;
Q cq;
P *pl,*pm;
DCP *ml;
Q *cl;
P **cp;
int *cn;
if ( m == 1 ) {
*pr = ps[0]; return;
}
pl = (P *)ALLOCA(m*sizeof(P));
ml = (DCP *)ALLOCA(m*sizeof(DCP));
cl = (Q *)ALLOCA(m*sizeof(Q));
for ( i = 0; i < m; i++ )
monomialfctr(vl,ps[i],&pl[i],&ml[i]);
gcdmonomial(vl,ml,m,&mg);
for ( i = 0; i < m; i++ ) {
ptozp(pl[i],1,&cl[i],&t); pl[i] = t;
}
for ( i = 1, cq = cl[0]; i < m; i++ ) {
gcdn(NM(cl[i]),NM(cq),&c); NTOQ(c,1,cq);
}
for ( i = 0; i < m; i++ )
if ( NUM(pl[i]) ) {
mulp(vl,(P)cq,mg,pr); return;
}
for ( i = 0, nvl = vl, avl = 0; nvl && i < m; i++ ) {
clctv(vl,pl[i],&tvl);
intersectv(nvl,tvl,&svl); nvl = svl;
mergev(vl,avl,tvl,&svl); avl = svl;
}
if ( !nvl ) {
mulp(vl,(P)cq,mg,pr); return;
}
if ( !NEXT(avl) ) {
nuezgcdnpzmain(vl,pl,m,&t); mulp(vl,t,(P)cq,&s); mulp(vl,s,mg,pr);
return;
}
for ( tvl = nvl, i = 0; tvl; tvl = NEXT(tvl), i++ );
for ( tvl = avl, j = 0; tvl; tvl = NEXT(tvl), j++ );
if ( i == j ) {
/* all the pl[i]'s have the same variables */
sortplistbyhomdeg(pl,m); nezgcdnpzmain(nvl,pl,m,&t);
#if 0
/* search the minimal degree poly */
for ( i = 0; i < m; i++ ) {
for ( tvl = nvl; tvl; tvl = NEXT(tvl) ) {
dt = getdeg(tvl->v,pl[i]);
if ( tvl == nvl || dt < d1 ) {
v1 = tvl->v; d1 = dt;
}
}
if ( i == 0 || d1 < d ) {
v = v1; d = d1; j = i;
}
}
t = pl[0]; pl[0] = pl[j]; pl[j] = t;
if ( v != nvl->v ) {
reordvar(nvl,v,&mvl);
for ( i = 0; i < m; i++ ) {
reorderp(mvl,nvl,pl[i],&t); pl[i] = t;
}
nezgcdnpzmain(mvl,pl,m,&s); reorderp(nvl,mvl,s,&t);
} else
nezgcdnpzmain(nvl,pl,m,&t);
#endif
} else {
cp = (P **)ALLOCA(m*sizeof(P *));
cn = (int *)ALLOCA(m*sizeof(int));
for ( i = 0; i < m; i++ ) {
cp[i] = (P *)ALLOCA(lengthp(pl[i])*sizeof(P));
cn[i] = pcoef(vl,nvl,pl[i],cp[i]);
}
for ( i = j = 0; i < m; i++ )
j += cn[i];
pm = (P *)ALLOCA(j*sizeof(P));
for ( i = k = 0; i < m; i++ )
for ( j = 0; j < cn[i]; j++ )
pm[k++] = cp[i][j];
nezgcdnpz(vl,pm,k,&t);
}
mulp(vl,t,(P)cq,&s); mulp(vl,s,mg,pr);
}
void sortplistbyhomdeg(p,n)
P *p;
int n;
{
int i,j,k;
int *l;
P t;
l = (int *)ALLOCA(n*sizeof(int));
for ( i = 0; i < n; i++ )
l[i] = homdeg(p[i]);
for ( i = 0; i < n; i++ )
for ( j = i + 1; j < n; j++ )
if ( l[j] < l[i] ) {
t = p[i]; p[i] = p[j]; p[j] = t;
k = l[i]; l[i] = l[j]; l[j] = k;
}
}
void nuezgcdnpzmain(vl,ps,m,r)
