/*
* 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.
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* 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
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*
* $OpenXM: OpenXM_contrib2/asir2000/engine/dist.c,v 1.54 2018/07/10 05:29:36 noro Exp $
*/
#include "ca.h"
#define ORD_REVGRADLEX 0
#define ORD_GRADLEX 1
#define ORD_LEX 2
#define ORD_BREVGRADLEX 3
#define ORD_BGRADLEX 4
#define ORD_BLEX 5
#define ORD_BREVREV 6
#define ORD_BGRADREV 7
#define ORD_BLEXREV 8
#define ORD_ELIM 9
#define ORD_WEYL_ELIM 10
#define ORD_HOMO_WW_DRL 11
#define ORD_DRL_ZIGZAG 12
#define ORD_HOMO_WW_DRL_ZIGZAG 13
int cmpdl_drl_zigzag(), cmpdl_homo_ww_drl_zigzag();
int cmpdl_top_weight();
int (*cmpdl)()=cmpdl_revgradlex;
int (*cmpdl_tie_breaker)();
int (*primitive_cmpdl[3])() = {cmpdl_revgradlex,cmpdl_gradlex,cmpdl_lex};
Obj current_top_weight;
int current_top_weight_len;
int do_weyl;
int dp_nelim,dp_fcoeffs;
struct order_spec *dp_current_spec;
struct modorder_spec *dp_current_modspec;
int *dp_dl_work;
void comm_muld_trunc(VL vl,DP p1,DP p2,DL dl,DP *pr);
void comm_quod(VL vl,DP p1,DP p2,DP *pr);
void muldm_trunc(VL vl,DP p,MP m0,DL dl,DP *pr);
void muldc_trunc(VL vl,DP p,Obj c,DL dl,DP *pr);
int create_order_spec(VL vl,Obj obj,struct order_spec **specp);
void create_modorder_spec(int id,LIST shift,struct modorder_spec **s);
void order_init()
{
struct order_spec *spec;
create_order_spec(0,0,&spec);
initd(spec);
create_modorder_spec(0,0,&dp_current_modspec);
}
int has_sfcoef_p(Obj f);
int has_sfcoef(DP f)
{
MP t;
if ( !f )
return 0;
for ( t = BDY(f); t; t = NEXT(t) )
if ( has_sfcoef_p(t->c) )
break;
return t ? 1 : 0;
}
int has_sfcoef_p(Obj f)
{
DCP dc;
if ( !f )
return 0;
else if ( NUM(f) )
return (NID((Num)f) == N_GFS) ? 1 : 0;
else if ( POLY(f) ) {
for ( dc = DC((P)f); dc; dc = NEXT(dc) )
if ( has_sfcoef_p((Obj)COEF(dc)) )
return 1;
return 0;
} else
return 0;
}
extern Obj nd_top_weight;
void reset_top_weight()
{
cmpdl = cmpdl_tie_breaker;
cmpdl_tie_breaker = 0;
nd_top_weight = 0;
current_top_weight = 0;
current_top_weight_len = 0;
}
void initd(struct order_spec *spec)
{
int len,i,k,row;
Q **mat;
switch ( spec->id ) {
case 3:
cmpdl = cmpdl_composite;
dp_dl_work = (int *)MALLOC_ATOMIC(spec->nv*sizeof(int));
break;
case 2:
cmpdl = cmpdl_matrix;
dp_dl_work = (int *)MALLOC_ATOMIC(spec->nv*sizeof(int));
break;
case 1:
cmpdl = cmpdl_order_pair;
break;
default:
switch ( spec->ord.simple ) {
case ORD_REVGRADLEX:
cmpdl = cmpdl_revgradlex; break;
case ORD_GRADLEX:
cmpdl = cmpdl_gradlex; break;
case ORD_BREVGRADLEX:
cmpdl = cmpdl_brevgradlex; break;
case ORD_BGRADLEX:
cmpdl = cmpdl_bgradlex; break;
case ORD_BLEX:
cmpdl = cmpdl_blex; break;
case ORD_BREVREV:
cmpdl = cmpdl_brevrev; break;
case ORD_BGRADREV:
cmpdl = cmpdl_bgradrev; break;
case ORD_BLEXREV:
cmpdl = cmpdl_blexrev; break;
case ORD_ELIM:
cmpdl = cmpdl_elim; break;
case ORD_WEYL_ELIM:
cmpdl = cmpdl_weyl_elim; break;
case ORD_HOMO_WW_DRL:
cmpdl = cmpdl_homo_ww_drl; break;
case ORD_DRL_ZIGZAG:
cmpdl = cmpdl_drl_zigzag; break;
case ORD_HOMO_WW_DRL_ZIGZAG:
cmpdl = cmpdl_homo_ww_drl_zigzag; break;
case ORD_LEX: default:
cmpdl = cmpdl_lex; break;
}
break;
}
if ( current_top_weight ) {
cmpdl_tie_breaker = cmpdl;
cmpdl = cmpdl_top_weight;
if ( OID(current_top_weight) == O_VECT ) {
mat = (Q **)&BDY((VECT)current_top_weight);
row = 1;
} else {
mat = (Q **)BDY((MAT)current_top_weight);
row = ((MAT)current_top_weight)->row;
}
for ( k = 0, len = 0; k < row; k++ )
for ( i = 0; i < spec->nv; i++ )
if ( mat[k][i] )
len = MAX(PL(NM(mat[k][i])),len);
current_top_weight_len = len;
}
dp_current_spec = spec;
}
int dpm_ispot;
/* type=0 => TOP, type=1 => POT */
void initdpm(struct order_spec *spec,int type)
{
int len,i,k,row;
Q **mat;
initd(spec);
dpm_ispot = type;
}
void ptod(VL vl,VL dvl,P p,DP *pr)
{
int n,i,j,k;
VL tvl;
V v;
DL d;
MP m;
DCP dc;
DCP *w;
DP r,s,t,u;
P x,c;
if ( !p )
*pr = 0;
else if ( OID(p) > O_P )
error("ptod : only polynomials can be converted.");
else {
for ( n = 0, tvl = dvl; tvl; tvl = NEXT(tvl), n++ );
if ( NUM(p) ) {
NEWDL(d,n);
NEWMP(m); m->dl = d; C(m) = (Obj)p; NEXT(m) = 0; MKDP(n,m,*pr); (*pr)->sugar = 0;
} else {
for ( i = 0, tvl = dvl, v = VR(p);
tvl && tvl->v != v; tvl = NEXT(tvl), i++ );
if ( !tvl ) {
for ( dc = DC(p), k = 0; dc; dc = NEXT(dc), k++ );
w = (DCP *)ALLOCA(k*sizeof(DCP));
for ( dc = DC(p), j = 0; j < k; dc = NEXT(dc), j++ )
w[j] = dc;
for ( j = k-1, s = 0, MKV(v,x); j >= 0; j-- ) {
ptod(vl,dvl,COEF(w[j]),&t); pwrp(vl,x,DEG(w[j]),&c);
muldc(vl,t,(Obj)c,&r); addd(vl,r,s,&t); s = t;
}
*pr = s;
} else {
for ( dc = DC(p), k = 0; dc; dc = NEXT(dc), k++ );
w = (DCP *)ALLOCA(k*sizeof(DCP));
for ( dc = DC(p), j = 0; j < k; dc = NEXT(dc), j++ )
w[j] = dc;
for ( j = k-1, s = 0; j >= 0; j-- ) {
ptod(vl,dvl,COEF(w[j]),&t);
NEWDL(d,n); d->d[i] = QTOS(DEG(w[j]));
d->td = MUL_WEIGHT(d->d[i],i);
NEWMP(m); m->dl = d; C(m) = (Obj)ONE; NEXT(m) = 0; MKDP(n,m,u); u->sugar = d->td;
comm_muld(vl,t,u,&r); addd(vl,r,s,&t); s = t;
}
*pr = s;
}
}
}
#if 0
if ( !dp_fcoeffs && has_sfcoef(*pr) )
dp_fcoeffs = N_GFS;
#endif
}
void dtop(VL vl,VL dvl,DP p,Obj *pr)
{
int n,i,j,k;
DL d;
MP m;
MP *a;
P r;
Obj t,w,s,u;
Q q;
VL tvl;
if ( !p )
*pr = 0;
else {
for ( k = 0, m = BDY(p); m; m = NEXT(m), k++ );
a = (MP *)ALLOCA(k*sizeof(MP));
for ( j = 0, m = BDY(p); j < k; m = NEXT(m), j++ )
a[j] = m;
for ( n = p->nv, j = k-1, s = 0; j >= 0; j-- ) {
m = a[j];
t = C(m);
if ( NUM(t) && NID((Num)t) == N_M ) {
mptop((P)t,(P *)&u); t = u;
}
for ( i = 0, d = m->dl, tvl = dvl;
i < n; tvl = NEXT(tvl), i++ ) {
MKV(tvl->v,r); STOQ(d->d[i],q); pwrp(vl,r,q,(P *)&u);
arf_mul(vl,t,(Obj)u,&w); t = w;
}
arf_add(vl,s,t,&u); s = u;
}
*pr = s;
}
}
void nodetod(NODE node,DP *dp)
{
NODE t;
int len,i,td;
Q e;
DL d;
MP m;
DP u;
for ( t = node, len = 0; t; t = NEXT(t), len++ );
NEWDL(d,len);
for ( t = node, i = 0, td = 0; i < len; t = NEXT(t), i++ ) {
e = (Q)BDY(t);
if ( !e )
d->d[i] = 0;
else if ( !NUM(e) || !RATN(e) || !INT(e) )
error("nodetod : invalid input");
else {
d->d[i] = QTOS((Q)e); td += MUL_WEIGHT(d->d[i],i);
}
}
d->td = td;
NEWMP(m); m->dl = d; C(m) = (Obj)ONE; NEXT(m) = 0;
MKDP(len,m,u); u->sugar = td; *dp = u;
}
void nodetodpm(NODE node,Obj pos,DPM *dp)
{
NODE t;
int len,i,td;
Q e;
DL d;
DMM m;
DPM u;
for ( t = node, len = 0; t; t = NEXT(t), len++ );
NEWDL(d,len);
for ( t = node, i = 0, td = 0; i < len; t = NEXT(t), i++ ) {
e = (Q)BDY(t);
if ( !e )
d->d[i] = 0;
else if ( !NUM(e) || !RATN(e) || !INT(e) )
error("nodetodpm : invalid input");
else {
