File: [local] / OpenXM_contrib2 / asir2000 / builtin / dp-supp.c (download)
Revision 1.10, Mon Dec 11 02:00:40 2000 UTC (23 years, 5 months ago) by noro
Branch: MAIN
Changes since 1.9: +6 -1
lines
Defined a new monomial ordering. (ord=10 : 'reverse elimination order')
Modified 'lib/bfct' as follows.
1. bfct() now uses the trace lifting.
2. The Groebner basis check is replaced by another Groebner basis computation.
(See Algorithm 11.25 in the text book in OpenXM/doc/compalg.)
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/*
* Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
* All rights reserved.
*
* FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
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* redistribute, solely for non-commercial and non-profit purposes, the
* computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
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* third party developer retains all rights, including but not limited to
* copyrights, in and to the SOFTWARE.
*
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* $OpenXM: OpenXM_contrib2/asir2000/builtin/dp-supp.c,v 1.10 2000/12/11 02:00:40 noro Exp $
*/
#include "ca.h"
#include "base.h"
#include "parse.h"
#include "ox.h"
#define HMAG(p) (p_mag(BDY(p)->c))
extern int (*cmpdl)();
extern double pz_t_e,pz_t_d,pz_t_d1,pz_t_c;
extern int dp_nelim,dp_fcoeffs;
extern int NoGCD;
extern int GenTrace;
extern NODE TraceList;
/*
* content reduction
*
*/
void dp_ptozp(p,rp)
DP p,*rp;
{
MP m,mr,mr0;
int i,n;
Q *w;
Q dvr;
P t;
if ( !p )
*rp = 0;
else {
for ( m =BDY(p), n = 0; m; m = NEXT(m), n++ );
w = (Q *)ALLOCA(n*sizeof(Q));
for ( m =BDY(p), i = 0; i < n; m = NEXT(m), i++ )
if ( NUM(m->c) )
w[i] = (Q)m->c;
else
ptozp(m->c,1,&w[i],&t);
sortbynm(w,n);
qltozl(w,n,&dvr);
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
NEXTMP(mr0,mr); divsp(CO,m->c,(P)dvr,&mr->c); mr->dl = m->dl;
}
NEXT(mr) = 0; MKDP(p->nv,mr0,*rp); (*rp)->sugar = p->sugar;
}
}
void dp_ptozp2(p0,p1,hp,rp)
DP p0,p1;
DP *hp,*rp;
{
DP t,s,h,r;
MP m,mr,mr0,m0;
addd(CO,p0,p1,&t); dp_ptozp(t,&s);
if ( !p0 ) {
h = 0; r = s;
} else if ( !p1 ) {
h = s; r = 0;
} else {
for ( mr0 = 0, m = BDY(s), m0 = BDY(p0); m0;
m = NEXT(m), m0 = NEXT(m0) ) {
NEXTMP(mr0,mr); mr->c = m->c; mr->dl = m->dl;
}
NEXT(mr) = 0; MKDP(p0->nv,mr0,h); MKDP(p0->nv,m,r);
}
if ( h )
h->sugar = p0->sugar;
if ( r )
r->sugar = p1->sugar;
*hp = h; *rp = r;
}
void dp_idiv(p,c,rp)
DP p;
Q c;
DP *rp;
{
Q t;
N nm,q;
int sgn,s;
MP mr0,m,mr;
if ( !p )
*rp = 0;
else if ( MUNIQ((Q)c) )
*rp = p;
else if ( MUNIQ((Q)c) )
chsgnd(p,rp);
else {
nm = NM(c); sgn = SGN(c);
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
NEXTMP(mr0,mr);
divsn(NM((Q)(m->c)),nm,&q);
s = sgn*SGN((Q)(m->c));
NTOQ(q,s,t);
mr->c = (P)t;
mr->dl = m->dl;
}
NEXT(mr) = 0; MKDP(p->nv,mr0,*rp);
if ( *rp )
(*rp)->sugar = p->sugar;
}
}
void dp_mbase(hlist,mbase)
NODE hlist;
NODE *mbase;
{
DL *dl;
DL d;
int i,j,n,nvar,td;
n = length(hlist); nvar = ((DP)BDY(hlist))->nv;
dl = (DL *)MALLOC(n*sizeof(DL));
for ( i = 0; i < n; i++, hlist = NEXT(hlist) )
dl[i] = BDY((DP)BDY(hlist))->dl;
NEWDL(d,nvar); *mbase = 0;
while ( 1 ) {
insert_to_node(d,mbase,nvar);
for ( i = nvar-1; i >= 0; ) {
d->d[i]++; d->td++;
for ( j = 0; j < n; j++ ) {
if ( _dl_redble(dl[j],d,nvar) )
break;
}
if ( j < n ) {
for ( j = nvar-1; j >= i; j-- )
d->d[j] = 0;
for ( j = 0, td = 0; j < i; j++ )
td += d->d[j];
d->td = td;
i--;
} else