VL vl;
P *ps;
int m;
P *r;
{
P *tps;
P f,t;
int i;
for ( i = 0; i < m; i++ )
if ( NUM(ps[i]) ) {
*r = (P)ONE; return;
}
tps = (P *) ALLOCA(m*sizeof(P));
for ( i = 0; i < m; i++ )
tps[i] = ps[i];
sortplist(tps,m);
for ( i = 1, f = tps[0]; i < m && !NUM(f); i++ ) {
uezgcdpz(vl,f,tps[i],&t); f = t;
}
*r = f;
}
void gcdmonomial(vl,dcl,m,r)
VL vl;
DCP *dcl;
int m;
P *r;
{
int i,j,n;
P g,x,s,t;
Q d;
DCP dc;
VN vn;
for ( i = 0; i < m; i++ )
if ( !dcl[i] ) {
*r = (P)ONE; return;
}
for ( n = 0, dc = dcl[0]; dc; dc = NEXT(dc), n++ );
vn = (VN)ALLOCA(n*sizeof(struct oVN));
for ( i = 0, dc = dcl[0]; i < n; dc = NEXT(dc), i++ ) {
vn[i].v = VR(COEF(dc)); vn[i].n = QTOS(DEG(dc));
}
for ( i = 1; i < m; i++ ) {
for ( j = 0; j < n; j++ ) {
for ( dc = dcl[i]; dc; dc = NEXT(dc) )
if ( VR(COEF(dc)) == vn[j].v ) {
vn[j].n = MIN(vn[j].n,QTOS(DEG(dc))); break;
}
if ( !dc )
vn[j].n = 0;
}
for ( j = n-1; j >= 0 && !vn[j].n; j-- );
if ( j < 0 ) {
*r = (P)ONE; return;
} else
n = j+1;
}
for ( j = 0, g = (P)ONE; j < n; j++ )
if ( vn[j].n ) {
MKV(vn[j].v,x); STOQ(vn[j].n,d);
pwrp(vl,x,d,&t); mulp(vl,t,g,&s); g = s;
}
*r = g;
}
void nezgcdnpzmain(vl,pl,m,pr)
VL vl;
P *pl,*pr;
int m;
{
P *ppl,*pcl;
int i;
P cont,gcd,t,s;
DCP dc;
ppl = (P *)ALLOCA(m*sizeof(P));
pcl = (P *)ALLOCA(m*sizeof(P));
for ( i = 0; i < m; i++ )
pcp(vl,pl[i],&ppl[i],&pcl[i]);
nezgcdnpz(vl,pcl,m,&cont);
sqfrp(vl,ppl[0],&dc);
for ( dc = NEXT(dc), gcd = (P)ONE; dc; dc = NEXT(dc) ) {
if ( NUM(COEF(dc)) )
continue;
nezgcdnpp(vl,dc,ppl+1,m-1,&t);
if ( NUM(t) )
continue;
mulp(vl,gcd,t,&s); gcd = s;
}
mulp(vl,gcd,cont,pr);
}
void nezgcdnpp(vl,dc,pl,m,r)
VL vl;
DCP dc;
P *pl;
int m;
P *r;
{
int i,k;
P g,t,s,gcd;
P *pm;
nezgcdnp_sqfr_primitive(vl,COEF(dc),pl,m,&gcd);
if ( NUM(gcd) ) {
*r = (P)ONE; return;
}
pm = (P *) ALLOCA(m*sizeof(P));
for ( i = 0; i < m; i++ ) {
divsp(vl,pl[i],gcd,&pm[i]);
if ( NUM(pm[i]) ) {
*r = gcd; return;
}
}
for ( g = gcd, k = QTOS(DEG(dc))-1; k > 0; k-- ) {
nezgcdnp_sqfr_primitive(vl,g,pm,m,&t);
if ( NUM(t) )
break;
mulp(vl,gcd,t,&s); gcd = s;
for ( i = 0; i < m; i++ ) {
divsp(vl,pm[i],t,&s);
if ( NUM(s) ) {
*r = gcd; return;
}
pm[i] = s;
}
}
*r = gcd;
}
/*
* pr = gcd(p0,ps[0],...,ps[m-1])
*
* p0 is already square-free and primitive.
