/*
* 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/builtin/dp-supp.c,v 1.28 2004/02/05 08:28:53 noro Exp $
*/
#include "ca.h"
#include "base.h"
#include "inline.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(DP p,DP *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(DP p0,DP p1,DP *hp,DP *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(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(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 += MUL_WEIGHT(1,i);
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 += MUL_WEIGHT(d->d[j],j);
d->td = td;
i--;
} else
break;
}
if ( i < 0 )
break;
}
}
int _dl_redble(DL d1,DL 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(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(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(DP p,DP *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;
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;
void Pox_rpc();
void Pox_pop_local();
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(DP p0,DP p1,DP *hp,DP *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;
}
int have_sf_coef(P p)
{
DCP dc;
if ( !p )
return 0;
else if ( NUM(p) )
return NID((Num)p) == N_GFS ? 1 : 0;
else {
for ( dc = DC(p); dc; dc = NEXT(dc) )
if ( have_sf_coef(COEF(dc)) )
return 1;
return 0;
}
}
void head_coef(P p,Num *c)
{
if ( !p )
*c = 0;
else if ( NUM(p) )
*c = (Num)p;
else
head_coef(COEF(DC(p)),c);
}
void dp_monic_sf(DP p,DP *rp)
{
Num c;
if ( !p )
*rp = 0;
else {
head_coef(BDY(p)->c,&c);
divsdc(CO,p,(P)c,rp);
}
}
void dp_prim(DP p,DP *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 == N_GFS ) {
for ( m = BDY(p); m; m = NEXT(m) )
if ( OID(m->c) == O_N ) {
/* GCD of coeffs = 1 */
dp_monic_sf(p,rp);
return;
} else break;
/* compute GCD over the finite fieid */
for ( m = BDY(p), n = 0; m; m = NEXT(m), n++ );
w = (P *)ALLOCA(n*sizeof(P));
for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ )
w[i] = m->c;
gcdsf(CO,w,n,&g);
if ( NUM(g) )
dp_monic_sf(p,rp);
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,p1); p1->sugar = p->sugar;
dp_monic_sf(p1,rp);
}
return;
} 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 vl,P *pl,int m,P *pr)
{
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(DP p,int mod,DP *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(DP p,Q *rp)
{
VECT v;
dp_dtov(p,&v); igcdv(v,rp);
}
void dp_dtov(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(DP p1,DP 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 += MUL_WEIGHT(w[i],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_dup(DP p1,DP 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 += MUL_WEIGHT(w[i],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_dup(CO,s1,p1,&t); _free_dp(s1);
_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; chsgnp((P)c1,&m->c); NEXT(m) = 0;
_MKDP(n,m,s2); s2->sugar = d->td; _muld_dup(CO,s2,p2,&u); _free_dp(s2);
_addd_destructive(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(DP p1,DP 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 += MUL_WEIGHT(w[i],i);
}
NEWDL_NOINIT(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_NOINIT(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(DP p1,DP 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 += MUL_WEIGHT(w[i],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(DP p1,DP 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 += MUL_WEIGHT(w[i],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
* do content reduction over Z or Q(x,...)
