=================================================================== RCS file: /home/cvs/OpenXM_contrib2/asir2000/engine/dist.c,v retrieving revision 1.1 retrieving revision 1.53 diff -u -p -r1.1 -r1.53 --- OpenXM_contrib2/asir2000/engine/dist.c 1999/12/03 07:39:08 1.1 +++ OpenXM_contrib2/asir2000/engine/dist.c 2018/03/29 01:32:51 1.53 @@ -1,9 +1,54 @@ -/* $OpenXM: OpenXM/src/asir99/engine/dist.c,v 1.1.1.1 1999/11/10 08:12:26 noro Exp $ */ +/* + * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED + * All rights reserved. + * + * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited, + * non-exclusive and royalty-free license to use, copy, modify and + * redistribute, solely for non-commercial and non-profit purposes, the + * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and + * conditions of this Agreement. For the avoidance of doubt, you acquire + * only a limited right to use the SOFTWARE hereunder, and FLL or any + * third party developer retains all rights, including but not limited to + * copyrights, in and to the SOFTWARE. + * + * (1) FLL does not grant you a license in any way for commercial + * purposes. You may use the SOFTWARE only for non-commercial and + * non-profit purposes only, such as academic, research and internal + * business use. + * (2) The SOFTWARE is protected by the Copyright Law of Japan and + * international copyright treaties. If you make copies of the SOFTWARE, + * with or without modification, as permitted hereunder, you shall affix + * to all such copies of the SOFTWARE the above copyright notice. + * (3) An explicit reference to this SOFTWARE and its copyright owner + * shall be made on your publication or presentation in any form of the + * results obtained by use of the SOFTWARE. + * (4) In the event that you modify the SOFTWARE, you shall notify FLL by + * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification + * for such modification or the source code of the modified part of the + * SOFTWARE. + * + * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL + * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND + * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS + * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES' + * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY + * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY. + * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT, + * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY + * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL + * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES + * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES + * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY + * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF + * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART + * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY + * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE, + * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE. + * + * $OpenXM: OpenXM_contrib2/asir2000/engine/dist.c,v 1.52 2017/08/31 02:36:21 noro Exp $ +*/ #include "ca.h" -#define NV(p) ((p)->nv) -#define C(p) ((p)->c) - #define ORD_REVGRADLEX 0 #define ORD_GRADLEX 1 #define ORD_LEX 2 @@ -14,748 +59,2825 @@ #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 order_spec *dp_current_spec; +struct modorder_spec *dp_current_modspec; int *dp_dl_work; -int has_fcoef(DP); -int has_fcoef_p(P); +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); -int has_fcoef(f) -DP f; +void order_init() { - MP t; + struct order_spec *spec; - if ( !f ) - return 0; - for ( t = BDY(f); t; t = NEXT(t) ) - if ( has_fcoef_p(t->c) ) - break; - return t ? 