d->d[i] = QTOS((Q)e); td += MUL_WEIGHT(d->d[i],i);
}
}
d->td = td;
NEWDMM(m); m->dl = d; m->pos = QTOS((Q)pos); C(m) = (Obj)ONE; NEXT(m) = 0;
MKDPM(len,m,u); u->sugar = td; *dp = u;
}
void dtodpm(DP d,int pos,DPM *dp)
{
DMM mr0,mr;
MP m;
if ( !d ) *dp = 0;
else {
for ( m = BDY(d), mr0 = 0; m; m = NEXT(m) ) {
NEXTDMM(mr0,mr);
mr->dl = m->dl;
mr->pos = pos;
C(mr) = C(m);
}
MKDPM(d->nv,mr0,*dp); (*dp)->sugar = d->sugar;
}
}
int sugard(MP m)
{
int s;
for ( s = 0; m; m = NEXT(m) )
s = MAX(s,m->dl->td);
return s;
}
void addd(VL vl,DP p1,DP p2,DP *pr)
{
int n;
MP m1,m2,mr=0,mr0;
Obj t;
DL d;
if ( !p1 )
*pr = p2;
else if ( !p2 )
*pr = p1;
else {
if ( OID(p1) <= O_R ) {
n = NV(p2); NEWDL(d,n);
NEWMP(m1); m1->dl = d; C(m1) = (Obj)p1; NEXT(m1) = 0;
MKDP(n,m1,p1); (p1)->sugar = 0;
}
if ( OID(p2) <= O_R ) {
n = NV(p1); NEWDL(d,n);
NEWMP(m2); m2->dl = d; C(m2) = (Obj)p2; NEXT(m2) = 0;
MKDP(n,m2,p2); (p2)->sugar = 0;
}
for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; )
switch ( (*cmpdl)(n,m1->dl,m2->dl) ) {
case 0:
arf_add(vl,C(m1),C(m2),&t);
if ( t ) {
NEXTMP(mr0,mr); mr->dl = m1->dl; C(mr) = t;
}
m1 = NEXT(m1); m2 = NEXT(m2); break;
case 1:
NEXTMP(mr0,mr); mr->dl = m1->dl; C(mr) = C(m1);
m1 = NEXT(m1); break;
case -1:
NEXTMP(mr0,mr); mr->dl = m2->dl; C(mr) = C(m2);
m2 = NEXT(m2); break;
}
if ( !mr0 )
if ( m1 )
mr0 = m1;
else if ( m2 )
mr0 = m2;
else {
*pr = 0;
return;
}
else if ( m1 )
NEXT(mr) = m1;
else if ( m2 )
NEXT(mr) = m2;
else
NEXT(mr) = 0;
MKDP(NV(p1),mr0,*pr);
if ( *pr )
(*pr)->sugar = MAX(p1->sugar,p2->sugar);
}
}
/* for F4 symbolic reduction */
void symb_addd(DP p1,DP p2,DP *pr)
{
int n;
MP m1,m2,mr=0,mr0;
if ( !p1 )
*pr = p2;
else if ( !p2 )
*pr = p1;
else {
for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) {
NEXTMP(mr0,mr); C(mr) = (Obj)ONE;
switch ( (*cmpdl)(n,m1->dl,m2->dl) ) {
case 0:
mr->dl = m1->dl;
m1 = NEXT(m1); m2 = NEXT(m2); break;
case 1:
mr->dl = m1->dl;
m1 = NEXT(m1); break;
case -1:
mr->dl = m2->dl;
m2 = NEXT(m2); break;
}
}
if ( !mr0 )
if ( m1 )
mr0 = m1;
else if ( m2 )
mr0 = m2;
else {
*pr = 0;
return;
}
else if ( m1 )
NEXT(mr) = m1;
else if ( m2 )
NEXT(mr) = m2;
else
NEXT(mr) = 0;
MKDP(NV(p1),mr0,*pr);
if ( *pr )
(*pr)->sugar = MAX(p1->sugar,p2->sugar);
}
}
/*
* destructive merge of two list
*
* p1, p2 : list of DL
* return : a merged list
*/
NODE symb_merge(NODE m1,NODE m2,int n)
{
NODE top=0,prev,cur,m=0,t;
DL d1,d2;
if ( !m1 )
return m2;
else if ( !m2 )
return m1;
else {
switch ( (*cmpdl)(n,(DL)BDY(m1),(DL)BDY(m2)) ) {
case 0:
top = m1; m = NEXT(m2);
break;
case 1:
top = m1; m = m2;
break;
case -1:
top = m2; m = m1;
break;
}
prev = top; cur = NEXT(top);
/* BDY(prev) > BDY(m) always holds */
while ( cur && m ) {
d1 = (DL)BDY(cur);
d2 = (DL)BDY(m);
#if 1
switch ( (*cmpdl)(n,(DL)BDY(cur),(DL)BDY(m)) ) {
#else
/* XXX only valid for DRL */
if ( d1->td > d2->td )
c = 1;
else if ( d1->td < d2->td )
c = -1;
else {
for ( i = n-1; i >= 0 && d1->d[i] == d2->d[i]; i-- );
if ( i < 0 )
c = 0;
else if ( d1->d[i] < d2->d[i] )
c = 1;
else
c = -1;
}
switch ( c ) {
#endif
case 0:
m = NEXT(m);
prev = cur; cur = NEXT(cur);
break;
case 1:
t = NEXT(cur); NEXT(cur) = m; m = t;
prev = cur; cur = NEXT(cur);
break;
case -1:
NEXT(prev) = m; m = cur;
prev = NEXT(prev); cur = NEXT(prev);
break;
}
}
if ( !cur )
NEXT(prev) = m;
return top;
}
}
void _adddl(int n,DL d1,DL d2,DL d3)
{
int i;
d3->td = d1->td+d2->td;
for ( i = 0; i < n; i++ )
d3->d[i] = d1->d[i]+d2->d[i];
}
/* m1 <- m1 U dl*f, destructive */
NODE mul_dllist(DL dl,DP f);
NODE symb_mul_merge(NODE m1,DL dl,DP f,int n)
{
NODE top,prev,cur,n1;
DP g;
DL t,s;
MP m;
if ( !m1 )
return mul_dllist(dl,f);
else if ( !f )
return m1;
else {
m = BDY(f);
NEWDL_NOINIT(t,n);
_adddl(n,m->dl,dl,t);
top = m1; prev = 0; cur = m1;
while ( m ) {
switch ( (*cmpdl)(n,(DL)BDY(cur),t) ) {
case 0:
prev = cur; cur = NEXT(cur);
if ( !cur ) {
MKDP(n,m,g);
NEXT(prev) = mul_dllist(dl,g);
return top;
}
m = NEXT(m);
if ( m ) _adddl(n,m->dl,dl,t);
break;
case 1:
prev = cur; cur = NEXT(cur);
if ( !cur ) {
MKDP(n,m,g);
NEXT(prev) = mul_dllist(dl,g);
return top;
}
break;
case -1:
NEWDL_NOINIT(s,n);
s->td = t->td;
bcopy(t->d,s->d,n*sizeof(int));
NEWNODE(n1);
n1->body = (pointer)s;
NEXT(n1) = cur;
if ( !prev ) {
top = n1; cur = n1;
} else {
NEXT(prev) = n1; prev = n1;
}
m = NEXT(m);
if ( m ) _adddl(n,m->dl,dl,t);
break;
}
}
return top;
}
}
DLBUCKET symb_merge_bucket(DLBUCKET m1,DLBUCKET m2,int n)
{
DLBUCKET top,prev,cur,m,t;
if ( !m1 )
return m2;
else if ( !m2 )
return m1;
else {
if ( m1->td == m2->td ) {
top = m1;
BDY(top) = symb_merge(BDY(top),BDY(m2),n);
m = NEXT(m2);
} else if ( m1->td > m2->td ) {
top = m1; m = m2;
} else {
top = m2; m = m1;
}
prev = top; cur = NEXT(top);
/* prev->td > m->td always holds */
while ( cur && m ) {
if ( cur->td == m->td ) {
BDY(cur) = symb_merge(BDY(cur),BDY(m),n);
m = NEXT(m);
prev = cur; cur = NEXT(cur);
} else if ( cur->td > m->td ) {
t = NEXT(cur); NEXT(cur) = m; m = t;
prev = cur; cur = NEXT(cur);
} else {
NEXT(prev) = m; m = cur;
prev = NEXT(prev); cur = NEXT(prev);
}
}
if ( !cur )
NEXT(prev) = m;
return top;
}
}
void subd(VL vl,DP p1,DP p2,DP *pr)
{
DP t;
if ( !p2 )
*pr = p1;
else {
chsgnd(p2,&t); addd(vl,p1,t,pr);
}
}
void chsgnd(DP p,DP *pr)
{
MP m,mr=0,mr0;
Obj r;
if ( !p )
*pr = 0;
else if ( OID(p) <= O_R ) {
arf_chsgn((Obj)p,&r); *pr = (DP)r;
} else {
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
NEXTMP(mr0,mr); arf_chsgn(C(m),&C(mr)); mr->dl = m->dl;
}
NEXT(mr) = 0; MKDP(NV(p),mr0,*pr);
if ( *pr )
(*pr)->sugar = p->sugar;
}
}
void muld(VL vl,DP p1,DP p2,DP *pr)
{
if ( ! do_weyl )
comm_muld(vl,p1,p2,pr);
else
weyl_muld(vl,p1,p2,pr);
}
void comm_muld(VL vl,DP p1,DP p2,DP *pr)
{
MP m;
DP s,t,u;
int i,l,l1;
static MP *w;
static int wlen;
if ( !p1 || !p2 )
*pr = 0;
else if ( OID(p1) != O_DP )
muldc(vl,p2,(Obj)p1,pr);
else if ( OID(p2) != O_DP )
muldc(vl,p1,(Obj)p2,pr);
else {
for ( m = BDY(p1), l1 = 0; m; m = NEXT(m), l1++ );
for ( m = BDY(p2), l = 0; m; m = NEXT(m), l++ );
if ( l1 < l ) {
t = p1; p1 = p2; p2 = t;
l = l1;
}
if ( l > wlen ) {
if ( w ) GCFREE(w);
w = (MP *)MALLOC(l*sizeof(MP));
wlen = l;
}
for ( m = BDY(p2), i = 0; i < l; m = NEXT(m), i++ )
w[i] = m;
for ( s = 0, i = l-1; i >= 0; i-- ) {
muldm(vl,p1,w[i],&t); addd(vl,s,t,&u); s = u;
}
bzero(w,l*sizeof(MP));
*pr = s;
}
}
/* discard terms which is not a multiple of dl */
void comm_muld_trunc(VL vl,DP p1,DP p2,DL dl,DP *pr)
{
MP m;
DP s,t,u;
int i,l,l1;
static MP *w;
static int wlen;
if ( !p1 || !p2 )
*pr = 0;
else if ( OID(p1) != O_DP )
muldc_trunc(vl,p2,(Obj)p1,dl,pr);
else if ( OID(p2) != O_DP )