* do nothing over finite fields
*
*/
void dp_red(DP p0,DP p1,DP p2,DP *head,DP *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;
P p[2];
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 == N_GFS ) {
p[0] = (P)c1; p[1] = (P)c2;
gcdsf(CO,p,2,&g);
divsp(CO,(P)c1,g,&a); c1 = (Q)a; divsp(CO,(P)c2,g,&a); c2 = (Q)a;
} else 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;
}
/* m-reduction over a field */
void dp_red_f(DP p1,DP p2,DP *rest)
{
int i,n;
DL d1,d2,d;
MP m;
DP t,s;
Obj a,b;
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;
divr(CO,(Obj)BDY(p1)->c,(Obj)BDY(p2)->c,&a); chsgnr(a,&b);
C(m) = (P)b;
NEXT(m) = 0; MKDP(n,m,s); s->sugar = d->td;
muld(CO,s,p2,&t); addd(CO,p1,t,rest);
}
void dp_red_mod(DP p0,DP p1,DP p2,int mod,DP *head,DP *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,s,p2,&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(DP p1,DP p2,int mod,DP *rp)
{
int i,n;
DL d1,d2,d;
MP m;
DP t,s;
int c,c1,c2;
extern int do_weyl;
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);
c2 = ITOS(BDY(p1)->c);
DMAR(c,c2,0,mod,c1);
_NEWMP(m); m->dl = d; m->c = STOI(mod-c1); NEXT(m) = 0;
#if 0
_MKDP(n,m,s); s->sugar = d->td;
_mulmd_dup(mod,s,p2,&t); _free_dp(s);
#else
if ( do_weyl ) {
_MKDP(n,m,s); s->sugar = d->td;
_mulmd_dup(mod,s,p2,&t); _free_dp(s);
} else {
_mulmdm_dup(mod,p2,m,&t); _FREEMP(m);
}
#endif
/* 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(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;
}
/* nf computation over Z */
void dp_nf_z(NODE b,DP g,DP *ps,int full,int 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;
}
/* nf computation over a field */
void dp_nf_f(NODE b,DP g,DP *ps,int full,DP *rp)
{
DP u,p,d,s,t;
NODE l;
MP m,mr;
int i,n;
int *wb;
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));
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_f(g,p,&u);
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;
}
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;
addd(CO,d,t,&s); d = s;
dp_rest(g,&t); g = t;
}
}
if ( d )
d->sugar = sugar;
*rp = d;
}
/* nf computation over GF(mod) (only for internal use) */
void dp_nf_mod(NODE b,DP g,DP *ps,int mod,int 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(NODE b,DP g,DP *ps,int mod,int 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(NODE b,DP g,DP *ps,int mod,int full,DP *rp)
{
DP u,p,d;
NODE l;
MP m,mrd;
int sugar,psugar,n,h_reducible;
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);
}
/* reduction by linear base over a field */
void dp_lnf_f(DP p1,DP p2,NODE g,DP *r1p,DP *r2p)
{
DP r1,r2,b1,b2,t,s;
Obj c,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));
divr(CO,(Obj)ONE,(Obj)BDY(b1)->c,&c1);
mulr(CO,c1,(Obj)BDY(r1)->c,&c2); chsgnr(c2,&c);
muldc(CO,b1,(P)c,&t); addd(CO,r1,t,&s); r1 = s;
muldc(CO,b2,(P)c,&t); addd(CO,r2,t,&s); r2 = s;
}
}
*r1p = r1; *r2p = r2;
}
/* reduction by linear base over GF(mod) */
void dp_lnf_mod(DP p1,DP p2,NODE g,int mod,DP *r1p,DP *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(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;
}
void dp_nf_tab_f(DP p,LIST *tab,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++;
muldc(CO,(DP)BDY(NEXT(BDY(tab[i]))),m->c,&t);
addd(CO,s,t,&u); s = u;