break;
}
if ( i < 0 )
break;
}
}
int _dl_redble(d1,d2,nvar)
DL d1,d2;
int nvar;
{
int i;
if ( d1->td > d2->td )
return 0;
for ( i = 0; i < nvar; i++ )
if ( d1->d[i] > d2->d[i] )
break;
if ( i < nvar )
return 0;
else
return 1;
}
void insert_to_node(d,n,nvar)
DL d;
NODE *n;
int nvar;
{
DL d1;
MP m;
DP dp;
NODE n0,n1,n2;
NEWDL(d1,nvar); d1->td = d->td;
bcopy((char *)d->d,(char *)d1->d,nvar*sizeof(int));
NEWMP(m); m->dl = d1; m->c = (P)ONE; NEXT(m) = 0;
MKDP(nvar,m,dp); dp->sugar = d->td;
if ( !(*n) ) {
MKNODE(n1,dp,0); *n = n1;
} else {
for ( n1 = *n, n0 = 0; n1; n0 = n1, n1 = NEXT(n1) )
if ( (*cmpdl)(nvar,d,BDY((DP)BDY(n1))->dl) > 0 ) {
MKNODE(n2,dp,n1);
if ( !n0 )
*n = n2;
else
NEXT(n0) = n2;
break;
}
if ( !n1 ) {
MKNODE(n2,dp,0); NEXT(n0) = n2;
}
}
}
void dp_vtod(c,p,rp)
Q *c;
DP p;
DP *rp;
{
MP mr0,m,mr;
int i;
if ( !p )
*rp = 0;
else {
for ( mr0 = 0, m = BDY(p), i = 0; m; m = NEXT(m), i++ ) {
NEXTMP(mr0,mr); mr->c = (P)c[i]; mr->dl = m->dl;
}
NEXT(mr) = 0; MKDP(p->nv,mr0,*rp);
(*rp)->sugar = p->sugar;
}
}
extern int mpi_mag;
extern int PCoeffs;
void dp_ptozp_d(p,rp)
DP p,*rp;
{
int i,j,k,l,n,nsep;
MP m;
NODE tn,n0,n1,n2,n3;
struct oVECT v;
VECT c,cs;
VECT qi,ri;
LIST *qr;
int s,id;
Obj dmy;
Q d0,d1,gcd,a,u,u1;
Q *q,*r;
STRING iqr_v;
pointer *b;
N qn,gn;
double get_rtime();
int blen;
NODE dist;
int ndist;
double t0;
double t_e,t_d,t_d1,t_c;
extern int DP_NFStat;
extern LIST Dist;
if ( !p )
*rp = 0;
else {
if ( PCoeffs ) {
dp_ptozp(p,rp); return;
}
if ( !Dist || p_mag(BDY(p)->c) <= mpi_mag ) {
dist = 0; ndist = 0;
if ( DP_NFStat ) fprintf(asir_out,"L");
} else {
dist = BDY(Dist); ndist = length(dist);
if ( DP_NFStat ) fprintf(asir_out,"D");
}
for ( m = BDY(p), n = 0; m; m = NEXT(m), n++ );
nsep = ndist + 1;
if ( n <= nsep ) {
dp_ptozp(p,rp); return;
}
t0 = get_rtime();
dp_dtov(p,&c);
igcdv_estimate(c,&d0);
t_e = get_rtime()-t0;
t0 = get_rtime();
dp_dtov(p,&c);
sepvect(c,nsep,&cs);
MKSTR(iqr_v,"iqr");
qr = (LIST *)CALLOC(nsep,sizeof(LIST));
q = (Q *)CALLOC(n,sizeof(Q));
r = (Q *)CALLOC(n,sizeof(Q));
for ( i = 0, tn = dist, b = BDY(cs); i < ndist; i++, tn = NEXT(tn) ) {
MKNODE(n3,d0,0); MKNODE(n2,b[i],n3);
MKNODE(n1,iqr_v,n2); MKNODE(n0,BDY(tn),n1);
Pox_rpc(n0,&dmy);
}
iqrv(b[i],d0,&qr[i]);
dp_dtov(p,&c);
for ( i = 0, tn = dist; i < ndist; i++, tn = NEXT(tn) ) {
Pox_pop_local(tn,&qr[i]);
if ( OID(qr[i]) == O_ERR ) {
printexpr(CO,(Obj)qr[i]);
error("dp_ptozp_d : aborted");
}
}
t_d = get_rtime()-t0;
t_d1 = t_d/n;
t0 = get_rtime();
for ( i = j = 0; i < nsep; i++ ) {
tn = BDY(qr[i]); qi = (VECT)BDY(tn); ri = (VECT)BDY(NEXT(tn));
for ( k = 0, l = qi->len; k < l; k++, j++ ) {
q[j] = (Q)BDY(qi)[k]; r[j] = (Q)BDY(ri)[k];
}
}
v.id = O_VECT; v.len = n; v.body = (pointer *)r; igcdv(&v,&d1);
if ( d1 ) {
gcdn(NM(d0),NM(d1),&gn); NTOQ(gn,1,gcd);
divsn(NM(d0),gn,&qn); NTOQ(qn,1,a);
for ( i = 0; i < n; i++ ) {
mulq(a,q[i],&u);
if ( r[i] ) {
divsn(NM(r[i]),gn,&qn); NTOQ(qn,SGN(r[i]),u1);
addq(u,u1,&q[i]);
} else
q[i] = u;
}
} else
gcd = d0;
dp_vtod(q,p,rp);
t_c = get_rtime()-t0;
blen=p_mag((P)gcd);
pz_t_e += t_e; pz_t_d += t_d; pz_t_d1 += t_d1; pz_t_c += t_c;
if ( 0 )
fprintf(stderr,"(%d,%d)",p_mag((P)d0)-blen,blen);
}
}
void dp_ptozp2_d(p0,p1,hp,rp)
DP p0,p1;
DP *hp,*rp;
{
DP t,s,h,r;
MP m,mr,mr0,m0;
addd(CO,p0,p1,&t); dp_ptozp_d(t,&s);
if ( !p0 ) {
h = 0; r = s;
} else if ( !p1 ) {
h = s; r = 0;
} else {
for ( mr0 = 0, m = BDY(s), m0 = BDY(p0); m0;
m = NEXT(m), m0 = NEXT(m0) ) {