muldc_trunc(vl,p1,(Obj)p2,dl,pr);
else {
for ( m = BDY(p1), l1 = 0; m; m = NEXT(m), l1++ );
for ( m = BDY(p2), l = 0; m; m = NEXT(m), l++ );
if ( l1 < l ) {
t = p1; p1 = p2; p2 = t;
l = l1;
}
if ( l > wlen ) {
if ( w ) GCFREE(w);
w = (MP *)MALLOC(l*sizeof(MP));
wlen = l;
}
for ( m = BDY(p2), i = 0; i < l; m = NEXT(m), i++ )
w[i] = m;
for ( s = 0, i = l-1; i >= 0; i-- ) {
muldm_trunc(vl,p1,w[i],dl,&t); addd(vl,s,t,&u); s = u;
}
bzero(w,l*sizeof(MP));
*pr = s;
}
}
void comm_quod(VL vl,DP p1,DP p2,DP *pr)
{
MP m=0,m0;
DP s,t;
int i,n,sugar;
DL d1,d2,d;
Q a,b;
if ( !p2 )
error("comm_quod : invalid input");
if ( !p1 )
*pr = 0;
else {
n = NV(p1);
d2 = BDY(p2)->dl;
m0 = 0;
sugar = p1->sugar;
while ( p1 ) {
d1 = BDY(p1)->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];
NEXTMP(m0,m);
m->dl = d;
divq((Q)BDY(p1)->c,(Q)BDY(p2)->c,&a); chsgnq(a,&b);
C(m) = (Obj)b;
muldm_trunc(vl,p2,m,d2,&t);
addd(vl,p1,t,&s); p1 = s;
C(m) = (Obj)a;
}
if ( m0 ) {
NEXT(m) = 0; MKDP(n,m0,*pr);
} else
*pr = 0;
/* XXX */
if ( *pr )
(*pr)->sugar = sugar - d2->td;
}
}
void muldm(VL vl,DP p,MP m0,DP *pr)
{
MP m,mr=0,mr0;
Obj c;
DL d;
int n;
if ( !p )
*pr = 0;
else {
for ( mr0 = 0, m = BDY(p), c = C(m0), d = m0->dl, n = NV(p);
m; m = NEXT(m) ) {
NEXTMP(mr0,mr);
if ( NUM(C(m)) && RATN(C(m)) && NUM(c) && RATN(c) )
mulq((Q)C(m),(Q)c,(Q *)&C(mr));
else
arf_mul(vl,C(m),c,&C(mr));
adddl(n,m->dl,d,&mr->dl);
}
NEXT(mr) = 0; MKDP(NV(p),mr0,*pr);
if ( *pr )
(*pr)->sugar = p->sugar + m0->dl->td;
}
}
void muldm_trunc(VL vl,DP p,MP m0,DL dl,DP *pr)
{
MP m,mr=0,mr0;
Obj c;
DL d,tdl;
int n,i;
if ( !p )
*pr = 0;
else {
n = NV(p);
NEWDL(tdl,n);
for ( mr0 = 0, m = BDY(p), c = C(m0), d = m0->dl;
m; m = NEXT(m) ) {
_adddl(n,m->dl,d,tdl);
for ( i = 0; i < n; i++ )
if ( tdl->d[i] < dl->d[i] )
break;
if ( i < n )
continue;
NEXTMP(mr0,mr);
mr->dl = tdl;
NEWDL(tdl,n);
if ( NUM(C(m)) && RATN(C(m)) && NUM(c) && RATN(c) )
mulq((Q)C(m),(Q)c,(Q *)&C(mr));
else
arf_mul(vl,C(m),(Obj)c,&C(mr));
}
if ( mr0 ) {
NEXT(mr) = 0; MKDP(NV(p),mr0,*pr);
} else
*pr = 0;
if ( *pr )
(*pr)->sugar = p->sugar + m0->dl->td;
}
}
void weyl_muld(VL vl,DP p1,DP p2,DP *pr)
{
MP m;
DP s,t,u;
int i,l;
static MP *w;
static int wlen;
if ( !p1 || !p2 )
*pr = 0;
else if ( OID(p1) != O_DP )
muldc(vl,p2,(Obj)p1,pr);
else if ( OID(p2) != O_DP )
muldc(vl,p1,(Obj)p2,pr);
else {
for ( m = BDY(p1), l = 0; m; m = NEXT(m), l++ );
if ( l > wlen ) {
if ( w ) GCFREE(w);
w = (MP *)MALLOC(l*sizeof(MP));
wlen = l;
}
for ( m = BDY(p1), i = 0; i < l; m = NEXT(m), i++ )
w[i] = m;
for ( s = 0, i = l-1; i >= 0; i-- ) {
weyl_muldm(vl,w[i],p2,&t); addd(vl,s,t,&u); s = u;
}
bzero(w,l*sizeof(MP));
*pr = s;
}
}
void actm(VL vl,int nv,MP m1,MP m2,DP *pr)
{
DL d1,d2,d;
int n2,i,j,k;
Q jq,c,c1;
MP m;
Obj t;
d1 = m1->dl;
d2 = m2->dl;
for ( i = 0; i < nv; i++ )
if ( d1->d[i] > d2->d[i] ) {
*pr = 0; return;
}
NEWDL(d,nv);
c = ONE;
for ( i = 0; i < nv; i++ ) {
for ( j = d2->d[i], k = d1->d[i]; k > 0; k--, j-- ) {
STOQ(j,jq); mulq(c,jq,&c1); c = c1;
}
d->d[i] = d2->d[i]-d1->d[i];
}
arf_mul(vl,C(m1),C(m2),&t);
NEWMP(m);
arf_mul(vl,(Obj)c,t,&C(m));
m->dl = d;
MKDP(nv,m,*pr);
}
void weyl_actd(VL vl,DP p1,DP p2,DP *pr)
{
int n;
MP m1,m2;
DP d,r,s;
if ( !p1 || !p2 ) *pr = 0;
else {
n = NV(p1);
r = 0;
for ( m1 = BDY(p1); m1; m1 = NEXT(m1) )
for ( m2 = BDY(p2); m2; m2 = NEXT(m2) ) {
actm(vl,n,m1,m2,&d);
addd(vl,r,d,&s); r = s;
}
*pr = r;
}
}
/* monomial * polynomial */
void weyl_muldm(VL vl,MP m0,DP p,DP *pr)
{
DP r,t,t1;
MP m;
DL d0;
int n,n2,l,i,j,tlen;
static MP *w,*psum;
static struct cdl *tab;
static int wlen;
static int rtlen;
if ( !p )
*pr = 0;
else {
for ( m = BDY(p), l = 0; m; m = NEXT(m), l++ );
if ( l > wlen ) {
if ( w ) GCFREE(w);
w = (MP *)MALLOC(l*sizeof(MP));
wlen = l;
}
for ( m = BDY(p), i = 0; i < l; m = NEXT(m), i++ )
w[i] = m;
n = NV(p); n2 = n>>1;
d0 = m0->dl;
for ( i = 0, tlen = 1; i < n2; i++ )
tlen *= d0->d[n2+i]+1;
if ( tlen > rtlen ) {
if ( tab ) GCFREE(tab);
if ( psum ) GCFREE(psum);
rtlen = tlen;
tab = (struct cdl *)MALLOC(rtlen*sizeof(struct cdl));
psum = (MP *)MALLOC(rtlen*sizeof(MP));
}
bzero(psum,tlen*sizeof(MP));
for ( i = l-1; i >= 0; i-- ) {
bzero(tab,tlen*sizeof(struct cdl));
weyl_mulmm(vl,m0,w[i],n,tab,tlen);
for ( j = 0; j < tlen; j++ ) {
if ( tab[j].c ) {
NEWMP(m); m->dl = tab[j].d; C(m) = (Obj)tab[j].c; NEXT(m) = psum[j];
psum[j] = m;
}
}
}
for ( j = tlen-1, r = 0; j >= 0; j-- )
if ( psum[j] ) {
MKDP(n,psum[j],t); addd(vl,r,t,&t1); r = t1;
}
if ( r )
r->sugar = p->sugar + m0->dl->td;
*pr = r;
}
}
/* m0 = x0^d0*x1^d1*... * dx0^e0*dx1^e1*... */
/* rtab : array of length (e0+1)*(e1+1)*... */
void weyl_mulmm(VL vl,MP m0,MP m1,int n,struct cdl *rtab,int rtablen)
{
Obj c,c0,c1;
DL d,d0,d1,dt;
int i,j,a,b,k,l,n2,s,min,curlen;
struct cdl *p;
static Q *ctab;
static struct cdl *tab;
static int tablen;
static struct cdl *tmptab;
static int tmptablen;
if ( !m0 || !m1 ) {
rtab[0].c = 0;
rtab[0].d = 0;
return;
}
c0 = C(m0); c1 = C(m1);
arf_mul(vl,c0,c1,&c);
d0 = m0->dl; d1 = m1->dl;
n2 = n>>1;
curlen = 1;
NEWDL(d,n);
if ( n & 1 )
/* offset of h-degree */
d->td = d->d[n-1] = d0->d[n-1]+d1->d[n-1];
else
d->td = 0;
rtab[0].c = c;
rtab[0].d = d;
if ( rtablen > tmptablen ) {
if ( tmptab ) GCFREE(tmptab);
tmptab = (struct cdl *)MALLOC(rtablen*sizeof(struct cdl));
tmptablen = rtablen;
}
for ( i = 0; i < n2; i++ ) {
a = d0->d[i]; b = d1->d[n2+i];
k = d0->d[n2+i]; l = d1->d[i];
/* degree of xi^a*(Di^k*xi^l)*Di^b */
a += l;
b += k;
s = MUL_WEIGHT(a,i)+MUL_WEIGHT(b,n2+i);
if ( !k || !l ) {
for ( j = 0, p = rtab; j < curlen; j++, p++ ) {
if ( p->c ) {
dt = p->d;
dt->d[i] = a;
dt->d[n2+i] = b;
dt->td += s;
}
}
curlen *= k+1;
continue;
}
if ( k+1 > tablen ) {
if ( tab ) GCFREE(tab);
if ( ctab ) GCFREE(ctab);
tablen = k+1;
tab = (struct cdl *)MALLOC(tablen*sizeof(struct cdl));
ctab = (Q *)MALLOC(tablen*sizeof(Q));
}
/* compute xi^a*(Di^k*xi^l)*Di^b */
min = MIN(k,l);
mkwc(k,l,ctab);
bzero(tab,(k+1)*sizeof(struct cdl));
if ( n & 1 )
for ( j = 0; j <= min; j++ ) {
NEWDL(d,n);
d->d[i] = a-j; d->d[n2+i] = b-j;
d->td = s;
d->d[n-1] = s-(MUL_WEIGHT(a-j,i)+MUL_WEIGHT(b-j,n2+i));
tab[j].d = d;
tab[j].c = (Obj)ctab[j];
}
else
for ( j = 0; j <= min; j++ ) {
NEWDL(d,n);
d->d[i] = a-j; d->d[n2+i] = b-j;
d->td = MUL_WEIGHT(a-j,i)+MUL_WEIGHT(b-j,n2+i); /* XXX */
tab[j].d = d;
tab[j].c = (Obj)ctab[j];
}
bzero(ctab,(min+1)*sizeof(Q));
comm_muld_tab(vl,n,rtab,curlen,tab,k+1,tmptab);
curlen *= k+1;
bcopy(tmptab,rtab,curlen*sizeof(struct cdl));
}
}
/* direct product of two cdl tables
rt[] = [
t[0]*t1[0],...,t[n-1]*t1[0],
t[0]*t1[1],...,t[n-1]*t1[1],
...