1 : 0; + create_order_spec(0,0,&spec); + initd(spec); + create_modorder_spec(0,0,&dp_current_modspec); } -int has_fcoef_p(f) -P f; +int has_sfcoef_p(Obj f); + +int has_sfcoef(DP f) { - DCP dc; + MP t; - if ( !f ) - return 0; - else if ( NUM(f) ) - return (NID((Num)f) == N_LM || NID((Num)f) == N_GF2N) ? 1 : 0; - else { - for ( dc = DC(f); dc; dc = NEXT(dc) ) - if ( has_fcoef_p(COEF(dc)) ) - return 1; - return 0; - } + if ( !f ) + return 0; + for ( t = BDY(f); t; t = NEXT(t) ) + if ( has_sfcoef_p(t->c) ) + break; + return t ? 1 : 0; } -void initd(spec) -struct order_spec *spec; +int has_sfcoef_p(Obj f) { - switch ( spec->id ) { - 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_LEX: default: - cmpdl = cmpdl_lex; break; - } - break; - } - dp_current_spec = *spec; + 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; } -void ptod(vl,dvl,p,pr) -VL vl,dvl; -P p; -DP *pr; +extern Obj nd_top_weight; + +void reset_top_weight() { - int isconst = 0; - int n,i; - VL tvl; - V v; - DL d; - MP m; - DCP dc; - DP r,s,t,u; - P x,c; + cmpdl = cmpdl_tie_breaker; + cmpdl_tie_breaker = 0; + nd_top_weight = 0; + current_top_weight = 0; + current_top_weight_len = 0; +} - if ( !p ) - *pr = 0; - else { - for ( n = 0, tvl = dvl; tvl; tvl = NEXT(tvl), n++ ); - if ( NUM(p) ) { - NEWDL(d,n); - NEWMP(m); m->dl = d; C(m) = 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), s = 0, MKV(v,x); dc; dc = NEXT(dc) ) { - ptod(vl,dvl,COEF(dc),&t); pwrp(vl,x,DEG(dc),&c); - muldc(vl,t,c,&r); addd(vl,r,s,&t); s = t; - } - *pr = s; - } else { - for ( dc = DC(p), s = 0; dc; dc = NEXT(dc) ) { - ptod(vl,dvl,COEF(dc),&t); - NEWDL(d,n); d->td = QTOS(DEG(dc)); d->d[i] = d->td; - NEWMP(m); m->dl = d; C(m) = (P)ONE; NEXT(m) = 0; MKDP(n,m,u); u->sugar = d->td; - muld(vl,t,u,&r); addd(vl,r,s,&t); s = t; - } - *pr = s; - } - } - } - if ( !dp_fcoeffs && has_fcoef(*pr) ) - dp_fcoeffs = 1; +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; } -void dtop(vl,dvl,p,pr) -VL vl,dvl; -DP p; -P *pr; +int dpm_ispot; + +/* type=0 => TOP, type=1 => POT */ +void initdpm(struct order_spec *spec,int type) { - int n,i; - DL d; - MP m; - P r,s,t,u,w; - Q q; - VL tvl; + int len,i,k,row; + Q **mat; - if ( !p ) - *pr = 0; - else { - for ( n = p->nv, m = BDY(p), s = 0; m; m = NEXT(m) ) { - t = C(m); - if ( NUM(t) && NID((Num)t) == N_M ) { - mptop(t,&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,&u); - mulp(vl,t,u,&w); t = w; - } - addp(vl,s,t,&u); s = u; - } - *pr = s; - } + initd(spec); + dpm_ispot = type; } -void nodetod(node,dp) -NODE node; -DP *dp; +void ptod(VL vl,VL dvl,P p,DP *pr) { - NODE t; - int len,i,td; - Q e; - DL d; - MP m; - DP u; + 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; - 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 += d->d[i]; - } - } - d->td = td; - NEWMP(m); m->dl = d; C(m) = (P)ONE; NEXT(m) = 0; - MKDP(len,m,u); u->sugar = td; *dp = u; + 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 } -int sugard(m) -MP m; +void dtop(VL vl,VL dvl,DP p,Obj *pr) { - int s; + int n,i,j,k; + DL d; + MP m; + MP *a; + P r; + Obj t,w,s,u; + Q q; + VL tvl; - for ( s = 0; m; m = NEXT(m) ) - s = MAX(s,m->dl->td); - return s; + 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 addd(vl,p1,p2,pr) -VL vl; -DP p1,p2,*pr; +void nodetod(NODE node,DP *dp) { - int n; - MP m1,m2,mr,mr0; - P t; + NODE t; + int len,i,td; + Q e; + DL d; + MP m; + DP u; - 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 ( (*cmpdl)(n,m1->dl,m2->dl) ) { - case 0: - addp(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 ( 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(p1,p2,pr) -DP p1,p2,*pr; +void symb_addd(DP p1,DP p2,DP *pr) { - int n; - MP m1,m2,mr,mr0; - P t; + 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) = (P)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); - } + 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); + } } -void