File: [local] / OpenXM_contrib2 / asir2018 / builtin / dp-supp.c (download)
Revision 1.19, Sat Sep 10 05:41:43 2022 UTC (19 months, 2 weeks ago) by noro
Branch: MAIN
CVS Tags: HEAD
Changes since 1.18: +5 -5
lines
dp_red(), dp_red_marked() call ezgcdp() instead of ezgcdpz() for computing
a polynomial gcd.
|
/*
* 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/asir2018/builtin/dp-supp.c,v 1.19 2022/09/10 05:41:43 noro Exp $
*/
#include "ca.h"
#include "base.h"
#include "inline.h"
#include "parse.h"
#include "ox.h"
#define HMAG(p) (p_mag((P)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;
int show_orderspec;
void print_composite_order_spec(struct order_spec *spec);
void dpm_rest(DPM,DPM *);
/*
* content reduction
*
*/
static NODE RatDenomList;
void init_denomlist()
{
RatDenomList = 0;
}
void add_denomlist(P f)
{
NODE n;
if ( OID(f)==O_P ) {
MKNODE(n,f,RatDenomList); RatDenomList = n;
}
}
LIST get_denomlist()
{
LIST l;
MKLIST(l,RatDenomList); RatDenomList = 0;
return l;
}
int dp_iszp(DP p)
{
MP m;
if ( !p ) return 1;
for ( m = BDY(p); m; m = NEXT(m))
if ( !INT(m->c) ) return 0;
return 1;
}
void dp_ptozp(DP p,DP *rp)
{
MP m,mr,mr0;
int i,n;
Q *w;
Z 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((P)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,(P)m->c,(P)dvr,(P *)&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;
}
int dpm_iszp(DPM p)
{
DMM m;
if ( !p ) return 1;
for ( m = BDY(p); m; m = NEXT(m))
if ( !INT(m->c) ) return 0;
return 1;
}
void dpm_ptozp(DPM p,Z *cont,DPM *rp)
{
DMM m,mr,mr0;
int i,n;
Q *w;
Z dvr;
P t;
if ( !p ) {
*rp = 0; *cont = ONE;
} 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((P)m->c,1,&w[i],&t);
sortbynm(w,n);
qltozl(w,n,&dvr);
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
NEXTDMM(mr0,mr); divsp(CO,(P)m->c,(P)dvr,(P *)&mr->c); mr->dl = m->dl; mr->pos = m->pos;
}
NEXT(mr) = 0; MKDPM(p->nv,mr0,*rp); (*rp)->sugar = p->sugar;
*cont = dvr;
}
}
void dpm_ptozp2(DPM p0,DPM p1,DPM *hp,DPM *rp)
{
DPM t,s,h,r;
DMM m,mr,mr0,m0;
Z cont;
adddpm(CO,p0,p1,&t); dpm_ptozp(t,&cont,&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) ) {
NEXTDMM(mr0,mr); mr->c = m->c; mr->dl = m->dl; mr->pos = m->pos;
}
NEXT(mr) = 0; MKDPM(p0->nv,mr0,h); MKDPM(p0->nv,m,r);
}
if ( h )
h->sugar = p0->sugar;
if ( r )
r->sugar = p1->sugar;
*hp = h; *rp = r;
}
void dp_ptozp3(DP p,Z *dvr,DP *rp)
{
MP m,mr,mr0;
int i,n;
Q *w;
P t;
if ( !p ) {
*rp = 0; *dvr = 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((P)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,(P)m->c,(P)(*dvr),(P *)&mr->c); mr->dl = m->dl;
}
NEXT(mr) = 0; MKDP(p->nv,mr0,*rp); (*rp)->sugar = p->sugar;
}
}
void dp_idiv(DP p,Z c,DP *rp)
{
MP mr0,m,mr;
if ( !p )
*rp = 0;
else if ( MUNIQ((Q)c) )
*rp = p;
else if ( MUNIQ((Q)c) )
chsgnd(p,rp);
else {
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
NEXTMP(mr0,mr);
divsz((Z)(m->c),c,(Z *)&mr->c);
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 *t;
int i,j,k,n,nvar,td;
n = length(hlist); nvar = ((DP)BDY(hlist))->nv;
dl = (DL *)MALLOC(n*sizeof(DL));
NEWDL(d,nvar); *mbase = 0;
for ( i = 0; i < n; i++, hlist = NEXT(hlist) ) {
dl[i] = BDY((DP)BDY(hlist))->dl;
/* trivial ideal check */
if ( (*cmpdl)(nvar,d,dl[i]) == 0 ) {
return;
}
}
/* zero-dim. ideal check */
for ( i = 0; i < nvar; i++ ) {
for ( j = 0; j < n; j++ ) {
for ( k = 0, t = dl[j]->d; k < nvar; k++ )
if ( k != i && t[k] != 0 ) break;
if ( k == nvar ) break;
}
if ( j == n )
error("dp_mbase : input ideal is not zero-dimensional");
}
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;
}
int _dl_redble_ext(DL d1,DL d2,DL quo,int nvar)
{
int i;
if ( (quo->td = d2->td-d1->td) < 0 )
return 0;
for ( i = 0; i < nvar; i++ )
if ( (quo->d[i] = d2->d[i]-d1->d[i]) < 0 )
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 = (Obj)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 = (Obj)c[i]; mr->dl = m->dl;
}
NEXT(mr) = 0; MKDP(p->nv,mr0,*rp);
(*rp)->sugar = p->sugar;
}
}
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((P)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;
Z dvr;
NODE tn;
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] = (P)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,(P)m->c,g,(P *)&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 = (Obj)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((P)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,(P)m->c,g,(P *)&mr->c); mr->dl = m->dl;
}
NEXT(mr) = 0; MKDP(p->nv,mr0,*rp); (*rp)->sugar = p->sugar;
add_denomlist(g);
}
}
}
void heu_nezgcdnpz(VL vl,P *pl,int m,P *pr)
{
int i,r;
P gcd,t,s1,s2,u;
Z rq;
DCP dc;
extern int DP_Print;
while ( 1 ) {
for ( i = 0, s1 = 0; i < m; i++ ) {
r = random(); UTOZ(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(); UTOZ(r,rq);
mulp(vl,pl[i],(P)rq,&t); addp(vl,s2,t,&u); s2 = u;
}
ezgcdp(vl,s1,s2,&gcd);
if ( DP_Print > 2 )
{ fprintf(asir_out,"(%d)",nmonop(gcd)); fflush(asir_out); }
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 = (P)m->c, m = NEXT(m); m; m = NEXT(m) ) {
gcdprsmp(CO,mod,g,(P)m->c,&t); g = t;
}
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
NEXTMP(mr0,mr); divsmp(CO,mod,(P)m->c,g,(P *)&mr->c); mr->dl = m->dl;
}
NEXT(mr) = 0; MKDP(p->nv,mr0,*rp); (*rp)->sugar = p->sugar;
}
}
void dp_cont(DP p,Z *rp)
{
VECT v;
dp_dtov(p,&v); gcdvz(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;
Z c,c1,c2;
Z gn;
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 = (Z)BDY(p1)->c; c2 = (Z)BDY(p2)->c;
if ( INT(c1) && INT(c2) ) {
gcdz(c1,c2,&gn);
if ( !UNIQ(gn) ) {
divsz(c1,gn,&c); c1 = c;
divsz(c2,gn,&c);c2 = c;
}
}
NEWMP(m); m->dl = d; m->c = (Obj)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 = (Obj)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,NULLP,s1,ONE);
MKLIST(hist,node);
MKNODE(TraceList,hist,0);
node = mknode(4,ONE,NULLP,NULLP,ONE);
chsgnd(s2,(DP *)&ARG2(node));
MKLIST(hist,node);
MKNODE(node,hist,TraceList); TraceList = node;
}
}
void dpm_sp(DPM p1,DPM p2,DPM *rp,DP *mul1,DP *mul2)
{
int i,n,td;
int *w;
DL d1,d2,d;
MP m;
DP s1,s2;
DPM t,u;
Z c,c1,c2;
Z gn;
n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
if ( BDY(p1)->pos != BDY(p2)->pos ) {
*mul1 = 0; *mul2 = 0; *rp = 0;
return;
}
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 = (Z)BDY(p1)->c; c2 = (Z)BDY(p2)->c;
if ( INT(c1) && INT(c2) ) {
gcdz(c1,c2,&gn);
if ( !UNIQ(gn) ) {
divsz(c1,gn,&c); c1 = c;
divsz(c2,gn,&c);c2 = c;
}
}
NEWMP(m); m->dl = d; m->c = (Obj)c2; NEXT(m) = 0;
MKDP(n,m,s1); s1->sugar = d->td; mulobjdpm(CO,(Obj)s1,p1,&t);
*mul1 = 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; m->c = (Obj)c1; NEXT(m) = 0;
MKDP(n,m,s2); s2->sugar = d->td; mulobjdpm(CO,(Obj)s2,p2,&u);
*mul2 = s2;
subdpm(CO,t,u,rp);
if ( GenTrace ) {
LIST hist;
NODE node;
node = mknode(4,ONE,NULLP,s1,ONE);
MKLIST(hist,node);
MKNODE(TraceList,hist,0);
node = mknode(4,ONE,NULLP,NULLP,ONE);
chsgnd(s2,(DP *)&ARG2(node));
MKLIST(hist,node);
MKNODE(node,hist,TraceList); TraceList = node;
}
}
DP dpm_sp_hm(DPM p1,DPM p2)
{
int i,n,td;
int *w;
DL d1,d2,d;
MP m;
DP s1;
n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl;
if ( BDY(p1)->pos != BDY(p2)->pos ) {
return 0;
}
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 = (Obj)ONE; NEXT(m) = 0;
MKDP(n,m,s1); s1->sugar = d->td;
return s1;
}
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;
Z c,c1,c2;
Z gn;
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 = (Z)BDY(p1)->c; c2 = (Z)BDY(p2)->c;
if ( INT(c1) && INT(c2) ) {
gcdz(c1,c2,&gn);
if ( !UNIQ(gn) ) {
divsz(c1,gn,&c); c1 = c;
divsz(c2,gn,&c);c2 = c;
}
}
_NEWMP(m); m->dl = d; m->c = (Obj)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,(P *)&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,NULLP,s1,ONE);