t[0]*t1[n1-1],...,t[n-1]*t1[n1-1]
]
*/
void comm_muld_tab(VL vl,int nv,struct cdl *t,int n,struct cdl *t1,int n1,struct cdl *rt)
{
int i,j;
struct cdl *p;
Obj c;
DL d;
bzero(rt,n*n1*sizeof(struct cdl));
for ( j = 0, p = rt; j < n1; j++ ) {
c = (Obj)t1[j].c;
d = t1[j].d;
if ( !c )
break;
for ( i = 0; i < n; i++, p++ ) {
if ( t[i].c ) {
arf_mul(vl,(Obj)t[i].c,c,(Obj *)&p->c);
adddl(nv,t[i].d,d,&p->d);
}
}
}
}
void muldc(VL vl,DP p,Obj c,DP *pr)
{
MP m,mr=0,mr0;
if ( !p || !c )
*pr = 0;
else if ( NUM(c) && UNIQ((Q)c) )
*pr = p;
else if ( NUM(c) && MUNIQ((Q)c) )
chsgnd(p,pr);
else {
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
NEXTMP(mr0,mr);
if ( NUM(C(m)) && RATN(C(m)) && NUM(c) && RATN(c) )
mulq((Q)C(m),(Q)c,(Q *)&C(mr));
else
arf_mul(vl,C(m),c,&C(mr));
mr->dl = m->dl;
}
NEXT(mr) = 0; MKDP(NV(p),mr0,*pr);
if ( *pr )
(*pr)->sugar = p->sugar;
}
}
void divdc(VL vl,DP p,Obj c,DP *pr)
{
Obj inv;
arf_div(vl,(Obj)ONE,c,&inv);
muld(vl,p,(DP)inv,pr);
}
void muldc_trunc(VL vl,DP p,Obj c,DL dl,DP *pr)
{
MP m,mr=0,mr0;
DL mdl;
int i,n;
if ( !p || !c ) {
*pr = 0; return;
}
n = NV(p);
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
mdl = m->dl;
for ( i = 0; i < n; i++ )
if ( mdl->d[i] < dl->d[i] )
break;
if ( i < n )
break;
NEXTMP(mr0,mr);
if ( NUM(C(m)) && RATN(C(m)) && NUM(c) && RATN(c) )
mulq((Q)C(m),(Q)c,(Q *)&C(mr));
else
arf_mul(vl,C(m),c,&C(mr));
mr->dl = m->dl;
}
NEXT(mr) = 0; MKDP(NV(p),mr0,*pr);
if ( *pr )
(*pr)->sugar = p->sugar;
}
void divsdc(VL vl,DP p,P c,DP *pr)
{
MP m,mr=0,mr0;
if ( !c )
error("disvsdc : division by 0");
else if ( !p )
*pr = 0;
else if ( OID(p) != O_DP )
error("divsdc : invalid argument");
else {
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
NEXTMP(mr0,mr); divsp(vl,(P)C(m),c,(P *)&C(mr)); mr->dl = m->dl;
}
NEXT(mr) = 0; MKDP(NV(p),mr0,*pr);
if ( *pr )
(*pr)->sugar = p->sugar;
}
}
void adddl(int n,DL d1,DL d2,DL *dr)
{
DL dt;
int i;
*dr = dt = (DL)MALLOC_ATOMIC((n+1)*sizeof(int));
dt->td = d1->td + d2->td;
for ( i = 0; i < n; i++ )
dt->d[i] = d1->d[i]+d2->d[i];
}
/* d1 += d2 */
void adddl_destructive(int n,DL d1,DL d2)
{
int i;
d1->td += d2->td;
for ( i = 0; i < n; i++ )
d1->d[i] += d2->d[i];
}
int compd(VL vl,DP p1,DP p2)
{
int n,t;
MP m1,m2;
if ( !p1 )
return p2 ? -1 : 0;
else if ( !p2 )
return 1;
else if ( NV(p1) != NV(p2) ) {
error("compd : size mismatch");
return 0; /* XXX */
} else {
for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2);
m1 && m2; m1 = NEXT(m1), m2 = NEXT(m2) )
if ( (t = (*cmpdl)(n,m1->dl,m2->dl)) ||
(t = arf_comp(vl,C(m1),C(m2)) ) )
return t;
if ( m1 )
return 1;
else if ( m2 )
return -1;
else
return 0;
}
}
int cmpdl_lex(int n,DL d1,DL d2)
{
int i;
for ( i = 0; i < n && d1->d[i] == d2->d[i]; i++ );
return i == n ? 0 : (d1->d[i] > d2->d[i] ? 1 : -1);
}
int cmpdl_revlex(int n,DL d1,DL d2)
{
int i;
for ( i = n - 1; i >= 0 && d1->d[i] == d2->d[i]; i-- );
return i < 0 ? 0 : (d1->d[i] < d2->d[i] ? 1 : -1);
}
int cmpdl_gradlex(int n,DL d1,DL d2)
{
if ( d1->td > d2->td )
return 1;
else if ( d1->td < d2->td )
return -1;
else
return cmpdl_lex(n,d1,d2);
}
int cmpdl_revgradlex(int n,DL d1,DL d2)
{
register int i,c;
register int *p1,*p2;
if ( d1->td > d2->td )
return 1;
else if ( d1->td < d2->td )
return -1;
else {
i = n-1;
p1 = d1->d+n-1;
p2 = d2->d+n-1;
while ( i >= 7 ) {
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
i -= 8;
}
switch ( i ) {
case 6:
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
return 0;
case 5:
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
return 0;
case 4:
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
return 0;
case 3:
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
return 0;
case 2:
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
return 0;
case 1:
c = (*p1--) - (*p2--); if ( c ) goto LAST;
c = (*p1--) - (*p2--); if ( c ) goto LAST;
return 0;
case 0:
c = (*p1--) - (*p2--); if ( c ) goto LAST;
return 0;
default:
return 0;
}
LAST:
if ( c > 0 ) return -1;
else return 1;
}
}
int cmpdl_blex(int n,DL d1,DL d2)
{
int c;
if ( (c = cmpdl_lex(n-1,d1,d2)) )
return c;
else {
c = d1->d[n-1] - d2->d[n-1];
return c > 0 ? 1 : c < 0 ? -1 : 0;
}
}
int cmpdl_bgradlex(int n,DL d1,DL d2)
{
int e1,e2,c;
e1 = d1->td - d1->d[n-1]; e2 = d2->td - d2->d[n-1];
if ( e1 > e2 )
return 1;
else if ( e1 < e2 )
return -1;
else {
c = cmpdl_lex(n-1,d1,d2);
if ( c )
return c;
else
return d1->td > d2->td ? 1 : d1->td < d2->td ? -1 : 0;
}
}
int cmpdl_brevgradlex(int n,DL d1,DL d2)
{
int e1,e2,c;
e1 = d1->td - d1->d[n-1]; e2 = d2->td - d2->d[n-1];
if ( e1 > e2 )
return 1;
else if ( e1 < e2 )
return -1;
else {
c = cmpdl_revlex(n-1,d1,d2);
if ( c )
return c;
else
return d1->td > d2->td ? 1 : d1->td < d2->td ? -1 : 0;
}
}
int cmpdl_brevrev(int n,DL d1,DL d2)
{
int e1,e2,f1,f2,c,i;
for ( i = 0, e1 = 0, e2 = 0; i < dp_nelim; i++ ) {
e1 += d1->d[i]; e2 += d2->d[i];
}
f1 = d1->td - e1; f2 = d2->td - e2;
if ( e1 > e2 )
return 1;
else if ( e1 < e2 )
return -1;
else {
c = cmpdl_revlex(dp_nelim,d1,d2);
if ( c )
return c;
else if ( f1 > f2 )
return 1;
else if ( f1 < f2 )
return -1;
else {
for ( i = n - 1; i >= dp_nelim && d1->d[i] == d2->d[i]; i-- );
return i < dp_nelim ? 0 : (d1->d[i] < d2->d[i] ? 1 : -1);
}
}
}
int cmpdl_bgradrev(int n,DL d1,DL d2)
{
int e1,e2,f1,f2,c,i;
for ( i = 0, e1 = 0, e2 = 0; i < dp_nelim; i++ ) {
e1 += d1->d[i]; e2 += d2->d[i];
}
f1 = d1->td - e1; f2 = d2->td - e2;
if ( e1 > e2 )
return 1;
else if ( e1 < e2 )
return -1;
else {
c = cmpdl_lex(dp_nelim,d1,d2);
if ( c )
return c;
else if ( f1 > f2 )
return 1;
else if ( f1 < f2 )
return -1;
else {
for ( i = n - 1; i >= dp_nelim && d1->d[i] == d2->d[i]; i-- );
return i < dp_nelim ? 0 : (d1->d[i] < d2->d[i] ? 1 : -1);
}
}
}
int cmpdl_blexrev(int n,DL d1,DL d2)
{
int e1,e2,f1,f2,c,i;
for ( i = 0, e1 = 0, e2 = 0; i < dp_nelim; i++ ) {
e1 += d1->d[i]; e2 += d2->d[i];
}
f1 = d1->td - e1; f2 = d2->td - e2;
c = cmpdl_lex(dp_nelim,d1,d2);
if ( c )
return c;
else if ( f1 > f2 )
return 1;
else if ( f1 < f2 )
return -1;
else {
for ( i = n - 1; i >= dp_nelim && d1->d[i] == d2->d[i]; i-- );
return i < dp_nelim ? 0 : (d1->d[i] < d2->d[i] ? 1 : -1);
}
}
int cmpdl_elim(int n,DL d1,DL d2)
{
int e1,e2,i;
for ( i = 0, e1 = 0, e2 = 0; i < dp_nelim; i++ ) {
e1 += d1->d[i]; e2 += d2->d[i];
}
if ( e1 > e2 )