NEXTMP(mr0,mr); mr->c = m->c; mr->dl = m->dl;
}
NEXT(mr) = 0; MKDP(p0->nv,mr0,h); MKDP(p0->nv,m,r);
}
if ( h )
h->sugar = p0->sugar;
if ( r )
r->sugar = p1->sugar;
*hp = h; *rp = r;
}
void dp_prim(p,rp)
DP p,*rp;
{
P t,g;
DP p1;
MP m,mr,mr0;
int i,n;
P *w;
Q *c;
Q dvr;
if ( !p )
*rp = 0;
else if ( dp_fcoeffs )
*rp = p;
else if ( NoGCD )
dp_ptozp(p,rp);
else {
dp_ptozp(p,&p1); p = p1;
for ( m = BDY(p), n = 0; m; m = NEXT(m), n++ );
if ( n == 1 ) {
m = BDY(p);
NEWMP(mr); mr->dl = m->dl; mr->c = (P)ONE; NEXT(mr) = 0;
MKDP(p->nv,mr,*rp); (*rp)->sugar = p->sugar;
return;
}
w = (P *)ALLOCA(n*sizeof(P));
c = (Q *)ALLOCA(n*sizeof(Q));
for ( m =BDY(p), i = 0; i < n; m = NEXT(m), i++ )
if ( NUM(m->c) ) {
c[i] = (Q)m->c; w[i] = (P)ONE;
} else
ptozp(m->c,1,&c[i],&w[i]);
qltozl(c,n,&dvr); heu_nezgcdnpz(CO,w,n,&t); mulp(CO,t,(P)dvr,&g);
if ( NUM(g) )
*rp = p;
else {
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
NEXTMP(mr0,mr); divsp(CO,m->c,g,&mr->c); mr->dl = m->dl;
}
NEXT(mr) = 0; MKDP(p->nv,mr0,*rp); (*rp)->sugar = p->sugar;
}
}
}
void heu_nezgcdnpz(vl,pl,m,pr)
VL vl;
P *pl,*pr;
int m;
{
int i,r;
P gcd,t,s1,s2,u;
Q rq;
while ( 1 ) {
for ( i = 0, s1 = 0; i < m; i++ ) {
r = random(); UTOQ(r,rq);
mulp(vl,pl[i],(P)rq,&t); addp(vl,s1,t,&u); s1 = u;
}
for ( i = 0, s2 = 0; i < m; i++ ) {
r = random(); UTOQ(r,rq);
mulp(vl,pl[i],(P)rq,&t); addp(vl,s2,t,&u); s2 = u;
}
ezgcdp(vl,s1,s2,&gcd);
for ( i = 0; i < m; i++ ) {
if ( !divtpz(vl,pl[i],gcd,&t) )
break;
}
if ( i == m )
break;
}
*pr = gcd;
}
void dp_prim_mod(p,mod,rp)
int mod;
DP p,*rp;
{
P t,g;
MP m,mr,mr0;
if ( !p )
*rp = 0;
else if ( NoGCD )
*rp = p;
else {
for ( m = BDY(p), g = m->c, m = NEXT(m); m; m = NEXT(m) ) {
gcdprsmp(CO,mod,g,m->c,&t); g = t;
}
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
NEXTMP(mr0,mr); divsmp(CO,mod,m->c,g,&mr->c); mr->dl = m->dl;
}
NEXT(mr) = 0; MKDP(p->nv,mr0,*rp); (*rp)->sugar = p->sugar;
}
}
void dp_cont(p,rp)
DP p;
Q *rp;
{
VECT v;
dp_dtov(p,&v); igcdv(v,rp);
}
void dp_dtov(dp,rp)
DP dp;
VECT *rp;
{
MP m,t;
int i,n;
VECT v;
pointer *p;
m = BDY(dp);
for ( t = m, n = 0; t; t = NEXT(t), n++ );
MKVECT(v,n);
for ( i = 0, p = BDY(v), t = m; i < n; t = NEXT(t), i++ )
p[i] = (pointer)(t->c);
*rp = v;
}
/*
* s-poly computation
*
*/
void dp_sp(p1,p2,rp)
DP p1,p2;
DP *rp;
{
int i,n,td;
int *w;
DL d1,d2,d;
MP m;
DP t,s1,s2,u;
Q c,c1,c2;
N gn,tn;
n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
w = (int *)ALLOCA(n*sizeof(int));
for ( i = 0, td = 0; i < n; i++ ) {
w[i] = MAX(d1->d[i],d2->d[i]); td += w[i];
}
NEWDL(d,n); d->td = td - d1->td;
for ( i = 0; i < n; i++ )
d->d[i] = w[i] - d1->d[i];
c1 = (Q)BDY(p1)->c; c2 = (Q)BDY(p2)->c;
if ( INT(c1) && INT(c2) ) {
gcdn(NM(c1),NM(c2),&gn);
if ( !UNIN(gn) ) {
divsn(NM(c1),gn,&tn); NTOQ(tn,SGN(c1),c); c1 = c;
divsn(NM(c2),gn,&tn); NTOQ(tn,SGN(c2),c); c2 = c;
}
}
NEWMP(m); m->dl = d; m->c = (P)c2; NEXT(m) = 0;
MKDP(n,m,s1); s1->sugar = d->td; muld(CO,s1,p1,&t);
NEWDL(d,n); d->td = td - d2->td;
for ( i = 0; i < n; i++ )
d->d[i] = w[i] - d2->d[i];
NEWMP(m); m->dl = d; m->c = (P)c1; NEXT(m) = 0;
MKDP(n,m,s2); s2->sugar = d->td; muld(CO,s2,p2,&u);
subd(CO,t,u,rp);
if ( GenTrace ) {
LIST hist;
NODE node;
node = mknode(4,ONE,0,s1,ONE);
MKLIST(hist,node);
MKNODE(TraceList,hist,0);
node = mknode(4,ONE,0,0,ONE);
chsgnd(s2,(DP *)&ARG2(node));
MKLIST(hist,node);
MKNODE(node,hist,TraceList); TraceList = node;
}
}
void dp_sp_mod(p1,p2,mod,rp)
DP p1,p2;
int mod;
DP *rp;
{