* ps[i] is at least primitive.
*
*/
void nezgcdnp_sqfr_primitive(vl,p0,ps,m,pr)
VL vl;
int m;
P p0,*ps,*pr;
{
/* variables */
P p00,g,h,g0,h0,a0,b0;
P lp0,lgp0,lp00,lg,lg0,cbd,tq,t;
P *lc;
P *tps;
VL nvl1,nvl2,nvl,tvl;
V v;
int i,j,k,d0,dg,dg0,dmin,z;
VN vn1;
int nv,flag,max;
/* set-up */
if ( NUM(p0) ) {
*pr = (P) ONE; return;
}
for ( v = VR(p0), i = 0; i < m; i++ )
if ( NUM(ps[i]) || (v != VR(ps[i])) ) {
*pr = (P)ONE; return;
}
tps = (P *) ALLOCA(m*sizeof(P));
for ( i = 0; i < m; i++ )
tps[i] = ps[i];
sortplist(tps,m);
/* deg(tps[0]) <= deg(tps[1]) <= ... */
if ( !cmpq(DEG(DC(p0)),ONE) ) {
if ( divcheck(vl,tps,m,(P)ONE,p0) )
*pr = p0;
else
*pr = (P)ONE;
return;
}
lp0 = LC(p0); dmin = d0 = deg(v,p0); lc = (P *)ALLOCA((m+1)*sizeof(P));
for ( lc[0] = lp0, i = 0; i < m; i++ )
lc[i+1] = LC(tps[i]);
clctv(vl,p0,&nvl);
for ( i = 0; i < m; i++ ) {
clctv(vl,tps[i],&nvl1); mergev(vl,nvl,nvl1,&nvl2); nvl = nvl2;
}
nezgcdnpz(nvl,lc,m+1,&lg);
mulp(nvl,p0,lg,&lgp0); k = dbound(v,lgp0)+1; cbound(nvl,lgp0,(Q *)&cbd);
for ( nv = 0, tvl = nvl; tvl; tvl = NEXT(tvl), nv++ );
W_CALLOC(nv,struct oVN,vn1);
for ( i = 0, tvl = NEXT(nvl); tvl; tvl = NEXT(tvl), i++ )
vn1[i].v = tvl->v;
/* main loop */
/* finally, 'max' random evaluations will be generated */
for ( max = 1, dg = deg(v,tps[0]) + 1; ; max = 2*max )
for ( z = 0; z < max; z++ ) {
for ( i = 0; vn1[i].v; i++ )
vn1[i].n = mt_genrand()%max;
/* find b s.t. LC(p0)(b), LC(tps[i])(b) != 0 */
substvp(nvl,p0,vn1,&p00);
flag = (!zerovpchk(nvl,lp0,vn1) && sqfrchk(p00));
for ( i = 0; flag && (i < m); i++ )
flag &= (!zerovpchk(nvl,LC(tps[i]),vn1));
if ( !flag )
continue;
/* substitute y -> b */
substvp(nvl,lg,vn1,&lg0); lp00 = LC(p00);
/* extended-gcd in 1-variable */
uexgcdnp(nvl,p00,tps,m,vn1,(Q)cbd,&g0,&h0,&a0,&b0,(Q *)&tq);
if ( NUM(g0) ) {
*pr = (P)ONE; return;
} else if ( dg > ( dg0 = deg(v,g0) ) ) {
dg = dg0;
if ( dg == d0 ) {
if ( divcheck(nvl,tps,m,lp0,p0) ) {
*pr = p0; return;
}