MKLIST(hist,node);
MKNODE(TraceList,hist,0);
node = mknode(4,ONE,NULLP,NULLP,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 = (Obj)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 = (Obj)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 = (Obj)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 = (Obj)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
*
* head+rest = dn*(p0+p1)+mult*p2
*/
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;
Z c,c1,c2,gn;
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 = (Z)BDY(p1)->c; c2 = (Z)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 = (Z)a; divsp(CO,(P)c2,g,&a); c2 = (Z)a;
} else if ( dp_fcoeffs ) {
/* do nothing */
} else if ( INT(c1) && INT(c2) ) {
gcdz(c1,c2,&gn);
if ( !UNIQ(gn) ) {
divsz(c1,gn,&c); c1 = c;
divsz(c2,gn,&c); c2 = c;
}
} else {
ezgcdp(CO,(P)c1,(P)c2,&g);
divsp(CO,(P)c1,g,&a); c1 = (Z)a; divsp(CO,(P)c2,g,&a); c2 = (Z)a;
add_denomlist(g);
}
NEWMP(m); m->dl = d; chsgnp((P)c1,(P *)&m->c); NEXT(m) = 0; MKDP(n,m,s); s->sugar = d->td;
*multp = s;
muld(CO,s,p2,&t); muldc(CO,p1,(Obj)c2,&s); addd(CO,s,t,&r);
muldc(CO,p0,(Obj)c2,&h);
*head = h; *rest = r; *dnp = (P)c2;
}
// head+rest = dn*(p0+p1)-mult*p2
void dpm_red(DPM p0,DPM p1,DPM p2,DPM *head,DPM *rest,P *dnp,DP *multp)
{
int i,n,pos;
DL d1,d2,d;
MP m;
DP s,ms;
DPM t,r,h,u,w;
Z c,c1,c2,gn;
P g,a;
P p[2];
n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl; pos = BDY(p1)->pos;
if ( pos != BDY(p2)->pos )
error("dpm_red : cannot happen");
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 = (Z)BDY(p1)->c; c2 = (Z)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 = (Z)a; divsp(CO,(P)c2,g,&a); c2 = (Z)a;
} else if ( dp_fcoeffs ) {
/* do nothing */
} else if ( INT(c1) && INT(c2) ) {
gcdz(c1,c2,&gn);
if ( !UNIQ(gn) ) {
divsz(c1,gn,&c); c1 = c;
divsz(c2,gn,&c); c2 = c;
}
} else {
ezgcdp(CO,(P)c1,(P)c2,&g);
divsp(CO,(P)c1,g,&a); c1 = (Z)a; divsp(CO,(P)c2,g,&a); c2 = (Z)a;
add_denomlist(g);
}
NEWMP(m); m->dl = d; m->c = (Obj)c1; NEXT(m) = 0; MKDP(n,m,s); s->sugar = d->td;
*multp = s;
chsgnd(s,&ms); mulobjdpm(CO,(Obj)ms,p2,&u); mulobjdpm(CO,(Obj)c2,p1,&w); adddpm(CO,w,u,&r);
mulobjdpm(CO,(Obj)c2,p0,&h);
*head = h; *rest = r; *dnp = (P)c2;
}
void dpm_red2(DPM p1,DPM p2,DPM *rest,P *dnp,DP *multp)
{
int i,n,pos;
DL d1,d2,d;
MP m;
DP s,ms;
DPM t,r,h,u,w;
Z c,c1,c2,gn;
P g,a;
P p[2];
n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(p2)->dl; pos = BDY(p1)->pos;
if ( pos != BDY(p2)->pos )
error("dpm_red : cannot happen");
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 = (Z)BDY(p1)->c; c2 = (Z)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 = (Z)a; divsp(CO,(P)c2,g,&a); c2 = (Z)a;
} else if ( dp_fcoeffs ) {
/* do nothing */
} else if ( INT(c1) && INT(c2) ) {
gcdz(c1,c2,&gn);
if ( !UNIQ(gn) ) {
divsz(c1,gn,&c); c1 = c;
divsz(c2,gn,&c); c2 = c;
}
} else {
ezgcdp(CO,(P)c1,(P)c2,&g);
divsp(CO,(P)c1,g,&a); c1 = (Z)a; divsp(CO,(P)c2,g,&a); c2 = (Z)a;
add_denomlist(g);
}
NEWMP(m); m->dl = d; m->c = (Obj)c1; NEXT(m) = 0; MKDP(n,m,s); s->sugar = d->td;
*multp = s;
chsgnd(s,&ms); mulobjdpm(CO,(Obj)ms,p2,&u); mulobjdpm(CO,(Obj)c2,p1,&w); adddpm(CO,w,u,&r);
*rest = r; *dnp = (P)c2;
}
/*
* m-reduction by a marked poly
* do content reduction over Z or Q(x,...)
* do nothing over finite fields
*
*/
void dp_red_marked(DP p0,DP p1,DP p2,DP hp2,DP *head,DP *rest,P *dnp,DP *multp)
{
int i,n;
DL d1,d2,d;
MP m;
DP t,s,r,h;
Z c,c1,c2,gn;
P g,a;
P p[2];
n = p1->nv; d1 = BDY(p1)->dl; d2 = BDY(hp2)->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 = (Z)BDY(p1)->c; c2 = (Z)BDY(hp2)->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 = (Z)a; divsp(CO,(P)c2,g,&a); c2 = (Z)a;
} else if ( dp_fcoeffs ) {
/* do nothing */
} else if ( INT(c1) && INT(c2) ) {
gcdz(c1,c2,&gn);
if ( !UNIQ(gn) ) {
divsz(c1,gn,&c); c1 = c;
divsz(c2,gn,&c); c2 = c;
}
} else {
ezgcdp(CO,(P)c1,(P)c2,&g);
divsp(CO,(P)c1,g,&a); c1 = (Z)a; divsp(CO,(P)c2,g,&a); c2 = (Z)a;
}
NEWMP(m); m->dl = d; m->c = (Obj)c1; NEXT(m) = 0; MKDP(n,m,s); s->sugar = d->td;
*multp = s;
muld(CO,s,p2,&t); muldc(CO,p1,(Obj)c2,&s); subd(CO,s,t,&r);
muldc(CO,p0,(Obj)c2,&h);
*head = h; *rest = r; *dnp = (P)c2;
}
void dp_red_marked_mod(DP p0,DP p1,DP p2,DP hp2,int mod,DP *head,DP *rest,P *dnp,DP *multp)
{
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(hp2)->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(hp2)->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; m->c = (Obj)c1; NEXT(m) = 0;
MKDP(n,m,s); s->sugar = d->td;
*multp = s;
mulmd(CO,mod,s,p2,&t);
if ( NUM(c2) ) {
submd(CO,mod,p1,t,&r); h = p0;
} else {
mulmdc(CO,mod,p1,c2,&s); submd(CO,mod,s,t,&r); mulmdc(CO,mod,p0,c2,&h);
}
*head = h; *rest = r; *dnp = 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) = (Obj)b;
NEXT(m) = 0; MKDP(n,m,s); s->sugar = d->td;
muld(CO,s,p2,&t); addd(CO,p1,t,rest);
}
void dpm_red_f(DPM p1,DPM p2,DPM *rest)
{
int i,n;
DL d1,d2,d;
MP m;
DPM t;
DP 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;
arf_div(CO,(Obj)BDY(p1)->c,(Obj)BDY(p2)->c,&a); arf_chsgn(a,&b);
C(m) = b;
NEXT(m) = 0; MKDP(n,m,s); s->sugar = d->td;
mulobjdpm(CO,(Obj)s,p2,&t); adddpm(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,(P *)&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 = (Obj)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] = ZTOS((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_removecont2(DP p1,DP p2,DP *r1p,DP *r2p,Z *contp)
{
struct oVECT v;
int i,n1,n2,n;
MP m,m0,t;
Z *w;
Z h;
if ( p1 ) {
for ( i = 0, m = BDY(p1); m; m = NEXT(m), i++ );
n1 = i;
} else
n1 = 0;
if ( p2 ) {
for ( i = 0, m = BDY(p2); m; m = NEXT(m), i++ );
n2 = i;
} else
n2 = 0;
n = n1+n2;
if ( !n ) {
*r1p = 0; *r2p = 0; *contp = ONE; return;
}
w = (Z *)ALLOCA(n*sizeof(Q));
v.len = n;
v.body = (pointer *)w;
i = 0;
if ( p1 )
for ( m = BDY(p1); i < n1; m = NEXT(m), i++ ) w[i] = (Z)m->c;
if ( p2 )
for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) w[i] = (Z)m->c;
h = w[0]; removecont_array((P *)w,n,1); divsz(h,w[0],contp);
i = 0;
if ( p1 ) {
for ( m0 = 0, t = BDY(p1); i < n1; i++, t = NEXT(t) ) {
NEXTMP(m0,m); m->c = (Obj)w[i]; m->dl = t->dl;
}
NEXT(m) = 0;
MKDP(p1->nv,m0,*r1p); (*r1p)->sugar = p1->sugar;
} else
*r1p = 0;
if ( p2 ) {
for ( m0 = 0, t = BDY(p2); i < n; i++, t = NEXT(t) ) {
NEXTMP(m0,m); m->c = (Obj)w[i]; m->dl = t->dl;
}
NEXT(m) = 0;
MKDP(p2->nv,m0,*r2p); (*r2p)->sugar = p2->sugar;
} else
*r2p = 0;
}
void dpm_removecont2(DPM p1,DPM p2,DPM *r1p,DPM *r2p,Z *contp)
{
struct oVECT v;
int i,n1,n2,n;
DMM m,m0,t;
Z *w;
Z h;
if ( p1 ) {
for ( i = 0, m = BDY(p1); m; m = NEXT(m), i++ );
n1 = i;
} else
n1 = 0;
if ( p2 ) {
for ( i = 0, m = BDY(p2); m; m = NEXT(m), i++ );
n2 = i;
} else
n2 = 0;
n = n1+n2;
if ( !n ) {
*r1p = 0; *r2p = 0; *contp = ONE; return;
}
w = (Z *)ALLOCA(n*sizeof(Q));
v.len = n;
v.body = (pointer *)w;
i = 0;
if ( p1 )
for ( m = BDY(p1); i < n1; m = NEXT(m), i++ ) w[i] = (Z)m->c;
if ( p2 )
for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) w[i] = (Z)m->c;
h = w[0]; removecont_array((P *)w,n,1); divsz(h,w[0],contp);
i = 0;
if ( p1 ) {
for ( m0 = 0, t = BDY(p1); i < n1; i++, t = NEXT(t) ) {
NEXTDMM(m0,m); m->c = (Obj)w[i]; m->dl = t->dl; m->pos = t->pos;
}
NEXT(m) = 0;
MKDPM(p1->nv,m0,*r1p); (*r1p)->sugar = p1->sugar;
} else
*r1p = 0;
if ( p2 ) {
for ( m0 = 0, t = BDY(p2); i < n; i++, t = NEXT(t) ) {
NEXTDMM(m0,m); m->c = (Obj)w[i]; m->dl = t->dl; m->pos = t->pos;
}
NEXT(m) = 0;
MKDPM(p2->nv,m0,*r2p); (*r2p)->sugar = p2->sugar;
} else
*r2p = 0;
}
/* true nf by a marked GB */