int i,n,td;
int *w;
DL d1,d2,d;
MP m;
DP t,s,u;
n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
w = (int *)ALLOCA(n*sizeof(int));
for ( i = 0, td = 0; i < n; i++ ) {
w[i] = MAX(d1->d[i],d2->d[i]); td += w[i];
}
NEWDL(d,n); d->td = td - d1->td;
for ( i = 0; i < n; i++ )
d->d[i] = w[i] - d1->d[i];
NEWMP(m); m->dl = d; m->c = (P)BDY(p2)->c; NEXT(m) = 0;
MKDP(n,m,s); s->sugar = d->td; mulmd(CO,mod,p1,s,&t);
NEWDL(d,n); d->td = td - d2->td;
for ( i = 0; i < n; i++ )
d->d[i] = w[i] - d2->d[i];
NEWMP(m); m->dl = d; m->c = (P)BDY(p1)->c; NEXT(m) = 0;
MKDP(n,m,s); s->sugar = d->td; mulmd(CO,mod,p2,s,&u);
submd(CO,mod,t,u,rp);
}
void _dp_sp_mod_dup(p1,p2,mod,rp)
DP p1,p2;
int mod;
DP *rp;
{
int i,n,td;
int *w;
DL d1,d2,d;
MP m;
DP t,s,u;
n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
w = (int *)ALLOCA(n*sizeof(int));
for ( i = 0, td = 0; i < n; i++ ) {
w[i] = MAX(d1->d[i],d2->d[i]); td += w[i];
}
_NEWDL(d,n); d->td = td - d1->td;
for ( i = 0; i < n; i++ )
d->d[i] = w[i] - d1->d[i];
_NEWMP(m); m->dl = d; m->c = BDY(p2)->c; NEXT(m) = 0;
_MKDP(n,m,s); s->sugar = d->td; _mulmd_dup(mod,s,p1,&t); _free_dp(s);
_NEWDL(d,n); d->td = td - d2->td;
for ( i = 0; i < n; i++ )
d->d[i] = w[i] - d2->d[i];
_NEWMP(m); m->dl = d; m->c = STOI(mod - ITOS(BDY(p1)->c)); NEXT(m) = 0;
_MKDP(n,m,s); s->sugar = d->td; _mulmd_dup(mod,s,p2,&u); _free_dp(s);
_addmd_destructive(mod,t,u,rp);
}
void _dp_sp_mod(p1,p2,mod,rp)
DP p1,p2;
int mod;
DP *rp;
{
int i,n,td;
int *w;
DL d1,d2,d;
MP m;
DP t,s,u;
n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
w = (int *)ALLOCA(n*sizeof(int));
for ( i = 0, td = 0; i < n; i++ ) {
w[i] = MAX(d1->d[i],d2->d[i]); td += w[i];
}
NEWDL(d,n); d->td = td - d1->td;
for ( i = 0; i < n; i++ )
d->d[i] = w[i] - d1->d[i];
NEWMP(m); m->dl = d; m->c = BDY(p2)->c; NEXT(m) = 0;
MKDP(n,m,s); s->sugar = d->td; mulmd_dup(mod,s,p1,&t);
NEWDL(d,n); d->td = td - d2->td;
for ( i = 0; i < n; i++ )
d->d[i] = w[i] - d2->d[i];
NEWMP(m); m->dl = d; m->c = STOI(mod - ITOS(BDY(p1)->c)); NEXT(m) = 0;
MKDP(n,m,s); s->sugar = d->td; mulmd_dup(mod,s,p2,&u);
addmd_destructive(mod,t,u,rp);
}
/*
* m-reduction
*
*/
void dp_red(p0,p1,p2,head,rest,dnp,multp)
DP p0,p1,p2;
DP *head,*rest;
P *dnp;
DP *multp;
{
int i,n;
DL d1,d2,d;
MP m;
DP t,s,r,h;
Q c,c1,c2;
N gn,tn;
P g,a;
n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
NEWDL(d,n); d->td = d1->td - d2->td;
for ( i = 0; i < n; i++ )
d->d[i] = d1->d[i]-d2->d[i];
c1 = (Q)BDY(p1)->c; c2 = (Q)BDY(p2)->c;
if ( dp_fcoeffs ) {
/* do nothing */
} else if ( INT(c1) && INT(c2) ) {
gcdn(NM(c1),NM(c2),&gn);
if ( !UNIN(gn) ) {
divsn(NM(c1),gn,&tn); NTOQ(tn,SGN(c1),c); c1 = c;
divsn(NM(c2),gn,&tn); NTOQ(tn,SGN(c2),c); c2 = c;
}
} else {
ezgcdpz(CO,(P)c1,(P)c2,&g);
divsp(CO,(P)c1,g,&a); c1 = (Q)a; divsp(CO,(P)c2,g,&a); c2 = (Q)a;
}
NEWMP(m); m->dl = d; chsgnp((P)c1,&m->c); NEXT(m) = 0; MKDP(n,m,s); s->sugar = d->td;
*multp = s;
muld(CO,s,p2,&t); muldc(CO,p1,(P)c2,&s); addd(CO,s,t,&r);
muldc(CO,p0,(P)c2,&h);
*head = h; *rest = r; *dnp = (P)c2;
}
void dp_red_mod(p0,p1,p2,mod,head,rest,dnp)
DP p0,p1,p2;
int mod;
DP *head,*rest;
P *dnp;
{
int i,n;
DL d1,d2,d;
MP m;
DP t,s,r,h;
P c1,c2,g,u;
n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
NEWDL(d,n); d->td = d1->td - d2->td;
for ( i = 0; i < n; i++ )
d->d[i] = d1->d[i]-d2->d[i];
c1 = (P)BDY(p1)->c; c2 = (P)BDY(p2)->c;
gcdprsmp(CO,mod,c1,c2,&g);
divsmp(CO,mod,c1,g,&u); c1 = u; divsmp(CO,mod,c2,g,&u); c2 = u;