}
*rp = s;
}
/*
* setting flags
*
*/
int create_order_spec(VL vl,Obj obj,struct order_spec **specp)
{
int i,j,n,s,row,col;
struct order_spec *spec;
struct order_pair *l;
NODE node,t,tn;
MAT m;
pointer **b;
int **w;
if ( vl && obj && OID(obj) == O_LIST )
return create_composite_order_spec(vl,(LIST)obj,specp);
*specp = spec = (struct order_spec *)MALLOC(sizeof(struct order_spec));
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;
}
void print_composite_order_spec(struct order_spec *spec)
{
int nv,n,len,i,j,k,start;
struct weight_or_block *worb;
nv = spec->nv;
n = spec->ord.composite.length;
worb = spec->ord.composite.w_or_b;
for ( i = 0; i < n; i++, worb++ ) {
len = worb->length;
printf("[ ");
switch ( worb->type ) {
case IS_DENSE_WEIGHT:
for ( j = 0; j < len; j++ )
printf("%d ",worb->body.dense_weight[j]);
for ( ; j < nv; j++ )
printf("0 ");
break;
case IS_SPARSE_WEIGHT:
for ( j = 0, k = 0; j < nv; j++ )
if ( j == worb->body.sparse_weight[k].pos )
printf("%d ",worb->body.sparse_weight[k++].value);
else
printf("0 ");
break;
case IS_BLOCK:
start = worb->body.block.start;
for ( j = 0; j < start; j++ ) printf("0 ");
switch ( worb->body.block.order ) {
case 0:
for ( k = 0; k < len; k++, j++ ) printf("R ");
break;
case 1:
for ( k = 0; k < len; k++, j++ ) printf("G ");
break;
case 2:
for ( k = 0; k < len; k++, j++ ) printf("L ");
break;
}
for ( ; j < nv; j++ ) printf("0 ");
break;
}
printf("]\n");
}
}
/* order = [w_or_b, w_or_b, ... ] */
/* w_or_b = w or b */
/* w = [1,2,...] or [x,1,y,2,...] */
/* b = [@lex,x,y,...,z] etc */
int create_composite_order_spec(VL vl,LIST order,struct order_spec **specp)
{
NODE wb,t,p;
struct order_spec *spec;
VL tvl;
int n,i,j,k,l,len;
int *dw;
struct sparse_weight *sw;
struct weight_or_block *w_or_b;
Obj a0;
NODE a;
V v;
Symbol sym;
int start;
/* l = number of vars in vl */
for ( l = 0, tvl = vl; tvl; tvl = NEXT(tvl), l++ );
/* n = number of primitives in order */
wb = BDY(order);
n = length(wb);
*specp = spec = (struct order_spec *)MALLOC(sizeof(struct order_spec));
spec->id = 3;
spec->obj = (Obj)order;
spec->nv = l;
spec->ord.composite.length = n;
w_or_b = spec->ord.composite.w_or_b = (struct weight_or_block *)
MALLOC(sizeof(struct weight_or_block)*n);
for ( t = wb, i = 0; t; t = NEXT(t), i++ ) {
a = BDY((LIST)BDY(t));
len = length(a);
a0 = (Obj)BDY(a);
if ( !a0 || OID(a0) == O_N ) {
/* a is a dense weight vector */
dw = (int *)MALLOC(sizeof(int)*len);
for ( j = 0, p = a; j < len; p = NEXT(p), j++ )
dw[j] = QTOS((Q)BDY(p));
w_or_b[i].type = IS_DENSE_WEIGHT;
w_or_b[i].length = len;
w_or_b[i].body.dense_weight = dw;
} else if ( OID(a0) == O_P ) {
/* a is a sparse weight vector */
len >>= 1;
sw = (struct sparse_weight *)
MALLOC(sizeof(struct sparse_weight)*len);
for ( j = 0, p = a; j < len; j++ ) {
v = VR((P)BDY(p)); p = NEXT(p);
for ( tvl = vl, k = 0; tvl && tvl->v != v;
k++, tvl = NEXT(tvl) );
if ( !tvl )
error("invalid variable name");
sw[j].pos = k;
sw[j].value = QTOS((Q)BDY(p)); p = NEXT(p);
}
w_or_b[i].type = IS_SPARSE_WEIGHT;
w_or_b[i].length = len;
w_or_b[i].body.sparse_weight = sw;
} else if ( OID(a0) == O_SYMBOL ) {
/* a is a block */
sym = (Symbol)a0; a = NEXT(a); len--;
for ( start = 0, tvl = vl; tvl->v != VR((P)BDY(a));