subd(vl,p1,p2,pr) -VL vl; -DP p1,p2,*pr; +/* + * destructive merge of two list + * + * p1, p2 : list of DL + * return : a merged list + */ + +NODE symb_merge(NODE m1,NODE m2,int n) { - DP t; + NODE top=0,prev,cur,m=0,t; + DL d1,d2; - if ( !p2 ) - *pr = p1; - else { - chsgnd(p2,&t); addd(vl,p1,t,pr); - } + 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 chsgnd(p,pr) -DP p,*pr; +void _adddl(int n,DL d1,DL d2,DL d3) { - MP m,mr,mr0; + int i; - if ( !p ) - *pr = 0; - else { - for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) { - NEXTMP(mr0,mr); chsgnp(C(m),&C(mr)); mr->dl = m->dl; - } - NEXT(mr) = 0; MKDP(NV(p),mr0,*pr); - if ( *pr ) - (*pr)->sugar = p->sugar; - } + d3->td = d1->td+d2->td; + for ( i = 0; i < n; i++ ) + d3->d[i] = d1->d[i]+d2->d[i]; } -void muld(vl,p1,p2,pr) -VL vl; -DP p1,p2,*pr; +/* 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) { - MP m; - DP s,t,u; + NODE top,prev,cur,n1; + DP g; + DL t,s; + MP m; - if ( !p1 || !p2 ) - *pr = 0; - else if ( OID(p1) <= O_P ) - muldc(vl,p2,(P)p1,pr); - else if ( OID(p2) <= O_P ) - muldc(vl,p1,(P)p2,pr); - else { - for ( m = BDY(p2), s = 0; m; m = NEXT(m) ) { - muldm(vl,p1,m,&t); addd(vl,s,t,&u); s = u; - } - *pr = s; - } + 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; + } } -void muldm(vl,p,m0,pr) -VL vl; -DP p; -MP m0; -DP *pr; +DLBUCKET symb_merge_bucket(DLBUCKET m1,DLBUCKET m2,int n) { - MP m,mr,mr0; - P c; - DL d; - int n; + DLBUCKET top,prev,cur,m,t; - 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 - mulp(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; - } + 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 muldc(vl,p,c,pr) -VL vl; -DP p; -P c; -DP *pr; +void subd(VL vl,DP p1,DP p2,DP *pr) { - MP m,mr,mr0; + DP t; - 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 - mulp(vl,C(m),c,&C(mr)); - mr->dl = m->dl; - } - NEXT(mr) = 0; MKDP(NV(p),mr0,*pr); - if ( *pr ) - (*pr)->sugar = p->sugar; - } + if ( !p2 ) + *pr = p1; + else { + chsgnd(p2,&t); addd(vl,p1,t,pr); + } } -void divsdc(vl,p,c,pr) -VL vl; -DP p; -P c; -DP *pr; +void chsgnd(DP p,DP *pr) { - MP m,mr,mr0; + MP m,mr=0,mr0; + Obj r; - if ( !c ) - error("disvsdc : division by 0"); - else if ( !p ) - *pr = 0; - else { - for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) { - NEXTMP(mr0,mr); divsp(vl,C(m),c,&C(mr)); mr->dl = m->dl; - } - NEXT(mr) = 0; MKDP(NV(p),mr0,*pr); - if ( *pr ) - (*pr)->sugar = p->sugar; - } + 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 adddl(n,d1,d2,dr) -int n; -DL d1,d2; -DL *dr; +void muld(VL vl,DP p1,DP p2,DP *pr) { - DL dt; - int i; + if ( ! do_weyl ) + comm_muld(vl,p1,p2,pr); + else + weyl_muld(vl,p1,p2,pr); +} - if ( !d1->td ) - *dr = d2; - else if ( !d2->td ) - *dr = d1; - else { - *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]; - } +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; + } } -int compd(vl,p1,p2) -VL vl; -DP p1,p2; +/* discard terms which is not a multiple of dl */ + +void comm_muld_trunc(VL vl,DP p1,DP p2,DL dl,DP *pr) { - int n,t; - MP m1,m2; + MP m; + DP s,t,u; + int i,l,l1; + static MP *w; + static int wlen; - if ( !p1 ) - return p2 ? -1 : 0; - else if ( !p2 ) - return 1; - 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 = compp(vl,C(m1),C(m2)) ) ) - return t; - if ( m1 ) - return 1; - else if ( m2 ) - return -1; - else - return 0; - } + 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; + } } -int cmpdl_lex(n,d1,d2) -int n; -DL d1,d2; +void comm_quod(VL vl,DP p1,DP p2,DP *pr) { - int i; + MP m=0,m0; + DP s,t; + int i,n,sugar; + DL d1,d2,d; + Q a,b; - for ( i = 0; i < n && d1->d[i] == d2->d[i]; i++ ); - return i == n ? 0 : (d1->d[i] > d2->d[i] ? 