void dp_true_nf_marked(NODE b,DP g,DP *ps,DP *hps,DP *rp,P *nmp,P *dnp)
{
DP u,p,d,s,t,dmy,hp;
NODE l;
MP m,mr;
int i,n,hmag;
int *wb;
int sugar,psugar,multiple;
P nm,tnm1,dn,tdn,tdn1;
Z cont;
multiple = 0;
hmag = multiple*HMAG(g);
nm = (P)ONE;
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] = ZTOS((Z)BDY(l));
sugar = g->sugar;
for ( d = 0; g; ) {
for ( u = 0, i = 0; i < n; i++ ) {
if ( dp_redble(g,hp = hps[wb[i]]) ) {
p = ps[wb[i]];
dp_red_marked(d,g,p,hp,&t,&u,&tdn,&dmy);
psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
sugar = MAX(sugar,psugar);
if ( !u ) {
goto last;
} else {
d = t;
mulp(CO,dn,tdn,&tdn1); dn = tdn1;
}
break;
}
}
if ( u ) {
g = u;
if ( multiple && ((d && HMAG(d)>hmag) || (HMAG(g)>hmag)) ) {
dp_removecont2(d,g,&t,&u,&cont); d = t; g = u;
mulp(CO,nm,(P)cont,&tnm1); nm = tnm1;
if ( d )
hmag = multiple*HMAG(d);
else
hmag = multiple*HMAG(g);
}
} 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;
}
}
last:
if ( d ) {
dp_removecont2(d,0,&t,&u,&cont); d = t;
mulp(CO,nm,(P)cont,&tnm1); nm = tnm1;
d->sugar = sugar;
}
*rp = d; *nmp = nm; *dnp = dn;
}
void dp_true_nf_marked_mod(NODE b,DP g,DP *ps,DP *hps,int mod,DP *rp,P *dnp)
{
DP hp,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)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] = ZTOS((Q)BDY(l));
sugar = g->sugar;
for ( d = 0; g; ) {
for ( u = 0, i = 0; i < n; i++ ) {
if ( dp_redble(g,hp = hps[wb[i]]) ) {
p = ps[wb[i]];
dp_red_marked_mod(d,g,p,hp,mod,&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;
mulmp(CO,mod,dn,tdn,&tdn1); dn = tdn1;
}
break;
}
}
if ( u )
g = u;
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;
}
/* true nf by a marked GB and collect quotients */
DP *dp_true_nf_and_quotient_marked (NODE b,DP g,DP *ps,DP *hps,DP *rp,P *dnp)
{
DP u,p,d,s,t,dmy,hp,mult;
DP *q;
NODE l;
MP m,mr;
int i,n,j;
int *wb;
int sugar,psugar,multiple;
P nm,tnm1,dn,tdn,tdn1;
Q cont;
dn = (P)ONE;
if ( !g ) {
*rp = 0; *dnp = dn; return 0;
}
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] = ZTOS((Q)BDY(l));
q = (DP *)MALLOC(n*sizeof(DP));
for ( i = 0; i < n; i++ ) q[i] = 0;
sugar = g->sugar;
for ( d = 0; g; ) {
for ( u = 0, i = 0; i < n; i++ ) {
if ( dp_redble(g,hp = hps[wb[i]]) ) {
p = ps[wb[i]];
dp_red_marked(d,g,p,hp,&t,&u,&tdn,&mult);
psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
sugar = MAX(sugar,psugar);
for ( j = 0; j < n; j++ ) {
muldc(CO,q[j],(Obj)tdn,&dmy); q[j] = dmy;
}
addd(CO,q[wb[i]],mult,&dmy); q[wb[i]] = dmy;
mulp(CO,dn,tdn,&tdn1); dn = tdn1;
d = t;
if ( !u ) goto last;
break;
}
}
if ( u ) {
g = u;
} 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;
}
}
last:
if ( d ) d->sugar = sugar;
*rp = d; *dnp = dn;
return q;
}
struct oEGT egred;
void mulcmp(Obj c,MP m);
void mulcdmm(Obj c,DMM m);
DP appendd(DP d,DP m)
{
MP t;
if ( !d ) return m;
for ( t = BDY(d); NEXT(t); t = NEXT(t) );
NEXT(t) = BDY(m);
return d;
}
DPM appenddpm(DPM d,DPM m)
{
DMM t;
if ( !d ) return m;
for ( t = BDY(d); NEXT(t); t = NEXT(t) );
NEXT(t) = BDY(m);
return d;
}
DP *dpm_nf_and_quotient(NODE b,DPM g,VECT psv,DPM *rp,P *dnp)
{
DPM u,p,s,t,d;
DP dmy,mult,zzz;
DPM *ps;
DP *q;
NODE l;
DMM m,mr;
MP mp;
int i,n,j,len,nv;
int *wb;
int sugar,psugar,multiple;
P nm,tnm1,dn,tdn,tdn1;
Q cont;
struct oEGT eg0,eg1;
dn = (P)ONE;
if ( !g ) {
*rp = 0; *dnp = dn; return 0;
}
nv = NV(g);
ps = (DPM *)BDY(psv);
len = psv->len;
if ( b ) {
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] = ZTOS((Q)BDY(l));
} else {
wb = (int *)ALLOCA(len*sizeof(int));
for ( i = j = 0; i < len; i++ )
if ( ps[i] ) wb[j++] = i;
n = j;
}
q = (DP *)MALLOC(len*sizeof(DP));
for ( i = 0; i < len; i++ ) q[i] = 0;
sugar = g->sugar;
for ( d = 0; g; ) {
for ( u = 0, i = 0; i < n; i++ ) {
if ( dpm_redble(g,p = ps[wb[i]]) ) {
// get_eg(&eg0);
dpm_red2(g,p,&u,&tdn,&mult);
// get_eg(&eg1); add_eg(&egred,&eg0,&eg1);
psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
sugar = MAX(sugar,psugar);
for ( j = 0; j < len; j++ ) {
if ( q[j] ) { mulcmp((Obj)tdn,BDY(q[j])); }
}
q[wb[i]] = appendd(q[wb[i]],mult);
mulp(CO,dn,tdn,&tdn1); dn = tdn1;
if ( d ) mulcdmm((Obj)tdn,BDY(d));
if ( !u ) goto last;
break;
}
}
if ( u ) {
g = u;
} else {
m = BDY(g); NEWDMM(mr); mr->dl = m->dl; mr->c = m->c; mr->pos = m->pos;
NEXT(mr) = 0; MKDPM(g->nv,mr,t); t->sugar = mr->dl->td;
d = appenddpm(d,t);
dpm_rest(g,&t); g = t;
}
}
last:
if ( d ) d->sugar = sugar;
*rp = d; *dnp = dn;
return q;
}
DPM dpm_nf_and_quotient2(NODE b,DPM g,VECT psv,DPM *rp,P *dnp)
{
DPM u,p,s,t,d,q;
DP dmy,mult,zzz;
DPM *ps;
NODE l;
DMM mr0,mq0,mr,mq,m;
MP mp;
int i,n,j,len,nv;
int *wb;
int sugar,psugar,multiple;
P nm,tnm1,dn,tdn,tdn1;
Q cont;
Obj c1;
struct oEGT eg0,eg1;
dn = (P)ONE;
if ( !g ) {
*rp = 0; *dnp = dn; return 0;
}
nv = NV(g);
ps = (DPM *)BDY(psv);
len = psv->len;
if ( b ) {
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] = ZTOS((Q)BDY(l));
} else {
wb = (int *)ALLOCA(len*sizeof(int));
for ( i = j = 0; i < len; i++ )
if ( ps[i] ) wb[j++] = i;
n = j;
}
sugar = g->sugar;
mq0 = 0;
mr0 = 0;
for ( ; g; ) {
for ( u = 0, i = 0; i < n; i++ ) {
if ( dpm_redble(g,p = ps[wb[i]]) ) {
dpm_red2(g,p,&u,&tdn,&mult);
psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
sugar = MAX(sugar,psugar);
for ( m = mq0; m; m = NEXT(m) ) {
arf_mul(CO,(Obj)tdn,m->c,&c1); m->c = c1;
}
for ( m = mr0; m; m = NEXT(m) ) {
arf_mul(CO,(Obj)tdn,m->c,&c1); m->c = c1;
}
NEXTDMM(mq0,mq);
mq->c = BDY(mult)->c; mq->dl = BDY(mult)->dl; mq->pos = wb[i]+1;
mulp(CO,dn,tdn,&tdn1); dn = tdn1;
if ( !u ) goto last;
break;
}
}
if ( u ) {
g = u;
} else {
m = BDY(g);
NEXTDMM(mr0,mr);
mr->dl = m->dl; mr->c = m->c; mr->pos = m->pos;
dpm_rest(g,&t); g = t;
}
}
last:
if ( mr0 ) {
NEXT(mr) = 0;
MKDPM(nv,mr0,d); d->sugar = sugar;
} else
d = 0;
if ( mq0 ) {
NEXT(mq) = 0;
MKDPM(nv,mq0,q); q->sugar = sugar;
} else
q = 0;
*rp = d; *dnp = dn;
return q;
}
DPM dpm_nf_and_quotient3(DPM g,VECT psv,DPM *rp,P *dnp)
{
DPM u,p,s,t,d,q;
DP dmy,mult,zzz;
DPM *ps;
NODE2 nd;
DMM mr0,mq0,mr,mq,m;
MP mp;
int i,n,j,len,nv,pos,max;
int *wb;
int sugar,psugar,multiple;
P nm,tnm1,dn,tdn,tdn1;
Q cont;
Obj c1;
struct oEGT eg0,eg1;
dn = (P)ONE;
if ( !g ) {
*rp = 0; *dnp = dn; return 0;
}
nv = NV(g);
sugar = g->sugar;
mq0 = 0;
mr0 = 0;
max = psv->len;
for ( ; g; ) {
pos = BDY(g)->pos;
u = 0;
if ( pos < max ) {
nd = (NODE2)BDY(psv)[pos];
for ( u = 0; nd; nd = NEXT(nd) ) {
if ( dpm_redble(g,p = (DPM)(nd->body1)) ) {
dpm_red2(g,p,&u,&tdn,&mult);
psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
sugar = MAX(sugar,psugar);
if ( !UNIZ(tdn) ) {
for ( m = mq0; m; m = NEXT(m) ) {
arf_mul(CO,(Obj)tdn,m->c,&c1); m->c = c1;
}
for ( m = mr0; m; m = NEXT(m) ) {
arf_mul(CO,(Obj)tdn,m->c,&c1); m->c = c1;
}
}
NEXTDMM(mq0,mq);
mq->c = BDY(mult)->c; mq->dl = BDY(mult)->dl; mq->pos = (long)nd->body2;
mulp(CO,dn,tdn,&tdn1); dn = tdn1;
if ( !u ) goto last;
break;
}
}
}
if ( u ) {
g = u;
} else {
m = BDY(g);
NEXTDMM(mr0,mr);
mr->dl = m->dl; mr->c = m->c; mr->pos = m->pos;
dpm_rest(g,&t); g = t;
}
}
last:
if ( mr0 ) {
NEXT(mr) = 0;
MKDPM(nv,mr0,d); d->sugar = sugar;
} else
d = 0;
if ( mq0 ) {
NEXT(mq) = 0;
MKDPM(nv,mq0,q); q->sugar = sugar;
} else
q = 0;
*rp = d; *dnp = dn;
return q;
}
DPM dpm_nf_and_quotient4(DPM g,DPM *ps,VECT psiv,DPM head,DPM *rp,P *dnp)
{
DPM u,p,s,t,d,q;
DP dmy,mult,zzz;
NODE nd;
DMM mr0,mq0,mr,mq,m;
MP mp;
int i,n,j,len,nv,pos,max;
int *wb;
int sugar,psugar,multiple;
P nm,tnm1,dn,tdn,tdn1,c;
Q cont;
Obj c1;
struct oEGT eg0,eg1;
dn = (P)ONE;
if ( !g ) {
*rp = 0; *dnp = dn; return 0;
}
nv = NV(g);
sugar = g->sugar;
mq0 = 0;
if ( head ) {
for ( m = BDY(head); m; m = NEXT(m) ) {
NEXTDMM(mq0,mq);
mq->c = m->c; mq->dl = m->dl; mq->pos = m->pos;
}
}
mr0 = 0;