if ( NUM(c2) ) {
divsmp(CO,mod,c1,c2,&u); c1 = u; c2 = (P)ONEM;
}
NEWMP(m); m->dl = d; chsgnmp(mod,(P)c1,&m->c); NEXT(m) = 0;
MKDP(n,m,s); s->sugar = d->td; mulmd(CO,mod,p2,s,&t);
if ( NUM(c2) ) {
addmd(CO,mod,p1,t,&r); h = p0;
} else {
mulmdc(CO,mod,p1,c2,&s); addmd(CO,mod,s,t,&r); mulmdc(CO,mod,p0,c2,&h);
}
*head = h; *rest = r; *dnp = c2;
}
struct oEGT eg_red_mod;
void _dp_red_mod_destructive(p1,p2,mod,rp)
DP p1,p2;
int mod;
DP *rp;
{
int i,n;
DL d1,d2,d;
MP m;
DP t,s;
int c,c1;
struct oEGT t0,t1;
n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
_NEWDL(d,n); d->td = d1->td - d2->td;
for ( i = 0; i < n; i++ )
d->d[i] = d1->d[i]-d2->d[i];
c = invm(ITOS(BDY(p2)->c),mod); c1 = dmar(c,ITOS(BDY(p1)->c),0,mod);
_NEWMP(m); m->dl = d; m->c = STOI(mod-c1); NEXT(m) = 0;
_MKDP(n,m,s); s->sugar = d->td;
_mulmd_dup(mod,s,p2,&t); _free_dp(s);
/* get_eg(&t0); */
_addmd_destructive(mod,p1,t,rp);
/* get_eg(&t1); add_eg(&eg_red_mod,&t0,&t1); */
}
/*
* normal form computation
*
*/
void dp_true_nf(b,g,ps,full,rp,dnp)
NODE b;
DP g;
DP *ps;
int full;
DP *rp;
P *dnp;
{
DP u,p,d,s,t,dmy;
NODE l;
MP m,mr;
int i,n;
int *wb;
int sugar,psugar;
P dn,tdn,tdn1;
dn = (P)ONE;
if ( !g ) {
*rp = 0; *dnp = dn; return;
}
for ( n = 0, l = b; l; l = NEXT(l), n++ );
wb = (int *)ALLOCA(n*sizeof(int));
for ( i = 0, l = b; i < n; l = NEXT(l), i++ )
wb[i] = QTOS((Q)BDY(l));
sugar = g->sugar;
for ( d = 0; g; ) {
for ( u = 0, i = 0; i < n; i++ ) {
if ( dp_redble(g,p = ps[wb[i]]) ) {
dp_red(d,g,p,&t,&u,&tdn,&dmy);
psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
sugar = MAX(sugar,psugar);
if ( !u ) {
if ( d )
d->sugar = sugar;
*rp = d; *dnp = dn; return;
} else {
d = t;
mulp(CO,dn,tdn,&tdn1); dn = tdn1;
}
break;
}
}
if ( u )
g = u;
else if ( !full ) {
if ( g ) {
MKDP(g->nv,BDY(g),t); t->sugar = sugar; g = t;
}
*rp = g; *dnp = dn; return;
} else {
m = BDY(g); NEWMP(mr); mr->dl = m->dl; mr->c = m->c;
NEXT(mr) = 0; MKDP(g->nv,mr,t); t->sugar = mr->dl->td;
addd(CO,d,t,&s); d = s;
dp_rest(g,&t); g = t;
}
}
if ( d )
d->sugar = sugar;
*rp = d; *dnp = dn;
}
void dp_nf_ptozp(b,g,ps,full,multiple,rp)
NODE b;
DP g;
DP *ps;
int full,multiple;
DP *rp;
{
DP u,p,d,s,t,dmy1;
P dmy;
NODE l;
MP m,mr;
int i,n;
int *wb;
int hmag;
int sugar,psugar;
if ( !g ) {
*rp = 0; return;
}
for ( n = 0, l = b; l; l = NEXT(l), n++ );
wb = (int *)ALLOCA(n*sizeof(int));
for ( i = 0, l = b; i < n; l = NEXT(l), i++ )
wb[i] = QTOS((Q)BDY(l));
hmag = multiple*HMAG(g);
sugar = g->sugar;
for ( d = 0; g; ) {
for ( u = 0, i = 0; i < n; i++ ) {
if ( dp_redble(g,p = ps[wb[i]]) ) {
dp_red(d,g,p,&t,&u,&dmy,&dmy1);
psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
sugar = MAX(sugar,psugar);
if ( !u ) {
if ( d )
d->sugar = sugar;
*rp = d; return;
}
d = t;
break;
}
}
if ( u ) {
g = u;
if ( d ) {
if ( multiple && HMAG(d) > hmag ) {
dp_ptozp2(d,g,&t,&u); d = t; g = u;
hmag = multiple*HMAG(d);
}
} else {
if ( multiple && HMAG(g) > hmag ) {
dp_ptozp(g,&t); g = t;
hmag = multiple*HMAG(g);
}
}
}
else if ( !full ) {
if ( g ) {
MKDP(g->nv,BDY(g),t); t->sugar = sugar; g = t;
}
*rp = g; return;
} else {
m = BDY(g); NEWMP(mr); mr->dl = m->dl; mr->c = m->c;
NEXT(mr) = 0; MKDP(g->nv,mr,t); t->sugar = mr->dl->td;
addd(CO,d,t,&s); d = s;
dp_rest(g,&t); g = t;
}
}
if ( d )
d->sugar = sugar;
*rp = d;
}
void dp_nf_mod(b,g,ps,mod,full,rp)
NODE b;
DP g;
DP *ps;
int mod,full;
DP *rp;
{
DP u,p,d,s,t;
P dmy;
NODE l;
MP m,mr;
int sugar,psugar;
if ( !g ) {