} else if ( dg == deg(v,tps[0]) ) {
if ( divtpz(nvl,p0,tps[0],&t) &&
divcheck(nvl,tps+1,m-1,LC(tps[0]),tps[0]) ) {
*pr = tps[0]; return;
} else
break;
} else {
henmv(nvl,vn1,lgp0,g0,h0,a0,b0,lg,lp0,lg0,lp00,(Q)tq,k,&g,&h);
if ( divtpz(nvl,lgp0,g,&t) &&
divcheck(nvl,tps,m,lg,g) ) {
pcp(nvl,g,pr,&t); return;
}
}
}
}
}
void intersectv(vl1,vl2,vlp)
VL vl1,vl2,*vlp;
{
int i,n;
VL tvl;
VN tvn;
if ( !vl1 || !vl2 ) {
*vlp = 0; return;
}
for ( n = 0, tvl = vl1; tvl; tvl = NEXT(tvl), n++ );
tvn = (VN) ALLOCA(n*sizeof(struct oVN));
for ( i = 0, tvl = vl1; i < n; tvl = NEXT(tvl), i++ ) {
tvn[i].v = tvl->v; tvn[i].n = 0;
}
for ( tvl = vl2; tvl; tvl = NEXT(tvl) )
for ( i = 0; i < n; i++ )
if ( tvn[i].v == tvl->v ) {
tvn[i].n = 1; break;
}
vntovl(tvn,n,vlp);
}
int pcoef(vl,ivl,p,cp)
VL vl,ivl;
P p;
P *cp;
{
VL nvl,tvl,svl,mvl,mvl0;
P t;
if ( NUM(p) ) {
cp[0] = p; return 1;
} else {
clctv(vl,p,&nvl);
for ( tvl = nvl, mvl0 = 0; tvl; tvl = NEXT(tvl) ) {
for ( svl = ivl; svl; svl = NEXT(svl) )
if ( tvl->v == svl->v )
break;
if ( !svl ) {
if ( !mvl0 ) {
NEWVL(mvl0); mvl = mvl0;
} else {
NEWVL(NEXT(mvl)); mvl = NEXT(mvl);
}
mvl->v = tvl->v;
}
}
if ( mvl0 )
NEXT(mvl) = ivl;
else
mvl0 = ivl;
reorderp(mvl0,nvl,p,&t);
return pcoef0(mvl0,ivl,t,cp);
}
}
int pcoef0(vl,ivl,p,cp)
VL vl,ivl;
P p;
P *cp;
{
int cn,n;
DCP dc;
V v;
VL tvl;
if ( NUM(p) ) {
cp[0] = p; return 1;
} else {
for ( v = VR(p), tvl = ivl; tvl; tvl = NEXT(tvl) )
if ( v == tvl->v )
break;
if ( tvl ) {
cp[0] = p; return 1;
} else {
for ( dc = DC(p), n = 0; dc; dc = NEXT(dc) ) {
cn = pcoef0(vl,ivl,COEF(dc),cp); cp += cn; n += cn;
}
return n;
}
}
}
int lengthp(p)
P p;
{
int n;
DCP dc;
if ( NUM(p) )
return 1;
else {
for ( dc = DC(p), n = 0; dc; dc = NEXT(dc) )
n += lengthp(COEF(dc));
return n;
}
}
int nonzero_const_term(P p)
{
DCP dc;
if ( !p )
return 0;
else if ( NUM(p) )
return 1;
else {
dc = DC(p);
for ( ; NEXT(dc); dc = NEXT(dc) );
if ( DEG(dc) )
return 0;
else
return nonzero_const_term(COEF(dc));
}
}