max = psiv->len;
for ( ; g; ) {
pos = BDY(g)->pos;
u = 0;
if ( pos < max ) {
nd = (NODE)BDY(psiv)[pos];
for ( u = 0; nd; nd = NEXT(nd) ) {
if ( dpm_redble(g,p = ps[(long)(BDY(nd))-1]) ) {
dpm_red2(g,p,&u,&tdn,&mult);
psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
sugar = MAX(sugar,psugar);
if ( !UNIZ(tdn) ) {
for ( m = mq0; m; m = NEXT(m) ) {
arf_mul(CO,(Obj)tdn,m->c,&c1); m->c = c1;
}
for ( m = mr0; m; m = NEXT(m) ) {
arf_mul(CO,(Obj)tdn,m->c,&c1); m->c = c1;
}
}
NEXTDMM(mq0,mq);
mq->c = BDY(mult)->c;
mq->dl = BDY(mult)->dl; mq->pos = (long)BDY(nd);
mulp(CO,dn,tdn,&tdn1); dn = tdn1;
if ( !u ) goto last;
break;
}
}
}
if ( u ) {
g = u;
} else {
m = BDY(g);
NEXTDMM(mr0,mr);
mr->dl = m->dl; mr->c = m->c; mr->pos = m->pos;
dpm_rest(g,&t); g = t;
}
}
last:
if ( mr0 ) {
NEXT(mr) = 0;
MKDPM(nv,mr0,d); d->sugar = sugar;
} else
d = 0;
if ( mq0 ) {
NEXT(mq) = 0;
MKDPM(nv,mq0,q); q->sugar = sugar;
} else
q = 0;
*rp = d; *dnp = dn;
return q;
}
/* an intermediate version for calling from the user language */
/* XXX : i, j must be positive */
DPM dpm_sp_nf_asir(VECT psv,int i,int j,DPM *nf)
{
DPM *ps;
int n,k,nv,s1,s2,sugar,max,pos,psugar;
DPM g,u,p,d,q,t;
DMM mq0,mq,mr0,mr,m;
DP mult,t1,t2;
P dn,tdn,tdn1;
NODE nd;
Obj c1;
ps = (DPM *)BDY(psv);
n = psv->len;
nv = ps[1]->nv;
dpm_sp(ps[i],ps[j],&g,&t1,&t2);
mq0 = 0;
NEXTDMM(mq0,mq); mq->c = BDY(t1)->c; mq->pos = i; mq->dl = BDY(t1)->dl;
NEXTDMM(mq0,mq); chsgnp((P)BDY(t2)->c,(P *)&mq->c); mq->pos = j; mq->dl = BDY(t2)->dl;
if ( !g ) {
NEXT(mq) = 0;
MKDPM(nv,mq0,d);
s1 = BDY(t1)->dl->td + ps[i]->sugar;
s2 = BDY(t2)->dl->td + ps[j]->sugar;
d->sugar = MAX(s1,s2);
*nf = 0;
return d;
}
dn = (P)ONE;
sugar = g->sugar;
mr0 = 0;
while ( g ) {
pos = BDY(g)->pos;
for ( u = 0, k = 1; k < n; k++ ) {
if ( (p=ps[k])!=0 && pos == BDY(p)->pos && dpm_redble(g,p) ) {
dpm_red2(g,p,&u,&tdn,&mult);
psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
sugar = MAX(sugar,psugar);
if ( !UNIZ(tdn) ) {
for ( m = mq0; m; m = NEXT(m) ) {
arf_mul(CO,(Obj)tdn,m->c,&c1); m->c = c1;
}
for ( m = mr0; m; m = NEXT(m) ) {
arf_mul(CO,(Obj)tdn,m->c,&c1); m->c = c1;
}
}
NEXTDMM(mq0,mq);
chsgnp((P)BDY(mult)->c,(P *)&mq->c);
mq->dl = BDY(mult)->dl; mq->pos = k;
mulp(CO,dn,tdn,&tdn1); dn = tdn1;
if ( !u ) goto last;
break;
}
}
if ( u ) {
g = u;
} else {
m = BDY(g);
NEXTDMM(mr0,mr);
mr->dl = m->dl; mr->c = m->c; mr->pos = m->pos;
dpm_rest(g,&t); g = t;
}
}
last:
if ( mr0 ) {
NEXT(mr) = 0; MKDPM(nv,mr0,d); d->sugar = sugar;
} else
d = 0;
NEXT(mq) = 0; MKDPM(nv,mq0,q); q->sugar = sugar;
*nf = d;
return q;
}
DPM dpm_sp_nf(VECT psv,VECT psiv,int i,int j,DPM *nf)
{
DPM *ps;
int n,nv,s1,s2,sugar,max,pos,psugar;
DPM g,u,p,d,q,t;
DMM mq0,mq,mr0,mr,m;
DP mult,t1,t2;
P dn,tdn,tdn1;
NODE nd;
Obj c1;
ps = (DPM *)BDY(psv);
n = psv->len;
nv = ps[i]->nv;
dpm_sp(ps[i],ps[j],&g,&t1,&t2);
mq0 = 0;
NEXTDMM(mq0,mq); mq->c = BDY(t1)->c; mq->pos = i; mq->dl = BDY(t1)->dl;
NEXTDMM(mq0,mq); chsgnp((P)BDY(t2)->c,(P *)&mq->c); mq->pos = j; mq->dl = BDY(t2)->dl;
if ( !g ) {
NEXT(mq) = 0;
MKDPM(nv,mq0,d);
s1 = BDY(t1)->dl->td + ps[i]->sugar;
s2 = BDY(t2)->dl->td + ps[j]->sugar;
d->sugar = MAX(s1,s2);
*nf = 0;
return d;
}
dn = (P)ONE;
sugar = g->sugar;
mr0 = 0;
max = psiv->len;
while ( g ) {
pos = BDY(g)->pos;
u = 0;
if ( pos < max ) {
nd = (NODE)BDY(psiv)[pos];
for ( u = 0; nd; nd = NEXT(nd) ) {
if ( dpm_redble(g,p = ps[(long)(BDY(nd))]) ) {
dpm_red2(g,p,&u,&tdn,&mult);
psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
sugar = MAX(sugar,psugar);
if ( !UNIZ(tdn) ) {
for ( m = mq0; m; m = NEXT(m) ) {
arf_mul(CO,(Obj)tdn,m->c,&c1); m->c = c1;
}
for ( m = mr0; m; m = NEXT(m) ) {
arf_mul(CO,(Obj)tdn,m->c,&c1); m->c = c1;
}
}
NEXTDMM(mq0,mq);
chsgnp((P)BDY(mult)->c,(P *)&mq->c);
mq->dl = BDY(mult)->dl; mq->pos = (long)BDY(nd);
mulp(CO,dn,tdn,&tdn1); dn = tdn1;
if ( !u ) goto last;
break;
}
}
}
if ( u ) {
g = u;
} else {
m = BDY(g);
NEXTDMM(mr0,mr);
mr->dl = m->dl; mr->c = m->c; mr->pos = m->pos;
dpm_rest(g,&t); g = t;
}
}
last:
if ( mr0 ) {
NEXT(mr) = 0; MKDPM(nv,mr0,d); d->sugar = sugar;
} else
d = 0;
NEXT(mq) = 0; MKDPM(nv,mq0,q); q->sugar = sugar;
*nf = d;
return q;
}
/* psiv is a vector of lists of Z */
DPM dpm_sp_nf_zlist(VECT psv,VECT psiv,int i,int j,int top,DPM *nf)
{
DPM *ps;
int n,nv,s1,s2,sugar,max,pos,psugar;
DPM g,u,p,d,q,t;
DMM mq0,mq,mr0,mr,m;
DP mult,t1,t2;
P dn,tdn,tdn1;
NODE nd;
Obj c1;
ps = (DPM *)BDY(psv);
n = psv->len;
nv = ps[i]->nv;
dpm_sp(ps[i],ps[j],&g,&t1,&t2);
mq0 = 0;
NEXTDMM(mq0,mq); mq->c = BDY(t1)->c; mq->pos = i; mq->dl = BDY(t1)->dl;
NEXTDMM(mq0,mq); chsgnp((P)BDY(t2)->c,(P *)&mq->c); mq->pos = j; mq->dl = BDY(t2)->dl;
if ( !g ) {
NEXT(mq) = 0;
MKDPM(nv,mq0,d);
s1 = BDY(t1)->dl->td + ps[i]->sugar;
s2 = BDY(t2)->dl->td + ps[j]->sugar;
d->sugar = MAX(s1,s2);
*nf = 0;
return d;
}
dn = (P)ONE;
sugar = g->sugar;
mr0 = 0;
max = psiv->len;
while ( g ) {
pos = BDY(g)->pos;
u = 0;
if ( pos < max ) {
nd = BDY((LIST)BDY(psiv)[pos]);
for ( u = 0; nd; nd = NEXT(nd) ) {
if ( dpm_redble(g,p = ps[ZTOS((Q)BDY(nd))]) ) {
dpm_red2(g,p,&u,&tdn,&mult);
psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
sugar = MAX(sugar,psugar);
if ( !UNIZ(tdn) ) {
for ( m = mq0; m; m = NEXT(m) ) {
arf_mul(CO,(Obj)tdn,m->c,&c1); m->c = c1;
}
for ( m = mr0; m; m = NEXT(m) ) {
arf_mul(CO,(Obj)tdn,m->c,&c1); m->c = c1;
}
}
NEXTDMM(mq0,mq);
chsgnp((P)BDY(mult)->c,(P *)&mq->c);
mq->dl = BDY(mult)->dl; mq->pos = ZTOS((Q)BDY(nd));
mulp(CO,dn,tdn,&tdn1); dn = tdn1;
if ( !u ) goto last;
break;
}
}
}
if ( u ) {
g = u;
} else if ( !top ) {
m = BDY(g);
NEXTDMM(mr0,mr);
mr->dl = m->dl; mr->c = m->c; mr->pos = m->pos;
dpm_rest(g,&t); g = t;
} else {
*nf = g;
if ( mq0 ) {
NEXT(mq) = 0; MKDPM(nv,mq0,q); q->sugar = sugar;
} else
q = 0;
return q;
}
}
last:
if ( mr0 ) {
NEXT(mr) = 0; MKDPM(nv,mr0,d); d->sugar = sugar;
} else
d = 0;
NEXT(mq) = 0; MKDPM(nv,mq0,q); q->sugar = sugar;
*nf = d;
return q;
}
DP *dp_true_nf_and_quotient_marked_mod(NODE b,DP g,DP *ps,DP *hps,int mod,DP *rp,P *dnp)
{
DP u,p,d,s,t,dmy,hp,mult;
DP *q;
NODE l;
MP m,mr;
int i,n,j;
int *wb;
int sugar,psugar;
P dn,tdn,tdn1;
for ( n = 0, l = b; l; l = NEXT(l), n++ );
q = (DP *)MALLOC(n*sizeof(DP));
for ( i = 0; i < n; i++ ) q[i] = 0;
dn = (P)ONEM;
if ( !g ) {
*rp = 0; *dnp = dn; return 0;
}
wb = (int *)ALLOCA(n*sizeof(int));
for ( i = 0, l = b; i < n; l = NEXT(l), i++ )
wb[i] = ZTOS((Q)BDY(l));
sugar = g->sugar;
for ( d = 0; g; ) {
for ( u = 0, i = 0; i < n; i++ ) {
if ( dp_redble(g,hp = hps[wb[i]]) ) {
p = ps[wb[i]];
dp_red_marked_mod(d,g,p,hp,mod,&t,&u,&tdn,&mult);
psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
sugar = MAX(sugar,psugar);
for ( j = 0; j < n; j++ ) {
mulmdc(CO,mod,q[j],(P)tdn,&dmy); q[j] = dmy;
}
addmd(CO,mod,q[wb[i]],mult,&dmy); q[wb[i]] = dmy;
mulmp(CO,mod,dn,tdn,&tdn1); dn = tdn1;
d = t;
if ( !u ) goto last;
break;
}
}
if ( u )
g = u;
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;
}
}
last:
if ( d )
d->sugar = sugar;
*rp = d; *dnp = dn;
return q;
}
/* 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] = ZTOS((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 dpm_nf_z(NODE b,DPM g,VECT psv,int full,int multiple,DPM *rp)
{
DPM *ps;
DPM u,p,d,s,t;
DP dmy1;
P dmy;
Z cont;
NODE l;
DMM m,mr;
int i,n;
int *wb;
int hmag;
int sugar,psugar;
if ( !g ) {
*rp = 0; return;
}
if ( b ) {
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] = ZTOS((Q)BDY(l));
ps = (DPM *)BDY(psv);
} else {
n = psv->len;
wb = (int *)MALLOC(n*sizeof(int));
for ( i = 0; i < n; i++ ) wb[i] = i;
ps = (DPM *)BDY(psv);
}
hmag = multiple*HMAG(g);
sugar = g->sugar;
for ( d = 0; g; ) {
for ( u = 0, i = 0; i < n; i++ ) {