*rp = 0; return;
}
sugar = g->sugar;
for ( d = 0; g; ) {
for ( u = 0, l = b; l; l = NEXT(l) ) {
if ( dp_redble(g,p = ps[(int)BDY(l)]) ) {
dp_red_mod(d,g,p,mod,&t,&u,&dmy);
psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
sugar = MAX(sugar,psugar);
if ( !u ) {
if ( d )
d->sugar = sugar;
*rp = d; return;
}
d = t;
break;
}
}
if ( u )
g = u;
else if ( !full ) {
if ( g ) {
MKDP(g->nv,BDY(g),t); t->sugar = sugar; g = t;
}
*rp = g; return;
} else {
m = BDY(g); NEWMP(mr); mr->dl = m->dl; mr->c = m->c;
NEXT(mr) = 0; MKDP(g->nv,mr,t); t->sugar = mr->dl->td;
addmd(CO,mod,d,t,&s); d = s;
dp_rest(g,&t); g = t;
}
}
if ( d )
d->sugar = sugar;
*rp = d;
}
void dp_true_nf_mod(b,g,ps,mod,full,rp,dnp)
NODE b;
DP g;
DP *ps;
int mod,full;
DP *rp;
P *dnp;
{
DP u,p,d,s,t;
NODE l;
MP m,mr;
int i,n;
int *wb;
int sugar,psugar;
P dn,tdn,tdn1;
dn = (P)ONEM;
if ( !g ) {
*rp = 0; *dnp = dn; return;
}
for ( n = 0, l = b; l; l = NEXT(l), n++ );
wb = (int *)ALLOCA(n*sizeof(int));
for ( i = 0, l = b; i < n; l = NEXT(l), i++ )
wb[i] = QTOS((Q)BDY(l));
sugar = g->sugar;
for ( d = 0; g; ) {
for ( u = 0, i = 0; i < n; i++ ) {
if ( dp_redble(g,p = ps[wb[i]]) ) {
dp_red_mod(d,g,p,mod,&t,&u,&tdn);
psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
sugar = MAX(sugar,psugar);
if ( !u ) {
if ( d )
d->sugar = sugar;
*rp = d; *dnp = dn; return;
} else {
d = t;
mulmp(CO,mod,dn,tdn,&tdn1); dn = tdn1;
}
break;
}
}
if ( u )
g = u;
else if ( !full ) {
if ( g ) {
MKDP(g->nv,BDY(g),t); t->sugar = sugar; g = t;
}
*rp = g; *dnp = dn; return;
} else {
m = BDY(g); NEWMP(mr); mr->dl = m->dl; mr->c = m->c;
NEXT(mr) = 0; MKDP(g->nv,mr,t); t->sugar = mr->dl->td;
addmd(CO,mod,d,t,&s); d = s;
dp_rest(g,&t); g = t;
}
}
if ( d )
d->sugar = sugar;
*rp = d; *dnp = dn;
}
void _dp_nf_mod_destructive(b,g,ps,mod,full,rp)
NODE b;
DP g;
DP *ps;
int mod,full;
DP *rp;
{
DP u,p,d,s,t;
NODE l;
MP m,mr,mrd;
int sugar,psugar,n,h_reducible,i;
if ( !g ) {
*rp = 0; return;
}
sugar = g->sugar;
n = g->nv;
for ( d = 0; g; ) {
for ( h_reducible = 0, l = b; l; l = NEXT(l) ) {
if ( dp_redble(g,p = ps[(int)BDY(l)]) ) {
h_reducible = 1;
psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
_dp_red_mod_destructive(g,p,mod,&u); g = u;
sugar = MAX(sugar,psugar);
if ( !g ) {
if ( d )
d->sugar = sugar;
_dptodp(d,rp); _free_dp(d); return;
}
break;
}
}
if ( !h_reducible ) {
/* head term is not reducible */
if ( !full ) {
if ( g )
g->sugar = sugar;
_dptodp(g,rp); _free_dp(g); return;
} else {
m = BDY(g);
if ( NEXT(m) ) {
BDY(g) = NEXT(m); NEXT(m) = 0;
} else {
_FREEDP(g); g = 0;
}
if ( d ) {
for ( mrd = BDY(d); NEXT(mrd); mrd = NEXT(mrd) );
NEXT(mrd) = m;
} else {
_MKDP(n,m,d);
}
}
}
}
if ( d )
d->sugar = sugar;
_dptodp(d,rp); _free_dp(d);
}
void dp_lnf_mod(p1,p2,g,mod,r1p,r2p)
DP p1,p2;
NODE g;
int mod;
DP *r1p,*r2p;
{
DP r1,r2,b1,b2,t,s;
P c;
MQ c1,c2;
NODE l,b;
int n;
if ( !p1 ) {
*r1p = p1; *r2p = p2; return;
}
n = p1->nv;
for ( l = g, r1 = p1, r2 = p2; l; l = NEXT(l) ) {
if ( !r1 ) {
*r1p = r1; *r2p = r2; return;
}
b = BDY((LIST)BDY(l)); b1 = (DP)BDY(b);
if ( dl_equal(n,BDY(r1)->dl,BDY(b1)->dl) ) {
b2 = (DP)BDY(NEXT(b));
invmq(mod,(MQ)BDY(b1)->c,&c1);
mulmq(mod,c1,(MQ)BDY(r1)->c,&c2); chsgnmp(mod,(P)c2,&c);
mulmdc(CO,mod,b1,c,&t); addmd(CO,mod,r1,t,&s); r1 = s;
mulmdc(CO,mod,b2,c,&t); addmd(CO,mod,r2,t,&s); r2 = s;
}
}
*r1p = r1; *r2p = r2;
}
void dp_nf_tab_mod(p,tab,mod,rp)
DP p;
LIST *tab;
int mod;
DP *rp;
{
DP s,t,u;
MP m;
DL h;
int i,n;
if ( !p ) {