tvl = NEXT(tvl), start++ );
for ( p = NEXT(a), tvl = NEXT(tvl); p;
p = NEXT(p), tvl = NEXT(tvl) )
if ( tvl->v != VR((P)BDY(p)) ) break;
if ( p )
error("a block must be contiguous");
w_or_b[i].type = IS_BLOCK;
w_or_b[i].length = len;
w_or_b[i].body.block.start = start;
if ( !strcmp(sym->name,"@grlex") )
w_or_b[i].body.block.order = 0;
else if ( !strcmp(sym->name,"@glex") )
w_or_b[i].body.block.order = 1;
else if ( !strcmp(sym->name,"@lex") )
w_or_b[i].body.block.order = 2;
else
error("invalid ordernam");
}
}
if ( 1 ) print_composite_order_spec(spec);
}
/*
* converters
*
*/
void dp_homo(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(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(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(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(struct order_spec *old,int n,struct order_spec **newp)
{
struct order_pair *l;
int length,nv,row,i,j;
int **newm,**oldm;
struct order_spec *new;
*newp = new = (struct order_spec *)MALLOC(sizeof(struct order_spec));
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(Q *w,int n,Q *dvr)
{
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(Q *a,Q *b)
{
return cmpn((*a)?NM(*a):0,(*b)?NM(*b):0);
}
void sortbynm(Q *w,int n)
{
qsort(w,n,sizeof(Q),(int (*)(const void *,const void *))comp_nm);
}
/*
* simple operations
*
*/
int dp_redble(DP p1,DP 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(DP p1,DP 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(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(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(DP p,DP *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(int nv,DL dl1,DL dl2,DL dl)
{
register int i, *d1, *d2, *d, td;
if ( !dl ) NEWDL(dl,nv);
d = dl->d, d1 = dl1->d, d2 = dl2->d;
for ( td = 0, i = 0; i < nv; d1++, d2++, d++, i++ ) {
*d = *d1 > *d2 ? *d1 : *d2;
td += MUL_WEIGHT(*d,i);
}
dl->td = td;
return dl;
}
int dl_equal(int nv,DL dl1,DL 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(DP p)
{
int i;
MP m;
if ( !p )
return 0;
else {
for ( i = 0, m = BDY(p); m; m = NEXT(m), i++ );
return i;
}
}
int dp_homogeneous(DP p)
{
MP m;
int d;
if ( !p )
return 1;
else {
m = BDY(p);
d = m->dl->td;
m = NEXT(m);
for ( ; m; m = NEXT(m) ) {
if ( m->dl->td != d )
return 0;
}
return 1;
}
}
void _print_mp(int nv,MP m)
{
int i;
if ( !m )
return;
for ( ; m; m = NEXT(m) ) {
fprintf(stderr,"%d<",ITOS(C(m)));
for ( i = 0; i < nv; i++ ) {
fprintf(stderr,"%d",m->dl->d[i]);
if ( i != nv-1 )
fprintf(stderr," ");
}
fprintf(stderr,">",C(m));
}
fprintf(stderr,"\n");
}
static int cmp_mp_nvar;
int comp_mp(MP *a,MP *b)
{
return -(*cmpdl)(cmp_mp_nvar,(*a)->dl,(*b)->dl);
}
void dp_sort(DP p,DP *rp)
{
MP t,mp,mp0;
int i,n;
DP r;
MP *w;
if ( !p ) {
*rp = 0;
return;
}
for ( t = BDY(p), n = 0; t; t = NEXT(t), n++ );
w = (MP *)ALLOCA(n*sizeof(MP));
for ( t = BDY(p), i = 0; i < n; t = NEXT(t), i++ )
w[i] = t;
cmp_mp_nvar = NV(p);
qsort(w,n,sizeof(MP),(int (*)(const void *,const void *))comp_mp);
mp0 = 0;
for ( i = n-1; i >= 0; i-- ) {
NEWMP(mp); mp->dl = w[i]->dl; C(mp) = C(w[i]);
NEXT(mp) = mp0; mp0 = mp;
}
MKDP(p->nv,mp0,r);
r->sugar = p->sugar;
*rp = r;
}
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