if ( (p=ps[wb[i]])!=0 && dpm_redble(g,p) ) {
dpm_red2(g,p,&u,&dmy,&dmy1);
psugar = (BDY(g)->dl->td - BDY(p)->dl->td) + p->sugar;
sugar = MAX(sugar,psugar);
if ( d ) mulcdmm((Obj)dmy,BDY(d));
if ( !u ) {
if ( d )
d->sugar = sugar;
*rp = d; return;
}
break;
}
}
if ( u ) {
g = u;
if ( d ) {
if ( multiple && HMAG(d) > hmag ) {
dpm_ptozp2(d,g,&t,&u); d = t; g = u;
hmag = multiple*HMAG(d);
}
} else {
if ( multiple && HMAG(g) > hmag ) {
dpm_ptozp(g,&cont,&t); g = t;
hmag = multiple*HMAG(g);
}
}
}
else if ( !full ) {
if ( g ) {
MKDPM(g->nv,BDY(g),t); t->sugar = sugar; g = t;
}
*rp = g; return;
} else {
m = BDY(g); NEWDMM(mr); mr->dl = m->dl; mr->c = m->c; mr->pos = m->pos;
NEXT(mr) = 0; MKDPM(g->nv,mr,t); t->sugar = mr->dl->td;
d = appenddpm(d,t);
dpm_rest(g,&t); g = t;
}
}
if ( d )
d->sugar = sugar;
*rp = d;
}
void dpm_shift(DPM p,int s,DPM *r)
{
DMM m,mr0,mr;
DPM t;
if ( !p ) *r = 0;
else {
for ( m = BDY(p), mr0 = 0; m; m = NEXT(m) ) {
NEXTDMM(mr0,mr);
mr->dl = m->dl; mr->c = m->c; mr->pos = m->pos-s;
if ( mr->pos <= 0 )
error("dpm_shift : too large shift value");
}
NEXT(mr) = 0;
MKDPM(p->nv,mr0,t); t->sugar = p->sugar;
*r = t;
}
}
// up=sum{c*<<...:i>>|i<=s}, lo=sum{c*<<...:i>>|i>s}
void dpm_split(DPM p,int s,DPM *up,DPM *lo)
{
DMM m,mu0,mu,ml0,ml;
DPM t;
if ( !p ) {
*up = 0; *lo = 0;
} else {
for ( m = BDY(p), mu0 = ml0 = 0; m; m = NEXT(m) ) {
if ( m->pos <= s ) {
NEXTDMM(mu0,mu);
mu->dl = m->dl; mu->c = m->c; mu->pos = m->pos;
} else {
NEXTDMM(ml0,ml);
ml->dl = m->dl; ml->c = m->c; ml->pos = m->pos;
}
}
if ( mu0 ) {
NEXT(mu) = 0; MKDPM(p->nv,mu0,t); t->sugar = p->sugar;
*up = t;
} else
*up = 0;
if ( ml0 ) {
NEXT(ml) = 0; MKDPM(p->nv,ml0,t); t->sugar = p->sugar;
*lo = t;
} else
*lo = 0;
}
}
/* extract the component in DP of position s */
void dpm_extract(DPM p,int s,DP *r)
{
DMM m;
MP mu0,mu;
DP t;
if ( !p ) {
*r = 0; return;
}
for ( m = BDY(p), mu0 = 0; m; m = NEXT(m) ) {
if ( m->pos == s ) {
NEXTMP(mu0,mu);
mu->dl = m->dl; mu->c = m->c;
}
}
if ( mu0 ) {
NEXT(mu) = 0; MKDP(p->nv,mu0,t); t->sugar = p->sugar;
*r = t;
} else
*r = 0;
}
/* 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] = ZTOS((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;
}
void dpm_nf_f(NODE b,DPM g,VECT psv,int full,DPM *rp)
{
DPM *ps;
DPM u,p,d,s,t;
NODE l;
DMM m,mr;
int i,n;
int *wb;
int sugar,psugar;
if ( !g ) {
*rp = 0; return;
}
if ( b ) {
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] = ZTOS((Q)BDY(l));
ps = (DPM *)BDY(psv);
} else {
n = psv->len;
wb = (int *)MALLOC(n*sizeof(int));
for ( i = 0; i < n; i++ ) wb[i] = i;
ps = (DPM *)BDY(psv);
}
sugar = g->sugar;
for ( d = 0; g; ) {
for ( u = 0, i = 0; i < n; i++ ) {
if ( ( (p=ps[wb[i]]) != 0 ) && dpm_redble(g,p) ) {
dpm_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 ) {
MKDPM(g->nv,BDY(g),t); t->sugar = sugar; g = t;
}
*rp = g; return;
} else {
m = BDY(g); NEWDMM(mr); mr->dl = m->dl; mr->c = m->c; mr->pos = m->pos;
NEXT(mr) = 0; MKDPM(g->nv,mr,t); t->sugar = mr->dl->td;
adddpm(CO,d,t,&s); d = s;
dpm_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[(long)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] = ZTOS((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[(long)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,(Obj)c,&t); addd(CO,r1,t,&s); r1 = s;
muldc(CO,b2,(Obj)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]))),(P)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
* call create_order_spec with vl=0 to set old type order.
*
*/
int create_order_spec(VL vl,Obj obj,struct order_spec **specp)
{
int i,j,n,s,row,col,ret,wlen;
struct order_spec *spec;
struct order_pair *l;
Obj wp,wm;
NODE node,t,tn,wpair;
MAT m;
VECT v;
pointer **b,*bv;
int **w;
if ( vl && obj && OID(obj) == O_LIST ) {
ret = create_composite_order_spec(vl,(LIST)obj,specp);
if ( show_orderspec )
print_composite_order_spec(*specp);
return ret;
}
*specp = spec = (struct order_spec *)MALLOC(sizeof(struct order_spec));
if ( !obj || NUM(obj) ) {
spec->id = 0; spec->obj = obj;
spec->ord.simple = ZTOS((Q)obj);
return 1;
} else if ( OID(obj) == O_LIST ) {
/* module order */
node = BDY((LIST)obj);
if ( !BDY(node) || NUM(BDY(node)) ) {
switch ( length(node) ) {
case 2: /* [n,ord] */
create_order_spec(0,(Obj)BDY(NEXT(node)),&spec);
spec->id += 256; spec->obj = obj;
spec->top_weight = 0;
spec->module_rank = 0;
spec->module_top_weight = 0;
spec->module_ordtype = ZTOS((Z)BDY(node));
if ( spec->module_ordtype < 0 ) {
spec->pot_nelim = -spec->module_ordtype;
spec->module_ordtype = 1;
} else
spec->pot_nelim = 0;
break;
case 3: /* [n,[mlist1,mlist2,...],ord] or [n,[wv,wm],ord] */
spec->module_ordtype = ZTOS((Z)BDY(node));
if ( spec->module_ordtype < 0 ) {
spec->pot_nelim = -spec->module_ordtype;
spec->module_ordtype = 1;
} else
spec->pot_nelim = 0;
if ( spec->module_ordtype == 3 ) { /* schreyer order */
Obj baseobj;
struct order_spec *basespec;
int len;
NODE in;
LIST *la;
DMMstack stack;
DMMstack push_schreyer_order(LIST l,DMMstack s);
spec->id = 300; spec->obj = obj;
node = NEXT(node);
if ( !BDY(node) || OID(BDY(node)) != O_LIST )
error("create_order_spec : [mlist1,mlist,...] must be specified for defining a schreyer order");
stack = 0;
in = BDY((LIST)BDY(node));
len = length(in);
la = (LIST *)MALLOC(len*sizeof(LIST));
for ( i = 0; i < len; i++, in = NEXT(in) ) la[i] = (LIST)(BDY(in));
for ( i = len-1; i >= 0; i-- ) stack = push_schreyer_order(la[i],stack);
spec->dmmstack = stack;
node = NEXT(node);
baseobj = (Obj)BDY(node);
create_order_spec(0,baseobj,&basespec);
basespec->obj = baseobj;
spec->base = basespec;
} else if ( spec->module_ordtype == 4 ) { /* POT with base order [n,bord,ord] */
NODE base_ord;
int rank;
create_order_spec(0,(Obj)BDY(NEXT(NEXT(node))),&spec);
spec->id += 256; spec->obj = obj;
spec->top_weight = 0;
spec->module_rank = 0;
spec->module_top_weight = 0;
spec->pot_nelim = 0;
spec->module_ordtype = 4;
node = NEXT(node);
if ( !BDY(node) || OID(BDY(node)) != O_LIST )
error("create_order_spec : a permitation list must be specified");
base_ord = BDY((LIST)BDY(node));
spec->module_rank = rank = length(base_ord);
spec->module_base_ord = (int *)MALLOC_ATOMIC((rank+1)*sizeof(int));
for ( i = 1, t = base_ord; i <= rank; i++, t = NEXT(t) )
spec->module_base_ord[ZTOS((Q)BDY(t))] = i;
break;
} else { /* weighted order * [n,[wv,wm],ord] */
int ordtype;
ordtype = spec->module_ordtype;
create_order_spec(0,(Obj)BDY(NEXT(NEXT(node))),&spec);
spec->module_ordtype = ordtype;
spec->id += 256; spec->obj = obj;
node = NEXT(node);
if ( !BDY(node) || OID(BDY(node)) != O_LIST )
error("create_order_spec : [weight_for_poly,weight_for_modlue] must be specified as a module topweight");
wpair = BDY((LIST)BDY(node));
if ( length(wpair) != 2 )
error("create_order_spec : [weight_for_poly,weight_for_modlue] must be specified as a module topweight");
wp = BDY(wpair);
wm = BDY(NEXT(wpair));
if ( !wp || OID(wp) != O_LIST || !wm || OID(wm) != O_LIST )
error("create_order_spec : [weight_for_poly,weight_for_modlue] must be specified as a module topweight");
spec->nv = length(BDY((LIST)wp));
spec->top_weight = (int *)MALLOC_ATOMIC(spec->nv*sizeof(int));
for ( i = 0, t = BDY((LIST)wp); i < spec->nv; t = NEXT(t), i++ )
spec->top_weight[i] = ZTOS((Q)BDY(t));
spec->module_rank = length(BDY((LIST)wm));
spec->module_top_weight = (int *)MALLOC_ATOMIC(spec->module_rank*sizeof(int));
for ( i = 0, t = BDY((LIST)wm); i < spec->module_rank; t = NEXT(t), i++ )
spec->module_top_weight[i] = ZTOS((Q)BDY(t));
}
break;
default:
error("create_order_spec : invalid arguments for module order");
}
*specp = spec;
return 1;
} else {
/* block order in polynomial ring */