return 1;
else if ( e1 < e2 )
return -1;
else
return cmpdl_revgradlex(n,d1,d2);
}
int cmpdl_weyl_elim(int n,DL d1,DL d2)
{
int e1,e2,i;
for ( i = 1, e1 = 0, e2 = 0; i <= dp_nelim; i++ ) {
e1 += d1->d[n-i]; e2 += d2->d[n-i];
}
if ( e1 > e2 )
return 1;
else if ( e1 < e2 )
return -1;
else if ( d1->td > d2->td )
return 1;
else if ( d1->td < d2->td )
return -1;
else return -cmpdl_revlex(n,d1,d2);
}
/*
a special ordering
1. total order
2. (-w,w) for the first 2*m variables
3. DRL for the first 2*m variables
*/
extern int *current_weyl_weight_vector;
int cmpdl_homo_ww_drl(int n,DL d1,DL d2)
{
int e1,e2,m,i;
int *p1,*p2;
if ( d1->td > d2->td )
return 1;
else if ( d1->td < d2->td )
return -1;
m = n>>1;
for ( i = 0, e1 = e2 = 0, p1 = d1->d, p2 = d2->d; i < m; i++ ) {
e1 += current_weyl_weight_vector[i]*(p1[m+i] - p1[i]);
e2 += current_weyl_weight_vector[i]*(p2[m+i] - p2[i]);
}
if ( e1 > e2 )
return 1;
else if ( e1 < e2 )
return -1;
e1 = d1->td - d1->d[n-1];
e2 = d2->td - d2->d[n-1];
if ( e1 > e2 )
return 1;
else if ( e1 < e2 )
return -1;
for ( i= n - 1, p1 = d1->d+n-1, p2 = d2->d+n-1;
i >= 0 && *p1 == *p2; i--, p1--, p2-- );
return i < 0 ? 0 : (*p1 < *p2 ? 1 : -1);
}
int cmpdl_drl_zigzag(int n,DL d1,DL d2)
{
int i,t,m;
int *p1,*p2;
if ( d1->td > d2->td )
return 1;
else if ( d1->td < d2->td )
return -1;
else {
m = n>>1;
for ( i= m - 1, p1 = d1->d, p2 = d2->d; i >= 0; i-- ) {
if ( (t = p1[m+i] - p2[m+i]) ) return t > 0 ? -1 : 1;
if ( (t = p1[i] - p2[i]) ) return t > 0 ? -1 : 1;
}
return 0;
}
}
int cmpdl_homo_ww_drl_zigzag(int n,DL d1,DL d2)
{
int e1,e2,m,i,t;
int *p1,*p2;
if ( d1->td > d2->td )
return 1;
else if ( d1->td < d2->td )
return -1;
m = n>>1;
for ( i = 0, e1 = e2 = 0, p1 = d1->d, p2 = d2->d; i < m; i++ ) {
e1 += current_weyl_weight_vector[i]*(p1[m+i] - p1[i]);
e2 += current_weyl_weight_vector[i]*(p2[m+i] - p2[i]);
}
if ( e1 > e2 )
return 1;
else if ( e1 < e2 )
return -1;
e1 = d1->td - d1->d[n-1];
e2 = d2->td - d2->d[n-1];
if ( e1 > e2 )
return 1;
else if ( e1 < e2 )
return -1;
for ( i= m - 1, p1 = d1->d, p2 = d2->d; i >= 0; i-- ) {
if ( (t = p1[m+i] - p2[m+i]) ) return t > 0 ? -1 : 1;
if ( (t = p1[i] - p2[i]) ) return t > 0 ? -1 : 1;
}
return 0;
}
int cmpdl_order_pair(int n,DL d1,DL d2)
{
int e1,e2,i,j,l;
int *t1,*t2;
int len,head;
struct order_pair *pair;
len = dp_current_spec->ord.block.length;
if ( n != dp_current_spec->nv )
error("cmpdl_order_pair : incompatible order specification");
pair = dp_current_spec->ord.block.order_pair;
head = 0;
for ( i = 0, t1 = d1->d, t2 = d2->d; i < len; i++ ) {
l = pair[i].length;
switch ( pair[i].order ) {
case 0:
for ( j = 0, e1 = e2 = 0; j < l; j++ ) {
e1 += MUL_WEIGHT(t1[j],head+j);
e2 += MUL_WEIGHT(t2[j],head+j);
}
if ( e1 > e2 )
return 1;
else if ( e1 < e2 )
return -1;
else {
for ( j = l - 1; j >= 0 && t1[j] == t2[j]; j-- );
if ( j >= 0 )
return t1[j] < t2[j] ? 1 : -1;
}
break;
case 1:
for ( j = 0, e1 = e2 = 0; j < l; j++ ) {
e1 += MUL_WEIGHT(t1[j],head+j);
e2 += MUL_WEIGHT(t2[j],head+j);
}
if ( e1 > e2 )
return 1;
else if ( e1 < e2 )
return -1;
else {
for ( j = 0; j < l && t1[j] == t2[j]; j++ );
if ( j < l )
return t1[j] > t2[j] ? 1 : -1;
}
break;
case 2:
for ( j = 0; j < l && t1[j] == t2[j]; j++ );
if ( j < l )
return t1[j] > t2[j] ? 1 : -1;
break;
default:
error("cmpdl_order_pair : invalid order"); break;
}
t1 += l; t2 += l; head += l;
}
return 0;
}
int cmpdl_composite(int nv,DL d1,DL d2)
{
int n,i,j,k,start,s,len;
int *dw;
struct sparse_weight *sw;
struct weight_or_block *worb;
int *w,*t1,*t2;
n = dp_current_spec->ord.composite.length;
worb = dp_current_spec->ord.composite.w_or_b;
w = dp_dl_work;
for ( i = 0, t1 = d1->d, t2 = d2->d; i < nv; i++ )
w[i] = t1[i]-t2[i];
for ( i = 0; i < n; i++, worb++ ) {
len = worb->length;
switch ( worb->type ) {
case IS_DENSE_WEIGHT:
dw = worb->body.dense_weight;
for ( j = 0, s = 0; j < len; j++ )
s += dw[j]*w[j];
if ( s > 0 ) return 1;
else if ( s < 0 ) return -1;
break;
case IS_SPARSE_WEIGHT:
sw = worb->body.sparse_weight;
for ( j = 0, s = 0; j < len; j++ )
s += sw[j].value*w[sw[j].pos];
if ( s > 0 ) return 1;
else if ( s < 0 ) return -1;
break;
case IS_BLOCK:
start = worb->body.block.start;
switch ( worb->body.block.order ) {
case 0:
for ( j = 0, k = start, s = 0; j < len; j++, k++ ) {
s += MUL_WEIGHT(w[k],k);
}
if ( s > 0 ) return 1;
else if ( s < 0 ) return -1;
else {
for ( j = k-1; j >= start && w[j] == 0; j-- );
if ( j >= start )
return w[j] < 0 ? 1 : -1;
}
break;
case 1:
for ( j = 0, k = start, s = 0; j < len; j++, k++ ) {
s += MUL_WEIGHT(w[k],k);
}
if ( s > 0 ) return 1;
else if ( s < 0 ) return -1;
else {
for ( j = 0, k = start; j < len && w[j] == 0; j++, k++ );
if ( j < len )
return w[j] > 0 ? 1 : -1;
}
break;
case 2:
for ( j = 0, k = start; j < len && w[j] == 0; j++, k++ );
if ( j < len )
return w[j] > 0 ? 1 : -1;
break;
}
break;
}
}
return 0;
}
int cmpdl_matrix(int n,DL d1,DL d2)
{
int *v,*w,*t1,*t2;
int s,i,j,len;
int **matrix;
for ( i = 0, t1 = d1->d, t2 = d2->d, w = dp_dl_work; i < n; i++ )
w[i] = t1[i]-t2[i];
len = dp_current_spec->ord.matrix.row;
matrix = dp_current_spec->ord.matrix.matrix;
for ( j = 0; j < len; j++ ) {
v = matrix[j];
for ( i = 0, s = 0; i < n; i++ )
s += v[i]*w[i];
if ( s > 0 )
return 1;
else if ( s < 0 )
return -1;
}
return 0;
}
int cmpdl_top_weight(int n,DL d1,DL d2)
{
int *w;
N sum,wm,wma,t;
Q **mat;
Q *a;
struct oN tn;
int len,i,sgn,tsgn,row,k;
int *t1,*t2;
w = (int *)ALLOCA(n*sizeof(int));
len = current_top_weight_len+3;
t1 = d1->d; t2 = d2->d;
for ( i = 0; i < n; i++ ) w[i] = t1[i]-t2[i];
sum = (N)W_ALLOC(len); sgn = 0;
wm = (N)W_ALLOC(len);
wma = (N)W_ALLOC(len);
if ( OID(current_top_weight) == O_VECT ) {
mat = (Q **)&BDY((VECT)current_top_weight);
row = 1;
} else {
mat = (Q **)BDY((MAT)current_top_weight);
row = ((MAT)current_top_weight)->row;
}
for ( k = 0; k < row; k++ ) {
a = mat[k];
for ( i = 0; i < n; i++ ) {
if ( !a[i] || !w[i] ) continue;
tn.p = 1;
if ( w[i] > 0 ) {
tn.b[0] = w[i]; tsgn = 1;
} else {
tn.b[0] = -w[i]; tsgn = -1;
}
_muln(NM(a[i]),&tn,wm);
if ( !sgn ) {
sgn = tsgn;
t = wm; wm = sum; sum = t;
} else if ( sgn == tsgn ) {
_addn(sum,wm,wma);
if ( !PL(wma) )
sgn = 0;
t = wma; wma = sum; sum = t;
} else {
sgn *= _subn(sum,wm,wma);
t = wma; wma = sum; sum = t;
}
}
if ( sgn > 0 ) return 1;