*rp = p; return;
}
n = p->nv;
for ( s = 0, i = 0, m = BDY(p); m; m = NEXT(m) ) {
h = m->dl;
while ( !dl_equal(n,h,BDY((DP)BDY(BDY(tab[i])))->dl ) )
i++;
mulmdc(CO,mod,(DP)BDY(NEXT(BDY(tab[i]))),m->c,&t);
addmd(CO,mod,s,t,&u); s = u;
}
*rp = s;
}
/*
* setting flags
*
*/
int create_order_spec(obj,spec)
Obj obj;
struct order_spec *spec;
{
int i,j,n,s,row,col;
struct order_pair *l;
NODE node,t,tn;
MAT m;
pointer **b;
int **w;
if ( !obj || NUM(obj) ) {
spec->id = 0; spec->obj = obj;
spec->ord.simple = QTOS((Q)obj);
return 1;
} else if ( OID(obj) == O_LIST ) {
node = BDY((LIST)obj);
for ( n = 0, t = node; t; t = NEXT(t), n++ );
l = (struct order_pair *)MALLOC_ATOMIC(n*sizeof(struct order_pair));
for ( i = 0, t = node, s = 0; i < n; t = NEXT(t), i++ ) {
tn = BDY((LIST)BDY(t)); l[i].order = QTOS((Q)BDY(tn));
tn = NEXT(tn); l[i].length = QTOS((Q)BDY(tn));
s += l[i].length;
}
spec->id = 1; spec->obj = obj;
spec->ord.block.order_pair = l;
spec->ord.block.length = n; spec->nv = s;
return 1;
} else if ( OID(obj) == O_MAT ) {
m = (MAT)obj; row = m->row; col = m->col; b = BDY(m);
w = almat(row,col);
for ( i = 0; i < row; i++ )
for ( j = 0; j < col; j++ )
w[i][j] = QTOS((Q)b[i][j]);
spec->id = 2; spec->obj = obj;
spec->nv = col; spec->ord.matrix.row = row;
spec->ord.matrix.matrix = w;
return 1;
} else
return 0;
}
/*
* converters
*
*/
void dp_homo(p,rp)
DP p;
DP *rp;
{
MP m,mr,mr0;
int i,n,nv,td;
DL dl,dlh;
if ( !p )
*rp = 0;
else {
n = p->nv; nv = n + 1;
m = BDY(p); td = sugard(m);
for ( mr0 = 0; m; m = NEXT(m) ) {
NEXTMP(mr0,mr); mr->c = m->c;
dl = m->dl;
mr->dl = dlh = (DL)MALLOC_ATOMIC((nv+1)*sizeof(int));
dlh->td = td;
for ( i = 0; i < n; i++ )
dlh->d[i] = dl->d[i];
dlh->d[n] = td - dl->td;
}
NEXT(mr) = 0; MKDP(nv,mr0,*rp); (*rp)->sugar = p->sugar;
}
}
void dp_dehomo(p,rp)
DP p;
DP *rp;
{
MP m,mr,mr0;
int i,n,nv;
DL dl,dlh;
if ( !p )
*rp = 0;
else {
n = p->nv; nv = n - 1;
m = BDY(p);
for ( mr0 = 0; m; m = NEXT(m) ) {
NEXTMP(mr0,mr); mr->c = m->c;
dlh = m->dl;
mr->dl = dl = (DL)MALLOC_ATOMIC((nv+1)*sizeof(int));
dl->td = dlh->td - dlh->d[nv];
for ( i = 0; i < nv; i++ )
dl->d[i] = dlh->d[i];
}
NEXT(mr) = 0; MKDP(nv,mr0,*rp); (*rp)->sugar = p->sugar;
}
}
void dp_mod(p,mod,subst,rp)
DP p;
int mod;
NODE subst;
DP *rp;
{
MP m,mr,mr0;
P t,s,s1;
V v;
NODE tn;
if ( !p )
*rp = 0;
else {
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
for ( tn = subst, s = m->c; tn; tn = NEXT(tn) ) {
v = VR((P)BDY(tn)); tn = NEXT(tn);
substp(CO,s,v,(P)BDY(tn),&s1); s = s1;
}
ptomp(mod,s,&t);
if ( t ) {
NEXTMP(mr0,mr); mr->c = t; mr->dl = m->dl;
}
}
if ( mr0 ) {
NEXT(mr) = 0; MKDP(p->nv,mr0,*rp); (*rp)->sugar = p->sugar;
} else
*rp = 0;
}
}
void dp_rat(p,rp)
DP p;
DP *rp;
{
MP m,mr,mr0;
if ( !p )
*rp = 0;
else {
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
NEXTMP(mr0,mr); mptop(m->c,&mr->c); mr->dl = m->dl;
}
if ( mr0 ) {
NEXT(mr) = 0; MKDP(p->nv,mr0,*rp); (*rp)->sugar = p->sugar;
} else
*rp = 0;
}
}
void homogenize_order(old,n,new)
struct order_spec *old,*new;
int n;
{
struct order_pair *l;
int length,nv,row,i,j;
int **newm,**oldm;
switch ( old->id ) {
case 0:
switch ( old->ord.simple ) {
case 0:
new->id = 0; new->ord.simple = 0; break;
case 1:
l = (struct order_pair *)
MALLOC_ATOMIC(2*sizeof(struct order_pair));
l[0].length = n; l[0].order = 1;
l[1].length = 1; l[1].order = 2;
new->id = 1;
new->ord.block.order_pair = l;
new->ord.block.length = 2; new->nv = n+1;
break;
case 2:
new->id = 0; new->ord.simple = 1; break;
case 3: case 4: case 5:
new->id = 0; new->ord.simple = old->ord.simple+3;
dp_nelim = n-1; break;
case 6: case 7: case 8: case 9:
new->id = 0; new->ord.simple = old->ord.simple; break;
default:
error("homogenize_order : invalid input");
}
break;
case 1:
length = old->ord.block.length;
l = (struct order_pair *)
MALLOC_ATOMIC((length+1)*sizeof(struct order_pair));
bcopy((char *)old->ord.block.order_pair,(char *)l,length*sizeof(struct order_pair));
l[length].order = 2; l[length].length = 1;
new->id = 1; new->nv = n+1;
new->ord.block.order_pair = l;
new->ord.block.length = length+1;
break;
case 2:
nv = old->nv; row = old->ord.matrix.row;
oldm = old->ord.matrix.matrix; newm = almat(row+1,nv+1);
for ( i = 0; i <= nv; i++ )
newm[0][i] = 1;
for ( i = 0; i < row; i++ ) {
for ( j = 0; j < nv; j++ )
newm[i+1][j] = oldm[i][j];
newm[i+1][j] = 0;
}
new->id = 2; new->nv = nv+1;
new->ord.matrix.row = row+1; new->ord.matrix.matrix = newm;
break;
default:
error("homogenize_order : invalid input");
}
}
void qltozl(w,n,dvr)
Q *w,*dvr;
int n;
{
N nm,dn;
N g,l1,l2,l3;
Q c,d;
int i;
struct oVECT v;
for ( i = 0; i < n; i++ )
if ( w[i] && !INT(w[i]) )
break;
if ( i == n ) {
v.id = O_VECT; v.len = n; v.body = (pointer *)w;
igcdv(&v,dvr); return;
}
c = w[0]; nm = NM(c); dn = INT(c) ? ONEN : DN(c);
for ( i = 1; i < n; i++ ) {
c = w[i]; l1 = INT(c) ? ONEN : DN(c);
gcdn(nm,NM(c),&g); nm = g;
gcdn(dn,l1,&l2); muln(dn,l1,&l3); divsn(l3,l2,&dn);
}
if ( UNIN(dn) )
NTOQ(nm,1,d);
else
NDTOQ(nm,dn,1,d);
*dvr = d;
}
int comp_nm(a,b)
Q *a,*b;
{
return cmpn((*a)?NM(*a):0,(*b)?NM(*b):0);
}
void sortbynm(w,n)
Q *w;
int n;
{
qsort(w,n,sizeof(Q),(int (*)(const void *,const void *))comp_nm);
}
/*
* simple operations
*
*/
int dp_redble(p1,p2)
DP p1,p2;
{
int i,n;
DL d1,d2;
d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
if ( d1->td < d2->td )
return 0;
else {
for ( i = 0, n = p1->nv; i < n; i++ )
if ( d1->d[i] < d2->d[i] )
return 0;
return 1;
}
}
void dp_subd(p1,p2,rp)
DP p1,p2;
DP *rp;
{
int i,n;
DL d1,d2,d;
MP m;
DP s;
n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
NEWDL(d,n); d->td = d1->td - d2->td;
for ( i = 0; i < n; i++ )
d->d[i] = d1->d[i]-d2->d[i];
NEWMP(m); m->dl = d; m->c = (P)ONE; NEXT(m) = 0;
MKDP(n,m,s); s->sugar = d->td;
*rp = s;
}
void dltod(d,n,rp)
DL d;
int n;
DP *rp;
{
MP m;
DP s;
NEWMP(m); m->dl = d; m->c = (P)ONE; NEXT(m) = 0;
MKDP(n,m,s); s->sugar = d->td;
*rp = s;
}
void dp_hm(p,rp)
DP p;
DP *rp;
{
MP m,mr;
if ( !p )
*rp = 0;
else {
m = BDY(p);
NEWMP(mr); mr->dl = m->dl; mr->c = m->c; NEXT(mr) = 0;
MKDP(p->nv,mr,*rp); (*rp)->sugar = mr->dl->td; /* XXX */
}
}
void dp_rest(p,rp)
DP p,*rp;
{
MP m;
m = BDY(p);
if ( !NEXT(m) )
*rp = 0;
else {
MKDP(p->nv,NEXT(m),*rp);
if ( *rp )
(*rp)->sugar = p->sugar;
}
}
DL lcm_of_DL(nv,dl1,dl2,dl)
int nv;
DL dl1,dl2;
register DL dl;
{
register int n, *d1, *d2, *d, td;
if ( !dl ) NEWDL(dl,nv);
d = dl->d, d1 = dl1->d, d2 = dl2->d;
for ( td = 0, n = nv; --n >= 0; d1++, d2++, d++ )
td += (*d = *d1 > *d2 ? *d1 : *d2 );
dl->td = td;
return dl;
}
int dl_equal(nv,dl1,dl2)
int nv;
DL dl1, dl2;
{
register int *d1, *d2, n;
if ( dl1->td != dl2->td ) return 0;
for ( d1 = dl1->d, d2 = dl2->d, n = nv; --n >= 0; d1++, d2++ )
if ( *d1 != *d2 ) return 0;
return 1;
}
int dp_nt(p)
DP p;
{
int i;
MP m;
if ( !p )
return 0;
else {
for ( i = 0, m = BDY(p); m; m = NEXT(m), i++ );
return i;
}
}
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