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 = ZTOS((Q)BDY(tn));
tn = NEXT(tn); l[i].length = ZTOS((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] = ZTOS((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");
}
}
struct order_spec *append_block(struct order_spec *spec,
int nv,int nalg,int ord)
{
MAT m,mat;
int i,j,row,col,n;
Z **b,**wp;
int **w;
NODE t,s,s0;
struct order_pair *l,*l0;
int n0,nv0;
LIST list0,list1,list;
Z oq,nq;
struct order_spec *r;
r = (struct order_spec *)MALLOC(sizeof(struct order_spec));
switch ( spec->id ) {
case 0:
STOZ(spec->ord.simple,oq); STOZ(nv,nq);
t = mknode(2,oq,nq); MKLIST(list0,t);
STOZ(ord,oq); STOZ(nalg,nq);
t = mknode(2,oq,nq); MKLIST(list1,t);
t = mknode(2,list0,list1); MKLIST(list,t);
l = (struct order_pair *)MALLOC_ATOMIC(2*sizeof(struct order_pair));
l[0].order = spec->ord.simple; l[0].length = nv;
l[1].order = ord; l[1].length = nalg;
r->id = 1; r->obj = (Obj)list;
r->ord.block.order_pair = l;
r->ord.block.length = 2;
r->nv = nv+nalg;
break;
case 1:
if ( spec->nv != nv )
error("append_block : number of variables mismatch");
l0 = spec->ord.block.order_pair;
n0 = spec->ord.block.length;
nv0 = spec->nv;
list0 = (LIST)spec->obj;
n = n0+1;
l = (struct order_pair *)MALLOC_ATOMIC(n*sizeof(struct order_pair));
for ( i = 0; i < n0; i++ )
l[i] = l0[i];
l[i].order = ord; l[i].length = nalg;
for ( t = BDY(list0), s0 = 0; t; t = NEXT(t) ) {
NEXTNODE(s0,s); BDY(s) = BDY(t);
}
STOZ(ord,oq); STOZ(nalg,nq);
t = mknode(2,oq,nq); MKLIST(list,t);
NEXTNODE(s0,s); BDY(s) = (pointer)list; NEXT(s) = 0;
MKLIST(list,s0);
r->id = 1; r->obj = (Obj)list;
r->ord.block.order_pair = l;
r->ord.block.length = n;
r->nv = nv+nalg;
break;
case 2:
if ( spec->nv != nv )
error("append_block : number of variables mismatch");
m = (MAT)spec->obj;
row = m->row; col = m->col; b = (Z **)BDY(m);
w = almat(row+nalg,col+nalg);
MKMAT(mat,row+nalg,col+nalg); wp = (Z **)BDY(mat);
for ( i = 0; i < row; i++ )
for ( j = 0; j < col; j++ ) {
w[i][j] = ZTOS(b[i][j]);
wp[i][j] = b[i][j];
}
for ( i = 0; i < nalg; i++ ) {
w[i+row][i+col] = 1;
wp[i+row][i+col] = ONE;
}
r->id = 2; r->obj = (Obj)mat;
r->nv = col+nalg; r->ord.matrix.row = row+nalg;
r->ord.matrix.matrix = w;
break;
case 3:
default:
/* XXX */
error("append_block : not implemented yet");
}
return r;
}
int comp_sw(struct sparse_weight *a, struct sparse_weight *b)
{
if ( a->pos > b->pos ) return 1;
else if ( a->pos < b->pos ) return -1;
else return 0;
}
/* 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,start,end,len,w;
int *dw;
struct sparse_weight *sw;
struct weight_or_block *w_or_b;
Obj a0;
NODE a;
V v,sv,ev;
SYMBOL sym;
int *top;
/* 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+1));
/* top : register the top variable in each w_or_b specification */
top = (int *)ALLOCA(l*sizeof(int));
for ( i = 0; i < l; i++ ) top[i] = 0;
for ( t = wb, i = 0; t; t = NEXT(t), i++ ) {
if ( !BDY(t) || OID((Obj)BDY(t)) != O_LIST )
error("a list of lists must be specified for the key \"order\"");
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++ ) {
if ( !INT((Q)BDY(p)) )
error("a dense weight vector must be specified as a list of integers");
dw[j] = ZTOS((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;
/* find the top */
for ( k = 0; k < len && !dw[k]; k++ );
if ( k < len ) top[k] = 1;
} 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++ ) {
if ( !BDY(p) || OID((P)BDY(p)) != O_P )
error("a sparse weight vector must be specified as [var1,weight1,...]");
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 in a sparse weight vector");
sw[j].pos = k;
if ( !INT((Q)BDY(p)) )
error("a sparse weight vector must be specified as [var1,weight1,...]");
sw[j].value = ZTOS((Q)BDY(p)); p = NEXT(p);
}
qsort(sw,len,sizeof(struct sparse_weight),
(int (*)(const void *,const void *))comp_sw);
w_or_b[i].type = IS_SPARSE_WEIGHT;
w_or_b[i].length = len;
w_or_b[i].body.sparse_weight = sw;
/* find the top */
for ( k = 0; k < len && !sw[k].value; k++ );
if ( k < len ) top[sw[k].pos] = 1;
} else if ( OID(a0) == O_RANGE ) {
/* [range(v1,v2),w] */
sv = VR((P)(((RANGE)a0)->start));
ev = VR((P)(((RANGE)a0)->end));
for ( tvl = vl, start = 0; tvl && tvl->v != sv; start++, tvl = NEXT(tvl) );
if ( !tvl )
error("invalid range");
for ( end = start; tvl && tvl->v != ev; end++, tvl = NEXT(tvl) );
if ( !tvl )
error("invalid range");
len = end-start+1;
sw = (struct sparse_weight *)
MALLOC(sizeof(struct sparse_weight)*len);
w = ZTOS((Q)BDY(NEXT(a)));
for ( tvl = vl, k = 0; k < start; k++, tvl = NEXT(tvl) );
for ( j = 0 ; k <= end; k++, tvl = NEXT(tvl), j++ ) {
sw[j].pos = k;
sw[j].value = w;
}
w_or_b[i].type = IS_SPARSE_WEIGHT;
w_or_b[i].length = len;
w_or_b[i].body.sparse_weight = sw;
/* register the top */
if ( w ) top[start] = 1;
} else if ( OID(a0) == O_SYMBOL ) {
/* a is a block */
sym = (SYMBOL)a0; a = NEXT(a); len--;
if ( OID((Obj)BDY(a)) == O_RANGE ) {
sv = VR((P)(((RANGE)BDY(a))->start));
ev = VR((P)(((RANGE)BDY(a))->end));
for ( tvl = vl, start = 0; tvl && tvl->v != sv; start++, tvl = NEXT(tvl) );
if ( !tvl )
error("invalid range");
for ( end = start; tvl && tvl->v != ev; end++, tvl = NEXT(tvl) );
if ( !tvl )
error("invalid range");
len = end-start+1;
} else {
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 ( !BDY(p) || OID((P)BDY(p)) != O_P )
error("a block must be specified as [ordsymbol,var1,var2,...]");
if ( tvl->v != VR((P)BDY(p)) ) break;
}
if ( p )
error("a block must be contiguous in the variable list");
}
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 ordername");
/* register the tops */
for ( j = 0, k = start; j < len; j++, k++ )
top[k] = 1;
}
}
for ( k = 0; k < l && top[k]; k++ );
if ( k < l ) {
/* incomplete order specification; add @grlex */
w_or_b[n].type = IS_BLOCK;
w_or_b[n].length = l;
w_or_b[n].body.block.start = 0;
w_or_b[n].body.block.order = 0;
spec->ord.composite.length = n+1;
}
return 1;
}
/* module order spec */
void create_modorder_spec(int id,LIST shift,struct modorder_spec **s)
{
struct modorder_spec *spec;
NODE n,t;
LIST list;
int *ds;
int i,l;
Z q;
*s = spec = (struct modorder_spec *)MALLOC(sizeof(struct modorder_spec));
spec->id = id;
if ( shift ) {
n = BDY(shift);
spec->len = l = length(n);
spec->degree_shift = ds = (int *)MALLOC_ATOMIC(l*sizeof(int));
for ( t = n, i = 0; t; t = NEXT(t), i++ )
ds[i] = ZTOS((Q)BDY(t));
} else {
spec->len = 0;
spec->degree_shift = 0;
}
STOZ(id,q);
n = mknode(2,q,shift);
MKLIST(list,n);
spec->obj = (Obj)list;
}
/*
* converters
*
*/
void dpm_homo(DPM p,DPM *rp)
{
DMM m,mr,mr0,t;
int i,n,nv,td;
DL dl,dlh;
if ( !p )
*rp = 0;
else {
n = p->nv; nv = n + 1;
m = BDY(p);
td = 0;
for ( t = m; t; t = NEXT(t) )
if ( m->dl->td > td ) td = m->dl->td;
for ( mr0 = 0; m; m = NEXT(m) ) {
NEXTDMM(mr0,mr); mr->c = m->c; mr->pos = m->pos;
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; MKDPM(nv,mr0,*rp); (*rp)->sugar = p->sugar;
}
}
void dpm_dehomo(DPM p,DPM *rp)
{
DMM 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) ) {
NEXTDMM(mr0,mr); mr->c = m->c; mr->pos = m->pos;
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; MKDPM(nv,mr0,*rp); (*rp)->sugar = p->sugar;
}
}
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 = (P)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 = (Obj)t; mr->dl = m->dl;
}
}
if ( mr0 ) {
NEXT(mr) = 0; MKDP(p->nv,mr0,*rp); (*rp)->sugar = p->sugar;
} else
*rp = 0;
}
}
void dpm_mod(DPM p,int mod,DPM *rp)
{
DMM m,mr,mr0;
P t;
V v;
NODE tn;
if ( !p )
*rp = 0;
else {
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
ptomp(mod,(P)m->c,&t);
if ( t ) {
NEXTDMM(mr0,mr); mr->c = (Obj)t; mr->dl = m->dl;
}
}
if ( mr0 ) {