else if ( sgn < 0 ) return -1;
}
return (*cmpdl_tie_breaker)(n,d1,d2);
}
GeoBucket create_bucket()
{
GeoBucket g;
g = CALLOC(1,sizeof(struct oGeoBucket));
g->m = 32;
return g;
}
int length(NODE d);
void add_bucket(GeoBucket g,NODE d,int nv)
{
int l,k,m;
l = length(d);
for ( k = 0, m = 1; l > m; k++, m <<= 1 );
/* 2^(k-1) < l <= 2^k */
d = symb_merge(g->body[k],d,nv);
for ( ; length(d) > (1<<(k)); k++ ) {
g->body[k] = 0;
d = symb_merge(g->body[k+1],d,nv);
}
g->body[k] = d;
g->m = MAX(g->m,k);
}
DL remove_head_bucket(GeoBucket g,int nv)
{
int j,i,c,m;
DL d;
j = -1;
m = g->m;
for ( i = 0; i <= m; i++ ) {
if ( !g->body[i] )
continue;
if ( j < 0 ) j = i;
else {
c = (*cmpdl)(nv,g->body[i]->body,g->body[j]->body);
if ( c > 0 )
j = i;
else if ( c == 0 )
g->body[i] = NEXT(g->body[i]);
}
}
if ( j < 0 )
return 0;
else {
d = g->body[j]->body;
g->body[j] = NEXT(g->body[j]);
return d;
}
}
/* DPV functions */
void adddv(VL vl,DPV p1,DPV p2,DPV *pr)
{
int i,len;
DP *e;
if ( !p1 || !p2 )
error("adddv : invalid argument");
else if ( p1->len != p2->len )
error("adddv : size mismatch");
else {
len = p1->len;
e = (DP *)MALLOC(p1->len*sizeof(DP));
for ( i = 0; i < len; i++ )
addd(vl,p1->body[i],p2->body[i],&e[i]);
MKDPV(len,e,*pr);
(*pr)->sugar = MAX(p1->sugar,p2->sugar);
}
}
void subdv(VL vl,DPV p1,DPV p2,DPV *pr)
{
int i,len;
DP *e;
if ( !p1 || !p2 )
error("subdv : invalid argument");
else if ( p1->len != p2->len )
error("subdv : size mismatch");
else {
len = p1->len;
e = (DP *)MALLOC(p1->len*sizeof(DP));
for ( i = 0; i < len; i++ )
subd(vl,p1->body[i],p2->body[i],&e[i]);
MKDPV(len,e,*pr);
(*pr)->sugar = MAX(p1->sugar,p2->sugar);
}
}
void chsgndv(DPV p1,DPV *pr)
{
int i,len;
DP *e;
if ( !p1 )
error("subdv : invalid argument");
else {
len = p1->len;
e = (DP *)MALLOC(p1->len*sizeof(DP));
for ( i = 0; i < len; i++ )
chsgnd(p1->body[i],&e[i]);
MKDPV(len,e,*pr);
(*pr)->sugar = p1->sugar;
}
}
void muldv(VL vl,DP p1,DPV p2,DPV *pr)
{
int i,len;
DP *e;
len = p2->len;
e = (DP *)MALLOC(p2->len*sizeof(DP));
if ( !p1 ) {
MKDPV(len,e,*pr);
(*pr)->sugar = 0;
} else {
for ( i = 0; i < len; i++ )
muld(vl,p1,p2->body[i],&e[i]);
MKDPV(len,e,*pr);
(*pr)->sugar = p1->sugar + p2->sugar;
}
}
int compdv(VL vl,DPV p1,DPV p2)
{
int i,t,len;
if ( p1->len != p2->len ) {
error("compdv : size mismatch");
return 0; /* XXX */
} else {
len = p1->len;
for ( i = 0; i < len; i++ )
if ( (t = compd(vl,p1->body[i],p2->body[i])) )
return t;
return 0;
}
}
int ni_next(int *a,int n)
{
int i,j,k,kj;
/* find the first nonzero a[j] */
for ( j = 0; j < n && a[j] == 0; j++ );
/* find the first zero a[k] after a[j] */
for ( k = j; k < n && a[k] == 1; k++ );
if ( k == n ) return 0;
/* a[0] = 0, ... , a[j-1] = 0, a[j] = 1, ..., a[k-1] = 1, a[k] = 0 */
/* a[0] = 1,..., a[k-j-2] = 1, a[k-j-1] = 0, ..., a[k-1] = 0, a[k] = 1 */
kj = k-j-1;
for ( i = 0; i < kj; i++ ) a[i] = 1;
for ( ; i < k; i++ ) a[i] = 0;
a[k] = 1;
return 1;
}
int comp_nbm(NBM a,NBM b)
{
int d,i,ai,bi;
int *ab,*bb;
if ( a->d > b->d ) return 1;
else if ( a->d < b->d ) return -1;
else {
d = a->d; ab = a->b; bb = b->b;
#if 0
w = (d+31)/32;
for ( i = 0; i < w; i++ )
if ( ab[i] > bb[i] ) return 1;
else if ( ab[i] < bb[i] ) return -1;
#else
for ( i = 0; i < d; i++ ) {
ai = NBM_GET(ab,i);
bi = NBM_GET(bb,i);
if ( ai > bi ) return 1;
else if ( ai < bi ) return -1;
}
#endif
return 0;
}
}
NBM mul_nbm(NBM a,NBM b)
{
int ad,bd,d,i,j;
int *ab,*bb,*mb;
NBM m;
ad = a->d; bd = b->d; ab = a->b; bb = b->b;
d = ad + bd;
NEWNBM(m); NEWNBMBDY(m,d);
m->d = d; mulp(CO,a->c,b->c,&m->c); mb = m->b;
j = 0;
for ( i = 0; i < ad; i++, j++ )
if ( NBM_GET(ab,i) ) NBM_SET(mb,j);
else NBM_CLR(mb,j);
for ( i = 0; i < bd; i++, j++ )
if ( NBM_GET(bb,i) ) NBM_SET(mb,j);
else NBM_CLR(mb,j);
return m;
}
NBP nbmtonbp(NBM m)
{
NODE n;
NBP u;
MKNODE(n,m,0);
MKNBP(u,n);
return u;
}
/* a=c*x*rest -> a0= x*rest, ah=x, ar=rest */
P separate_nbm(NBM a,NBP *a0,NBP *ah,NBP *ar)
{
int i,d1;
NBM t;
if ( !a->d ) error("separate_nbm : invalid argument");
if ( a0 ) {
NEWNBM(t); t->d = a->d; t->b = a->b; t->c = (P)ONE;
*a0 = nbmtonbp(t);
}
if ( ah ) {
NEWNBM(t); NEWNBMBDY(t,1); t->d = 1; t->c = (P)ONE;
if ( NBM_GET(a->b,0) ) NBM_SET(t->b,0);
else NBM_CLR(t->b,0);
*ah = nbmtonbp(t);
}
if ( ar ) {
d1 = a->d-1;
NEWNBM(t); NEWNBMBDY(t,d1); t->d = d1; t->c = (P)ONE;
for ( i = 0; i < d1; i++ ) {
if ( NBM_GET(a->b,i+1) ) NBM_SET(t->b,i);
else NBM_CLR(t->b,i);
}
*ar = nbmtonbp(t);
}
return a->c;
}
/* a=c*rest*x -> a0= rest*x, ar=rest, at=x */
P separate_tail_nbm(NBM a,NBP *a0,NBP *ar,NBP *at)
{
int i,d,d1;
NBM t;
if ( !(d=a->d) ) error("separate_tail_nbm : invalid argument");
if ( a0 ) {
NEWNBM(t); t->d = a->d; t->b = a->b; t->c = (P)ONE;
*a0 = nbmtonbp(t);
}
d1 = a->d-1;
if ( at ) {
NEWNBM(t); NEWNBMBDY(t,1); t->d = 1; t->c = (P)ONE;
if ( NBM_GET(a->b,d1) ) NBM_SET(t->b,0);
else NBM_CLR(t->b,0);
*at = nbmtonbp(t);
}
if ( ar ) {
NEWNBM(t); NEWNBMBDY(t,d1); t->d = d1; t->c = (P)ONE;
for ( i = 0; i < d1; i++ ) {
if ( NBM_GET(a->b,i) ) NBM_SET(t->b,i);
else NBM_CLR(t->b,i);
}
*ar = nbmtonbp(t);
}
return a->c;
}
NBP make_xky(int k)
{
int k1,i;
NBM t;
NEWNBM(t); NEWNBMBDY(t,k); t->d = k; t->c = (P)ONE;
k1 = k-1;
for ( i = 0; i < k1; i++ ) NBM_SET(t->b,i);
NBM_CLR(t->b,i);
return nbmtonbp(t);
}
/* a=c*x^(k-1)*y*rest -> a0= x^(k-1)*y*rest, ah=x^(k-1)*y, ar=rest */
P separate_xky_nbm(NBM a,NBP *a0,NBP *ah,NBP *ar)
{
int i,d1,k,k1;
NBM t;
if ( !a->d )
error("separate_nbm : invalid argument");
for ( i = 0; i < a->d && NBM_GET(a->b,i); i++ );
if ( i == a->d )
error("separate_nbm : invalid argument");
k1 = i;
k = i+1;
if ( a0 ) {
NEWNBM(t); t->d = a->d; t->b = a->b; t->c = (P)ONE;
*a0 = nbmtonbp(t);
}
if ( ah ) {
NEWNBM(t); NEWNBMBDY(t,k); t->d = k; t->c = (P)ONE;
for ( i = 0; i < k1; i++ ) NBM_SET(t->b,i);
NBM_CLR(t->b,i);
*ah = nbmtonbp(t);
}
if ( ar ) {
d1 = a->d-k;
NEWNBM(t); NEWNBMBDY(t,d1); t->d = d1; t->c = (P)ONE;
for ( i = 0; i < d1; i++ ) {
if ( NBM_GET(a->b,i+k) ) NBM_SET(t->b,i);
else NBM_CLR(t->b,i);
}
*ar = nbmtonbp(t);
}
return a->c;
}
void shuffle_mulnbp(VL vl,NBP p1,NBP p2, NBP *rp);
void harmonic_mulnbp(VL vl,NBP p1,NBP p2, NBP *rp);
void mulnbmnbp(VL vl,NBM m,NBP p, NBP *rp);
void mulnbpnbm(VL vl,NBP p,NBM m, NBP *rp);
NBP shuffle_mul_nbm(NBM a,NBM b)
{
NBP u,a0,ah,ar,b0,bh,br,a1,b1,t;