1 : -1); + 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; + } } -int cmpdl_revlex(n,d1,d2) -int n; -DL d1,d2; +void muldm(VL vl,DP p,MP m0,DP *pr) { - int i; + MP m,mr=0,mr0; + Obj c; + DL d; + int n; - 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); + 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; + } } -int cmpdl_gradlex(n,d1,d2) -int n; -DL d1,d2; +void muldm_trunc(VL vl,DP p,MP m0,DL dl,DP *pr) { - if ( d1->td > d2->td ) - return 1; - else if ( d1->td < d2->td ) - return -1; - else - return cmpdl_lex(n,d1,d2); + 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; + } } -int cmpdl_revgradlex(n,d1,d2) -int n; -DL d1,d2; +void weyl_muld(VL vl,DP p1,DP p2,DP *pr) { - if ( d1->td > d2->td ) - return 1; - else if ( d1->td < d2->td ) - return -1; - else - return cmpdl_revlex(n,d1,d2); + 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; + } } -int cmpdl_blex(n,d1,d2) -int n; -DL d1,d2; +void actm(VL vl,int nv,MP m1,MP m2,DP *pr) { - int c; + DL d1,d2,d; + int n2,i,j,k; + Q jq,c,c1; + MP m; + Obj t; - 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; - } + 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); } -int cmpdl_bgradlex(n,d1,d2) -int n; -DL d1,d2; +void weyl_actd(VL vl,DP p1,DP p2,DP *pr) { - int e1,e2,c; + int n; + MP m1,m2; + DP d,r,s; - 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; - } + 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; + } } -int cmpdl_brevgradlex(n,d1,d2) -int n; -DL d1,d2; +/* monomial * polynomial */ + +void weyl_muldm(VL vl,MP m0,DP p,DP *pr) { - int e1,e2,c; + 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; - 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; - } + 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; + } } -int cmpdl_brevrev(n,d1,d2) -int n; -DL d1,d2; +/* 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) { - int e1,e2,f1,f2,c,i; + 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; - 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); - } - } + + 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)); + } } -int cmpdl_bgradrev(n,d1,d2) -int n; -DL d1,d2; +/* 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 e1,e2,f1,f2,c,i; + int i,j; + struct cdl *p; + Obj c; + DL d; - 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); - } - } + 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); + } + } + } } -int cmpdl_blexrev(n,d1,d2) -int n; -DL d1,d2; +void muldc(VL vl,DP p,Obj c,DP *pr) { - int e1,e2,f1,f2,c,i; + MP m,mr=0,mr0; - 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); - } + 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; + } } -int cmpdl_elim(n,d1,d2) -int n; -DL d1,d2; +void divdc(VL vl,DP p,Obj c,DP *pr) { - int e1,e2,i; + Obj inv; - 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); + arf_div(vl,(Obj)ONE,c,&inv); + muld(vl,p,(DP)inv,pr); } -int cmpdl_order_pair(n,d1,d2) -int n; -DL d1,d2; +void muldc_trunc(VL vl,DP p,Obj c,DL dl,DP *pr) { - int e1,e2,i,j,l; - int *t1,*t2; - int len; - struct order_pair *pair; + MP m,mr=0,mr0; + DL mdl; + int i,n; - len = dp_current_spec.ord.block.length; - pair = dp_current_spec.ord.block.order_pair; + 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; +} - 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 += t1[j]; e2 += t2[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 += t1[j]; e2 += t2[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; - } - return 0; +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_P ) + 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; + } } -int cmpdl_matrix(n,d1,d2) -int n; -DL d1,d2; +void adddl(int n,DL d1,DL d2,DL *dr) { - int *v,*w,*t1,*t2; - int s,i,j,len; - int **matrix; + DL dt; + int i; - 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; + *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; + } +} +