NEXT(mr) = 0; MKDPM(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((P)m->c,(P *)&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;
int onv,nnv,nlen,olen,owlen;
struct weight_or_block *owb,*nwb;
*newp = new = (struct order_spec *)MALLOC(sizeof(struct order_spec));
bcopy((char *)old,(char *)new,sizeof(struct order_spec));
switch ( old->id ) {
case 0:
switch ( old->ord.simple ) {
case 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->ord.simple = 1; break;
case 3: case 4: case 5:
new->ord.simple = old->ord.simple+3;
dp_nelim = n-1; break;
case 6: case 7: case 8: case 9:
break;
default:
error("homogenize_order : invalid input");
}
break;
case 1: case 257:
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->nv = n+1;
new->ord.block.order_pair = l;
new->ord.block.length = length+1;
break;
case 2: case 258:
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->nv = nv+1;
new->ord.matrix.row = row+1; new->ord.matrix.matrix = newm;
break;
case 3: case 259:
onv = old->nv;
nnv = onv+1;
olen = old->ord.composite.length;
nlen = olen+1;
owb = old->ord.composite.w_or_b;
nwb = (struct weight_or_block *)
MALLOC(nlen*sizeof(struct weight_or_block));
for ( i = 0; i < olen; i++ ) {
nwb[i].type = owb[i].type;
switch ( owb[i].type ) {
case IS_DENSE_WEIGHT:
owlen = owb[i].length;
nwb[i].length = owlen+1;
nwb[i].body.dense_weight = (int *)MALLOC((owlen+1)*sizeof(int));
for ( j = 0; j < owlen; j++ )
nwb[i].body.dense_weight[j] = owb[i].body.dense_weight[j];
nwb[i].body.dense_weight[owlen] = 0;
break;
case IS_SPARSE_WEIGHT:
nwb[i].length = owb[i].length;
nwb[i].body.sparse_weight = owb[i].body.sparse_weight;
break;
case IS_BLOCK:
nwb[i].length = owb[i].length;
nwb[i].body.block = owb[i].body.block;
break;
}
}
nwb[i].type = IS_SPARSE_WEIGHT;
nwb[i].body.sparse_weight =
(struct sparse_weight *)MALLOC(sizeof(struct sparse_weight));
nwb[i].body.sparse_weight[0].pos = onv;
nwb[i].body.sparse_weight[0].value = 1;
new->nv = nnv;
new->ord.composite.length = nlen;
new->ord.composite.w_or_b = nwb;
print_composite_order_spec(new);
break;
case 256: /* simple module order */
switch ( old->ord.simple ) {
case 0:
break;
case 1:
l = (struct order_pair *)
MALLOC_ATOMIC(2*sizeof(struct order_pair));
l[0].length = n; l[0].order = old->ord.simple;
l[1].length = 1; l[1].order = 2;
new->id = 257;
new->ord.block.order_pair = l;
new->ord.block.length = 2; new->nv = n+1;
break;
case 2:
new->ord.simple = 1; break;
default:
error("homogenize_order : invalid input");
}
break;
default:
error("homogenize_order : invalid input");
}
}
int comp_nm(Q *a,Q *b)
{
Z z,nma,nmb;
nmq(*a,&z); absz(z,&nma);
nmq(*b,&z); absz(z,&nmb);
return cmpz(nma,nmb);
}
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;
}
}
int dpm_redble(DPM p1,DPM p2)
{
int i,n;
DL d1,d2;
if ( BDY(p1)->pos != BDY(p2)->pos ) return 0;
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 = (Obj)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 = (Obj)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_ht(DP p,DP *rp)
{
MP m,mr;
if ( !p )
*rp = 0;
else {
m = BDY(p);
NEWMP(mr); mr->dl = m->dl; mr->c = (Obj)ONE; NEXT(mr) = 0;
MKDP(p->nv,mr,*rp); (*rp)->sugar = mr->dl->td; /* XXX */
}
}
void dpm_hm(DPM p,DPM *rp)
{
DMM m,mr;
if ( !p )
*rp = 0;
else {
m = BDY(p);
NEWDMM(mr); mr->dl = m->dl; mr->c = m->c; mr->pos = m->pos; NEXT(mr) = 0;
MKDPM(p->nv,mr,*rp); (*rp)->sugar = mr->dl->td; /* XXX */
}
}
void dpm_ht(DPM p,DPM *rp)
{
DMM m,mr;
if ( !p )
*rp = 0;
else {
m = BDY(p);
NEWDMM(mr); mr->dl = m->dl; mr->pos = m->pos; mr->c = (Obj)ONE; NEXT(mr) = 0;
MKDPM(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;
}
}
void dpm_rest(DPM p,DPM *rp)
{
DMM m;
m = BDY(p);
if ( !NEXT(m) )
*rp = 0;
else {
MKDPM(p->nv,NEXT(m),*rp);
if ( *rp )
(*rp)->sugar = p->sugar;
}
}
int dp_getdeg(DP p)
{
int max,n,i;
MP m;
int *d;
if ( !p ) return 0;
n = p->nv;
max = 0;
for ( m = BDY(p); m; m = NEXT(m) ) {
d = m->dl->d;
for ( i = 0; i < n; i++ )
if ( d[i] > max ) max = d[i];
}
return max;
}
int dpm_getdeg(DPM p,int *r)
{
int max,n,i,rank;
DMM m;
int *d;
if ( !p ) return 0;
n = p->nv;
max = 0;
rank = 0;
for ( m = BDY(p); m; m = NEXT(m) ) {
d = m->dl->d;
for ( i = 0; i < n; i++ )
if ( d[i] > max ) max = d[i];
rank = MAX(rank,m->pos);
}
*r = rank;
return max;
}
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,"%ld<",ITOS(C(m)));
for ( i = 0; i < nv; i++ ) {
fprintf(stderr,"%d",m->dl->d[i]);
if ( i != nv-1 )
fprintf(stderr," ");
}
fprintf(stderr,">");
}
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;
}
DP extract_initial_term_from_dp(DP p,int *weight,int n);
LIST extract_initial_term(LIST f,int *weight,int n);
DP extract_initial_term_from_dp(DP p,int *weight,int n)
{
int w,t,i,top;
MP m,r0,r;
DP dp;
if ( !p ) return 0;
top = 1;
for ( m = BDY(p); m; m = NEXT(m) ) {
for ( i = 0, t = 0; i < n; i++ )
t += weight[i]*m->dl->d[i];
if ( top || t > w ) {
r0 = 0;
w = t;
top = 0;
}
if ( t == w ) {
NEXTMP(r0,r);
r->dl = m->dl;
r->c = m->c;
}
}
NEXT(r) = 0;
MKDP(p->nv,r0,dp);
return dp;
}
LIST extract_initial_term(LIST f,int *weight,int n)
{
NODE nd,r0,r;
Obj p;
LIST l;
nd = BDY(f);
for ( r0 = 0; nd; nd = NEXT(nd) ) {
NEXTNODE(r0,r);
p = (Obj)BDY(nd);
BDY(r) = (pointer)extract_initial_term_from_dp((DP)p,weight,n);
}
if ( r0 ) NEXT(r) = 0;
MKLIST(l,r0);
return l;
}
LIST dp_initial_term(LIST f,struct order_spec *ord)
{
int n,l,i;
struct weight_or_block *worb;
int *weight;
switch ( ord->id ) {
case 2: /* matrix order */
/* extract the first row */
n = ord->nv;
weight = ord->ord.matrix.matrix[0];
return extract_initial_term(f,weight,n);
case 3: /* composite order */
/* the first w_or_b */
worb = ord->ord.composite.w_or_b;
switch ( worb->type ) {
case IS_DENSE_WEIGHT:
n = worb->length;
weight = worb->body.dense_weight;
return extract_initial_term(f,weight,n);
case IS_SPARSE_WEIGHT:
n = ord->nv;
weight = (int *)ALLOCA(n*sizeof(int));
for ( i = 0; i < n; i++ ) weight[i] = 0;
l = worb->length;
for ( i = 0; i < l; i++ )
weight[worb->body.sparse_weight[i].pos]
= worb->body.sparse_weight[i].value;
return extract_initial_term(f,weight,n);
default:
error("dp_initial_term : unsupported order");
}
default:
error("dp_initial_term : unsupported order");
}
return 0;
}
int highest_order_dp(DP p,int *weight,int n);
LIST highest_order(LIST f,int *weight,int n);
int highest_order_dp(DP p,int *weight,int n)
{
int w,t,i,top;
MP m;
if ( !p ) return -1;
top = 1;
for ( m = BDY(p); m; m = NEXT(m) ) {
for ( i = 0, t = 0; i < n; i++ )
t += weight[i]*m->dl->d[i];
if ( top || t > w ) {
w = t;
top = 0;
}
}
return w;
}
LIST highest_order(LIST f,int *weight,int n)
{
int h;
NODE nd,r0,r;
Obj p;
LIST l;
Z q;
nd = BDY(f);
for ( r0 = 0; nd; nd = NEXT(nd) ) {
NEXTNODE(r0,r);
p = (Obj)BDY(nd);
h = highest_order_dp((DP)p,weight,n);
STOZ(h,q);
BDY(r) = (pointer)q;
}
if ( r0 ) NEXT(r) = 0;
MKLIST(l,r0);
return l;
}
LIST dp_order(LIST f,struct order_spec *ord)
{
int n,l,i;
struct weight_or_block *worb;
int *weight;
switch ( ord->id ) {
case 2: /* matrix order */
/* extract the first row */
n = ord->nv;
weight = ord->ord.matrix.matrix[0];
return highest_order(f,weight,n);
case 3: /* composite order */
/* the first w_or_b */
worb = ord->ord.composite.w_or_b;
switch ( worb->type ) {
case IS_DENSE_WEIGHT:
n = worb->length;
weight = worb->body.dense_weight;
return highest_order(f,weight,n);
case IS_SPARSE_WEIGHT:
n = ord->nv;
weight = (int *)ALLOCA(n*sizeof(int));
for ( i = 0; i < n; i++ ) weight[i] = 0;
l = worb->length;
for ( i = 0; i < l; i++ )
weight[worb->body.sparse_weight[i].pos]
= worb->body.sparse_weight[i].value;
return highest_order(f,weight,n);
default:
error("dp_initial_term : unsupported order");
}
default:
error("dp_initial_term : unsupported order");
}
return 0;
}
int dpv_ht(DPV p,DP *h)
{
int len,max,maxi,i,t;
DP *e;
MP m,mr;
len = p->len;
e = p->body;
max = -1;
maxi = -1;
for ( i = 0; i < len; i++ )
if ( e[i] && (t = BDY(e[i])->dl->td) > max ) {
max = t;
maxi = i;
}
if ( max < 0 ) {
*h = 0;
return -1;
} else {
m = BDY(e[maxi]);
NEWMP(mr); mr->dl = m->dl; mr->c = (Obj)ONE; NEXT(mr) = 0;
MKDP(e[maxi]->nv,mr,*h); (*h)->sugar = mr->dl->td; /* XXX */
return maxi;
}
}
/* return 1 if 0 <_w1 v && v <_w2 0 */
int in_c12(int n,int *v,int row1,int **w1,int row2, int **w2)
{
int t1,t2;
t1 = compare_zero(n,v,row1,w1);
t2 = compare_zero(n,v,row2,w2);
if ( t1 > 0 && t2 < 0 ) return 1;
else return 0;
}
/* 0 < u => 1, 0 > u => -1 */
int compare_zero(int n,int *u,int row,int **w)
{
int i,j,t;
int *wi;
for ( i = 0; i < row; i++ ) {
wi = w[i];
for ( j = 0, t = 0; j < n; j++ ) t += u[j]*wi[j];
if ( t > 0 ) return 1;
else if ( t < 0 ) return -1;
}
return 0;
}
/* functions for generic groebner walk */
/* u=0 means u=-infty */
int compare_facet_preorder(int n,int *u,int *v,
int row1,int **w1,int row2,int **w2)
{
int i,j,s,t,tu,tv;
int *w2i,*uv;
if ( !u ) return 1;
uv = W_ALLOC(n);
for ( i = 0; i < row2; i++ ) {
w2i = w2[i];
for ( j = 0, tu = tv = 0; j < n; j++ )
if ( (s = w2i[j]) != 0 ) {
tu += s*u[j]; tv += s*v[j];
}
for ( j = 0; j < n; j++ ) uv[j] = u[j]*tv-v[j]*tu;
t = compare_zero(n,uv,row1,w1);
if ( t > 0 ) return 1;
else if ( t < 0 ) return 0;
}
return 1;
}
Q inner_product_with_small_vector(VECT w,int *v)
{
int n,i;
Z q;
Q s,t,u;
n = w->len;
s = 0;
for ( i = 0; i < n; i++ ) {
STOZ(v[i],q); mulq((Q)w->body[i],(Q)q,&t); addq(t,s,&u); s = u;
}
return s;
}
Q compute_last_t(NODE g,NODE gh,Q t,VECT w1,VECT w2,NODE *homo,VECT *wp)
{
int n,i;
int *wt;
Q last,d1,d2,dn,nm,s,t1;
VECT wd,wt1,wt2,w;
NODE tg,tgh;
MP f;
int *h;
NODE r0,r;
MP m0,m;
DP d;
n = w1->len;
wt = W_ALLOC(n);
last = (Q)ONE;
/* t1 = 1-t */
for ( tg = g, tgh = gh; tg; tg = NEXT(tg), tgh = NEXT(tgh ) ) {
f = BDY((DP)BDY(tg));
h = BDY((DP)BDY(tgh))->dl->d;
for ( ; f; f = NEXT(f) ) {
for ( i = 0; i < n; i++ ) wt[i] = h[i]-f->dl->d[i];
for ( i = 0; i < n && !wt[i]; i++ );
if ( i == n ) continue;
d1 = inner_product_with_small_vector(w1,wt);
d2 = inner_product_with_small_vector(w2,wt);
nm = d1; subq(d1,d2,&dn);
/* if d1=d2 then nothing happens */
if ( !dn ) continue;
/* s satisfies ds = 0*/
divq(nm,dn,&s);
if ( cmpq(s,t) > 0 && cmpq(s,last) < 0 )
last = s;
else if ( !cmpq(s,t) ) {
if ( cmpq(d2,0) < 0 ) {
last = t;
break;
}
}
}
}
nmq(last,(Z *)&nm);
dnq(last,(Z *)&dn);
/* (1-n/d)*w1+n/d*w2 -> w=(d-n)*w1+n*w2 */
subq(dn,nm,&t1); mulvect(CO,(Obj)w1,(Obj)t1,(Obj *)&wt1);
mulvect(CO,(Obj)w2,(Obj)nm,(Obj *)&wt2); addvect(CO,wt1,wt2,&w);
r0 = 0;
for ( tg = g, tgh = gh; tg; tg = NEXT(tg), tgh = NEXT(tgh ) ) {
f = BDY((DP)BDY(tg));
h = BDY((DP)BDY(tgh))->dl->d;
for ( m0 = 0; f; f = NEXT(f) ) {
for ( i = 0; i < n; i++ ) wt[i] = h[i]-f->dl->d[i];
for ( i = 0; i < n && !wt[i]; i++ );
if ( !inner_product_with_small_vector(w,wt) ) {
NEXTMP(m0,m); m->c = f->c; m->dl = f->dl;
}
}
NEXT(m) = 0;
MKDP(((DP)BDY(tg))->nv,m0,d); d->sugar = ((DP)BDY(tg))->sugar;
NEXTNODE(r0,r); BDY(r) = (pointer)d;
}
NEXT(r) = 0;
*homo = r0;
*wp = w;
return last;
}
/* return 0 if last_w = infty */
NODE compute_last_w(NODE g,NODE gh,int n,int **w,
int row1,int **w1,int row2,int **w2)
{
DP d;
MP f,m0,m;
int *wt,*v,*h;
NODE t,s,n0,tn,n1,r0,r;
int i;
wt = W_ALLOC(n);
n0 = 0;
for ( t = g, s = gh; t; t = NEXT(t), s = NEXT(s) ) {
f = BDY((DP)BDY(t));
h = BDY((DP)BDY(s))->dl->d;
for ( ; f; f = NEXT(f) ) {
for ( i = 0; i < n; i++ ) wt[i] = h[i]-f->dl->d[i];
for ( i = 0; i < n && !wt[i]; i++ );
if ( i == n ) continue;
if ( in_c12(n,wt,row1,w1,row2,w2) &&
compare_facet_preorder(n,*w,wt,row1,w1,row2,w2) ) {
v = (int *)MALLOC_ATOMIC(n*sizeof(int));
for ( i = 0; i < n; i++ ) v[i] = wt[i];
MKNODE(n1,v,n0); n0 = n1;
}
}
}
if ( !n0 ) return 0;
for ( t = n0; t; t = NEXT(t) ) {
v = (int *)BDY(t);
for ( s = n0; s; s = NEXT(s) )
if ( !compare_facet_preorder(n,v,(int *)BDY(s),row1,w1,row2,w2) )
break;
if ( !s ) {
*w = v;
break;
}
}
if ( !t )
error("compute_last_w : cannot happen");
r0 = 0;
for ( t = g, s = gh; t; t = NEXT(t), s = NEXT(s) ) {
f = BDY((DP)BDY(t));
h = BDY((DP)BDY(s))->dl->d;
for ( m0 = 0; f; f = NEXT(f) ) {
for ( i = 0; i < n; i++ ) wt[i] = h[i]-f->dl->d[i];
for ( i = 0; i < n && !wt[i]; i++ );
if ( i == n ||
(compare_facet_preorder(n,wt,*w,row1,w1,row2,w2)
&& compare_facet_preorder(n,*w,wt,row1,w1,row2,w2)) ) {
NEXTMP(m0,m); m->c = f->c; m->dl = f->dl;
}
}
NEXT(m) = 0;
MKDP(((DP)BDY(t))->nv,m0,d); d->sugar = ((DP)BDY(t))->sugar;
NEXTNODE(r0,r); BDY(r) = (pointer)d;
}
NEXT(r) = 0;
return r0;
}
/* compute a sufficient set of d(f)=u-v */
NODE compute_essential_df(DP *g,DP *gh,int ng)
{
int nv,i,j,k,t,lj;
NODE r,r1,ri,rt,r0;
MP m;
MP *mj;
DL di,hj,dl,dlt;
int *d,*dt;
LIST l;
Z q;
nv = g[0]->nv;
r = 0;
for ( j = 0; j < ng; j++ ) {
for ( m = BDY(g[j]), lj = 0; m; m = NEXT(m), lj++ );
mj = (MP *)ALLOCA(lj*sizeof(MP));
for ( m = BDY(g[j]), k = 0; m; m = NEXT(m), k++ )
mj[k] = m;
for ( i = 0; i < lj; i++ ) {
for ( di = mj[i]->dl, k = i+1; k < lj; k++ )
if ( _dl_redble(di,mj[k]->dl,nv) ) break;
if ( k < lj ) mj[i] = 0;
}
hj = BDY(gh[j])->dl;
_NEWDL(dl,nv); d = dl->d;
r0 = r;
for ( i = 0; i < lj; i++ ) {
if ( mj[i] && !dl_equal(nv,di=mj[i]->dl,hj) ) {
for ( k = 0, t = 0; k < nv; k++ ) {
d[k] = hj->d[k]-di->d[k];
t += d[k];
}
dl->td = t;
#if 1
for ( rt = r0; rt; rt = NEXT(rt) ) {
dlt = (DL)BDY(rt);
if ( dlt->td != dl->td ) continue;
for ( dt = dlt->d, k = 0; k < nv; k++ )
if ( d[k] != dt[k] ) break;
if ( k == nv ) break;
}
#else
rt = 0;
#endif
if ( !rt ) {
MKNODE(r1,dl,r); r = r1;
_NEWDL(dl,nv); d = dl->d;
}
}
}
}
for ( rt = r; rt; rt = NEXT(rt) ) {
dl = (DL)BDY(rt); d = dl->d;
ri = 0;
for ( k = nv-1; k >= 0; k-- ) {
STOZ(d[k],q);
MKNODE(r1,q,ri); ri = r1;
}
MKNODE(r1,0,ri); MKLIST(l,r1);
BDY(rt) = (pointer)l;
}
return r;
}
int comp_bits_divisible(int *a,int *b,int n)
{
int bpi,i,wi,bi;
bpi = (sizeof(int)/sizeof(char))*8;
for ( i = 0; i < n; i++ ) {
wi = i/bpi; bi = i%bpi;
if ( !(a[wi]&(1<<bi)) && (b[wi]&(1<<bi)) ) return 0;
}
return 1;
}
int comp_bits_lex(int *a,int *b,int n)
{
int bpi,i,wi,ba,bb,bi;
bpi = (sizeof(int)/sizeof(char))*8;
for ( i = 0; i < n; i++ ) {
wi = i/bpi; bi = i%bpi;
ba = (a[wi]&(1<<bi))?1:0;
bb = (b[wi]&(1<<bi))?1:0;
if ( ba > bb ) return 1;
else if ( ba < bb ) return -1;
}
return 0;
}
NODE mono_raddec(NODE ideal)
{
DP p;
int nv,w,i,bpi,di,c,len;
int *d,*s,*u,*new;
NODE t,t1,v,r,rem,prev;
if( !ideal ) return 0;
p = (DP)BDY(ideal);
nv = NV(p);
bpi = (sizeof(int)/sizeof(char))*8;
w = (nv+(bpi-1))/bpi;
d = p->body->dl->d;
if ( !NEXT(ideal) ) {
for ( t = 0, i = nv-1; i >= 0; i-- ) {
if ( d[i] ) {
s = (int *)CALLOC(w,sizeof(int));
s[i/bpi] |= 1<<(i%bpi);
MKNODE(t1,s,t);
t = t1;
}
}
return t;
}
rem = mono_raddec(NEXT(ideal));
r = 0;
len = w*sizeof(int);
u = (int *)CALLOC(w,sizeof(int));
for ( i = nv-1; i >= 0; i-- ) {
if ( d[i] ) {
for ( t = rem; t; t = NEXT(t) ) {
bcopy((char *)BDY(t),(char *)u,len);
u[i/bpi] |= 1<<(i%bpi);
for ( v = r; v; v = NEXT(v) ) {
if ( comp_bits_divisible(u,(int *)BDY(v),nv) ) break;
}
if ( v ) continue;
for ( v = r, prev = 0; v; v = NEXT(v) ) {
if ( comp_bits_divisible((int *)BDY(v),u,nv) ) {
if ( prev ) NEXT(prev) = NEXT(v);
else r = NEXT(r);
} else prev =v;
}
for ( v = r, prev = 0; v; prev = v, v = NEXT(v) ) {
if ( comp_bits_lex(u,(int *)BDY(v),nv) < 0 ) break;
}
new = (int *)CALLOC(w,sizeof(int));
bcopy((char *)u,(char *)new,len);
MKNODE(t1,new,v);
if ( prev ) NEXT(prev) = t1;
else r = t1;
}
}
}
return r;
}
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