P ac,bc,c;
if ( !a->d || !b->d )
u = nbmtonbp(mul_nbm(a,b));
else {
ac = separate_nbm(a,&a0,&ah,&ar);
bc = separate_nbm(b,&b0,&bh,&br);
mulp(CO,ac,bc,&c);
shuffle_mulnbp(CO,ar,b0,&t); mulnbp(CO,ah,t,&a1);
shuffle_mulnbp(CO,a0,br,&t); mulnbp(CO,bh,t,&b1);
addnbp(CO,a1,b1,&t); mulnbp(CO,(NBP)c,t,&u);
}
return u;
}
NBP harmonic_mul_nbm(NBM a,NBM b)
{
NBP u,a0,ah,ar,b0,bh,br,a1,b1,t,s,abk,ab1;
P ac,bc,c;
if ( !a->d || !b->d )
u = nbmtonbp(mul_nbm(a,b));
else {
mulp(CO,a->c,b->c,&c);
ac = separate_xky_nbm(a,&a0,&ah,&ar);
bc = separate_xky_nbm(b,&b0,&bh,&br);
mulp(CO,ac,bc,&c);
harmonic_mulnbp(CO,ar,b0,&t); mulnbp(CO,ah,t,&a1);
harmonic_mulnbp(CO,a0,br,&t); mulnbp(CO,bh,t,&b1);
abk = make_xky(((NBM)BDY(BDY(ah)))->d+((NBM)BDY(BDY(bh)))->d);
harmonic_mulnbp(CO,ar,br,&t); mulnbp(CO,abk,t,&ab1);
addnbp(CO,a1,b1,&t); addnbp(CO,t,ab1,&s); mulnbp(CO,(NBP)c,s,&u);
}
return u;
}
void addnbp(VL vl,NBP p1,NBP p2, NBP *rp)
{
NODE b1,b2,br=0,br0;
NBM m1,m2,m;
P c;
if ( !p1 )
*rp = p2;
else if ( !p2 )
*rp = p1;
else {
for ( b1 = BDY(p1), b2 = BDY(p2), br0 = 0; b1 && b2; ) {
m1 = (NBM)BDY(b1); m2 = (NBM)BDY(b2);
switch ( comp_nbm(m1,m2) ) {
case 0:
addp(CO,m1->c,m2->c,&c);
if ( c ) {
NEXTNODE(br0,br);
NEWNBM(m); m->d = m1->d; m->c = c; m->b = m1->b;
BDY(br) = (pointer)m;
}
b1 = NEXT(b1); b2 = NEXT(b2); break;
case 1:
NEXTNODE(br0,br); BDY(br) = BDY(b1);
b1 = NEXT(b1); break;
case -1:
NEXTNODE(br0,br); BDY(br) = BDY(b2);
b2 = NEXT(b2); break;
}
}
if ( !br0 )
if ( b1 )
br0 = b1;
else if ( b2 )
br0 = b2;
else {
*rp = 0;
return;
}
else if ( b1 )
NEXT(br) = b1;
else if ( b2 )
NEXT(br) = b2;
else
NEXT(br) = 0;
MKNBP(*rp,br0);
}
}
void subnbp(VL vl,NBP p1,NBP p2, NBP *rp)
{
NBP t;
chsgnnbp(p2,&t);
addnbp(vl,p1,t,rp);
}
void chsgnnbp(NBP p,NBP *rp)
{
NODE r0,r=0,b;
NBM m,m1;
for ( r0 = 0, b = BDY(p); b; b = NEXT(b) ) {
NEXTNODE(r0,r);
m = (NBM)BDY(b);
NEWNBM(m1); m1->d = m->d; m1->b = m->b; chsgnp(m->c,&m1->c);
BDY(r) = m1;
}
if ( r0 ) NEXT(r) = 0;
MKNBP(*rp,r0);
}
void mulnbp(VL vl,NBP p1,NBP p2, NBP *rp)
{
NODE b,n;
NBP r,t,s;
NBM m;
if ( !p1 || !p2 ) {
*rp = 0; return;
}
if ( OID(p1) != O_NBP ) {
if ( !POLY(p1) )
error("mulnbp : invalid argument");
NEWNBM(m); m->d = 0; m->b = 0; m->c = (P)p1;
MKNODE(n,m,0); MKNBP(p1,n);
}
if ( OID(p2) != O_NBP ) {
if ( !POLY(p2) )
error("mulnbp : invalid argument");
NEWNBM(m); m->d = 0; m->b = 0; m->c = (P)p2;
MKNODE(n,m,0); MKNBP(p2,n);
}
if ( length(BDY(p1)) < length(BDY(p2)) ) {
for ( r = 0, b = BDY(p1); b; b = NEXT(b) ) {
mulnbmnbp(vl,(NBM)BDY(b),p2,&t);
addnbp(vl,r,t,&s); r = s;
}
*rp = r;
} else {
for ( r = 0, b = BDY(p2); b; b = NEXT(b) ) {
mulnbpnbm(vl,p1,(NBM)BDY(b),&t);
addnbp(vl,r,t,&s); r = s;
}
*rp = r;
}
}
void mulnbmnbp(VL vl,NBM m,NBP p, NBP *rp)
{
NODE b,r0,r=0;
if ( !p ) *rp = 0;
else {
for ( r0 = 0, b = BDY(p); b; b = NEXT(b) ) {
NEXTNODE(r0,r);
BDY(r) = mul_nbm(m,(NBM)BDY(b));
}
if ( r0 ) NEXT(r) = 0;
MKNBP(*rp,r0);
}
}
void mulnbpnbm(VL vl,NBP p,NBM m, NBP *rp)
{
NODE b,r0,r=0;
if ( !p ) *rp = 0;
else {
for ( r0 = 0, b = BDY(p); b; b = NEXT(b) ) {
NEXTNODE(r0,r);
BDY(r) = mul_nbm((NBM)BDY(b),m);
}
if ( r0 ) NEXT(r) = 0;
MKNBP(*rp,r0);
}
}
void pwrnbp(VL vl,NBP a,Q q,NBP *c)
{
int t;
NBP a1,a2;
N n1;
Q q1;
NBM m;
NODE r;
if ( !q ) {
NEWNBM(m); m->d = 0; m->c = (P)ONE; m->b = 0;
MKNODE(r,m,0); MKNBP(*c,r);
} else if ( !a )
*c = 0;
else if ( UNIQ(q) )
*c = a;
else {
t = divin(NM(q),2,&n1); NTOQ(n1,1,q1);
pwrnbp(vl,a,q1,&a1);
mulnbp(vl,a1,a1,&a2);
if ( t )
mulnbp(vl,a2,a,c);
else
*c = a2;
}
}
int compnbp(VL vl,NBP p1,NBP p2)
{
NODE n1,n2;
NBM m1,m2;
int t;
if ( !p1 )
return p2 ? -1 : 0;
else if ( !p2 )
return 1;
else {
for ( n1 = BDY(p1), n2 = BDY(p2);
n1 && n2; n1 = NEXT(n1), n2 = NEXT(n2) ) {
m1 = (NBM)BDY(n1); m2 = (NBM)BDY(n2);
if ( (t = comp_nbm(m1,m2)) || (t = compp(CO,m1->c,m2->c) ) )
return t;
}
if ( n1 )
return 1;
else if ( n2 )
return -1;
else
return 0;
}
}
void shuffle_mulnbp(VL vl,NBP p1,NBP p2, NBP *rp)
{
NODE b1,b2,n;
NBP r,t,s;
NBM m;
if ( !p1 || !p2 ) {
*rp = 0; return;
}
if ( OID(p1) != O_NBP ) {
if ( !POLY(p1) )
error("shuffle_mulnbp : invalid argument");
NEWNBM(m); m->d = 0; m->b = 0; m->c = (P)p1;
MKNODE(n,m,0); MKNBP(p1,n);
}
if ( OID(p2) != O_NBP ) {
if ( !POLY(p2) )
error("shuffle_mulnbp : invalid argument");
NEWNBM(m); m->d = 0; m->b = 0; m->c = (P)p2;
MKNODE(n,m,0); MKNBP(p2,n);
}
for ( r = 0, b1 = BDY(p1); b1; b1 = NEXT(b1) )
for ( m = BDY(b1), b2 = BDY(p2); b2; b2 = NEXT(b2) ) {
t = shuffle_mul_nbm(m,(NBM)BDY(b2));
addnbp(vl,r,t,&s); r = s;
}
*rp = r;
}
void harmonic_mulnbp(VL vl,NBP p1,NBP p2, NBP *rp)
{
NODE b1,b2,n;
NBP r,t,s;
NBM m;
if ( !p1 || !p2 ) {
*rp = 0; return;
}
if ( OID(p1) != O_NBP ) {
if ( !POLY(p1) )
error("harmonic_mulnbp : invalid argument");
NEWNBM(m); m->d = 0; m->b = 0; m->c = (P)p1;
MKNODE(n,m,0); MKNBP(p1,n);
}
if ( OID(p2) != O_NBP ) {
if ( !POLY(p2) )
error("harmonic_mulnbp : invalid argument");
NEWNBM(m); m->d = 0; m->b = 0; m->c = (P)p2;
MKNODE(n,m,0); MKNBP(p2,n);
}
for ( r = 0, b1 = BDY(p1); b1; b1 = NEXT(b1) )
for ( m = BDY(b1), b2 = BDY(p2); b2; b2 = NEXT(b2) ) {
t = harmonic_mul_nbm(m,(NBM)BDY(b2));
addnbp(vl,r,t,&s); r = s;
}
*rp = r;
}
#if 0
NBP shuffle_mul_nbm(NBM a,NBM b)
{
int ad,bd,d,i,ai,bi,bit,s;
int *ab,*bb,*wmb,*w;
NBM wm,tm;
P c,c1;
NODE r,t,t1,p;
NBP u;
ad = a->d; bd = b->d; ab = a->b; bb = b->b;
d = ad + bd;
w = (int *)ALLOCA(d*sizeof(int));
NEWNBM(wm); NEWNBMBDY(wm,d); wmb = wm->b;
for ( i = 0; i < ad; i++ ) w[i] = 1;
for ( ; i < d; i++ ) w[i] = 0;
mulp(CO,a->c,b->c,&c);
r = 0;
do {
wm->d = d; wm->c = c;
ai = 0; bi = 0;
for ( i = 0; i < d; i++ ) {
if ( w[i] ) { bit = NBM_GET(ab,ai); ai++; }
else { bit = NBM_GET(bb,bi); bi++; }
if ( bit ) NBM_SET(wmb,i);
else NBM_CLR(wmb,i);
}
for ( p = 0, t = r; t; p = t, t = NEXT(t) ) {
tm = (NBM)BDY(t);
s = comp_nbm(tm,wm);
if ( s < 0 ) {
/* insert */
MKNODE(t1,wm,t);
if ( !p ) r = t1;
else NEXT(p) = t1;
NEWNBM(wm); NEWNBMBDY(wm,d); wmb = wm->b;
break;
} else if ( s == 0 ) {
/* add coefs */
addp(CO,tm->c,c,&c1);
if ( c1 ) tm->c = c1;
else NEXT(p) = NEXT(t);
break;
}
}
if ( !t ) {
/* append */
MKNODE(t1,wm,t);
if ( !p ) r = t1;
else NEXT(p) = t1;
NEWNBM(wm); NEWNBMBDY(wm,d); wmb = wm->b;
}
} while ( ni_next(w,d) );
MKNBP(u,r);
return u;
}
int nbmtoxky(NBM a,int *b)
{
int d,i,j,k;
int *p;
d = a->d; p = a->b;
for ( i = j = 0, k = 1; i < d; i++ ) {
if ( !NBM_GET(p,i) ) {
b[j++] = k;
k = 1;
} else k++;
}
return j;
}
NBP harmonic_mul_nbm(NBM a,NBM b)
{
int da,db,d,la,lb,lmax,lmin,l,lab,la1,lb1,lab1;
int i,j,k,ia,ib,s;
int *wa,*wb,*w,*wab,*wa1,*wmb;
P c,c1;
NBM wm,tm;
NODE r,t1,t,p;
NBP u;
da = a->d; db = b->d; d = da+db;
wa = (int *)ALLOCA(da*sizeof(int));
wb = (int *)ALLOCA(db*sizeof(int));
la = nbmtoxky(a,wa);
lb = nbmtoxky(b,wb);
mulp(CO,a->c,b->c,&c);
/* wa[0],..,wa[la-1] <-> x^wa[0]y x^wa[1]y .. */
/* lmax : total length */
lmax = la+lb;
lmin = la>lb?la:lb;
w = (int *)ALLOCA(lmax*sizeof(int));
/* position of a+b */
wab = (int *)ALLOCA(lmax*sizeof(int));
/* position of a */
wa1 = (int *)ALLOCA(lmax*sizeof(int));
NEWNBM(wm); NEWNBMBDY(wm,d); wmb = wm->b;
for ( l = lmin, r = 0; l <= lmax; l++ ) {
lab = lmax - l;
la1 = la - lab;
lb1 = lb - lab;
lab1 = l-lab;
/* partion l into three parts: a, b, a+b */
/* initialize wab */
for ( i = 0; i < lab; i++ ) wab[i] = 1;
for ( ; i < l; i++ ) wab[i] = 0;
do {
/* initialize wa1 */
for ( i = 0; i < la1; i++ ) wa1[i] = 1;
for ( ; i < lab1; i++ ) wa1[i] = 0;
do {
ia = 0; ib = 0;
for ( i = j = 0; i < l; i++ )
if ( wab[i] ) w[i] = wa[ia++]+wb[ib++];
else if ( wa1[j++] ) w[i] = wa[ia++];
else w[i] = wb[ib++];
for ( i = j = 0; i < l; i++ ) {
for ( k = w[i]-1; k > 0; k--, j++ ) NBM_SET(wmb,j);
NBM_CLR(wmb,j); j++;
}
wm->d = j; wm->c = c;
for ( p = 0, t = r; t; p = t, t = NEXT(t) ) {
tm = (NBM)BDY(t);
s = comp_nbm(tm,wm);
if ( s < 0 ) {
/* insert */
MKNODE(t1,wm,t);
if ( !p ) r = t1;
else NEXT(p) = t1;
NEWNBM(wm); NEWNBMBDY(wm,d); wmb = wm->b;
break;
} else if ( s == 0 ) {
/* add coefs */
addp(CO,tm->c,c,&c1);
if ( c1 ) tm->c = c1;
else NEXT(p) = NEXT(t);
break;
}
}
if ( !t ) {
/* append */
MKNODE(t1,wm,t);
if ( !p ) r = t1;
else NEXT(p) = t1;
NEWNBM(wm); NEWNBMBDY(wm,d); wmb = wm->b;
}
} while ( ni_next(wa1,lab1) );
} while ( ni_next(wab,l) );
}
MKNBP(u,r);
return u;
}
#endif
/* DPM functions */
int compdmm(int n,DMM m1,DMM m2)
{
int t;
if ( dpm_ispot ) {
if ( m1->pos < m2->pos ) return 1;
else if ( m1->pos > m2->pos ) return -1;
else return (*cmpdl)(n,m1->dl,m2->dl);
} else {
t = (*cmpdl)(n,m1->dl,m2->dl);
if ( t ) return t;
else if ( m1->pos < m2->pos ) return 1;
else if ( m1->pos > m2->pos ) return -1;
else return 0;
}
}
void adddpm(VL vl,DPM p1,DPM p2,DPM *pr)
{
int n;
DMM m1,m2,mr=0,mr0;
Obj t;
DL d;
if ( !p1 )
*pr = p2;
else if ( !p2 )
*pr = p1;
else {
for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; )
switch ( compdmm(n,m1,m2) ) {
case 0:
arf_add(vl,C(m1),C(m2),&t);
if ( t ) {
NEXTDMM(mr0,mr); mr->pos = m1->pos; mr->dl = m1->dl; C(mr) = t;
}
m1 = NEXT(m1); m2 = NEXT(m2); break;
case 1:
NEXTDMM(mr0,mr); mr->pos = m1->pos; mr->dl = m1->dl; C(mr) = C(m1);
m1 = NEXT(m1); break;
case -1:
NEXTDMM(mr0,mr); mr->pos = m2->pos; mr->dl = m2->dl; C(mr) = C(m2);
m2 = NEXT(m2); break;
}
if ( !mr0 )
if ( m1 )
mr0 = m1;
else if ( m2 )
mr0 = m2;
else {
*pr = 0;
return;
}
else if ( m1 )
NEXT(mr) = m1;
else if ( m2 )
NEXT(mr) = m2;
else
NEXT(mr) = 0;
MKDPM(NV(p1),mr0,*pr);
if ( *pr )
(*pr)->sugar = MAX(p1->sugar,p2->sugar);
}
}
void subdpm(VL vl,DPM p1,DPM p2,DPM *pr)
{
DPM t;
if ( !p2 )
*pr = p1;
else {
chsgndpm(p2,&t); adddpm(vl,p1,t,pr);
}
}
void chsgndpm(DPM p,DPM *pr)
{
DMM m,mr=0,mr0;
Obj r;
if ( !p )
*pr = 0;
else {
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
NEXTDMM(mr0,mr); arf_chsgn(C(m),&C(mr)); mr->pos = m->pos; mr->dl = m->dl;
}
NEXT(mr) = 0; MKDPM(NV(p),mr0,*pr);
if ( *pr )
(*pr)->sugar = p->sugar;
}
}
void mulcdpm(VL vl,Obj c,DPM p,DPM *pr)
{
DMM m,mr=0,mr0;
if ( !p || !c )
*pr = 0;
else if ( NUM(c) && UNIQ((Q)c) )
*pr = p;
else if ( NUM(c) && MUNIQ((Q)c) )
chsgndpm(p,pr);
else {
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
NEXTDMM(mr0,mr);
arf_mul(vl,C(m),c,&C(mr));
mr->pos = m->pos;
mr->dl = m->dl;
}
NEXT(mr) = 0; MKDPM(NV(p),mr0,*pr);
if ( *pr )
(*pr)->sugar = p->sugar;
}
}
void comm_mulmpdpm(VL vl,MP m0,DPM p,DPM *pr)
{
DMM m,mr=0,mr0;
DL d;
Obj c;
int n;
if ( !p )
*pr = 0;
else {
n = NV(p);
d = m0->dl;
c = C(m0);
for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) {
NEXTDMM(mr0,mr);
arf_mul(vl,C(m),c,&C(mr));
mr->pos = m->pos;
adddl(n,m->dl,d,&mr->dl);
}
NEXT(mr) = 0; MKDPM(NV(p),mr0,*pr);
if ( *pr )
(*pr)->sugar = p->sugar;
}
}
void weyl_mulmpdpm(VL vl,MP m0,DPM p,DPM *pr)
{
DPM r,t,t1;
DMM m;
DL d0;
int n,n2,l,i,j,tlen;
struct oMP mp;
static DMM *w,*psum;
static struct cdl *tab;
static int wlen;
static int rtlen;
if ( !p )
*pr = 0;
else {
for ( m = BDY(p), l = 0; m; m = NEXT(m), l++ );
if ( l > wlen ) {
if ( w ) GCFREE(w);
w = (DMM *)MALLOC(l*sizeof(DMM));
wlen = l;
}
for ( m = BDY(p), i = 0; i < l; m = NEXT(m), i++ )
w[i] = m;
n = NV(p); n2 = n>>1;
d0 = m0->dl;
for ( i = 0, tlen = 1; i < n2; i++ )
tlen *= d0->d[n2+i]+1;
if ( tlen > rtlen ) {
if ( tab ) GCFREE(tab);
if ( psum ) GCFREE(psum);
rtlen = tlen;
tab = (struct cdl *)MALLOC(rtlen*sizeof(struct cdl));
psum = (DMM *)MALLOC(rtlen*sizeof(DMM));
}
bzero(psum,tlen*sizeof(DMM));
for ( i = l-1; i >= 0; i-- ) {
bzero(tab,tlen*sizeof(struct cdl));
mp.dl = w[i]->dl; mp.c = C(w[i]); mp.next = 0;
weyl_mulmm(vl,m0,&mp,n,tab,tlen);
for ( j = 0; j < tlen; j++ ) {
if ( tab[j].c ) {
NEWDMM(m); m->dl = tab[j].d; m->pos = w[i]->pos; C(m) = (Obj)tab[j].c; NEXT(m) = psum[j];
psum[j] = m;
}
}
}
for ( j = tlen-1, r = 0; j >= 0; j-- )
if ( psum[j] ) {
MKDPM(n,psum[j],t); adddpm(vl,r,t,&t1); r = t1;
}
if ( r )
r->sugar = p->sugar + m0->dl->td;
*pr = r;
}
}
void mulobjdpm(VL vl,Obj p1,DPM p2,DPM *pr)
{
MP m;
DPM s,t,u;
if ( !p1 || !p2 )
*pr = 0;
else if ( OID(p1) != O_DP )
mulcdpm(vl,p1,p2,pr);
else {
s = 0;
for ( m = BDY((DP)p1); m; m = NEXT(m) ) {
if ( do_weyl )
weyl_mulmpdpm(vl,m,p2,&t);
else
comm_mulmpdpm(vl,m,p2,&t);
adddpm(vl,s,t,&u); s = u;
}
*pr = s;
}
}
int compdpm(VL vl,DPM p1,DPM p2)
{
int n,t;
DMM m1,m2;
if ( !p1 )
return p2 ? -1 : 0;
else if ( !p2 )
return 1;
else if ( NV(p1) != NV(p2) ) {
error("compdpm : size mismatch");
return 0; /* XXX */
} else {
for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2);
m1 && m2; m1 = NEXT(m1), m2 = NEXT(m2) )
if ( (t = compdmm(n,m1,m2)) ||
(t = arf_comp(vl,C(m1),C(m2)) ) )
return t;
if ( m1 )
return 1;
else if ( m2 )
return -1;
else
return 0;
}
}