/* $OpenXM: OpenXM_contrib2/asir2018/engine/nd.c,v 1.37 2020/10/06 06:31:19 noro Exp $ */ #include "nd.h" int Nnd_add,Nf4_red; struct oEGT eg_search,f4_symb,f4_conv,f4_elim1,f4_elim2; int diag_period = 6; int weight_check = 1; int (*ndl_compare_function)(UINT *a1,UINT *a2); /* for general module order */ int (*ndl_base_compare_function)(UINT *a1,UINT *a2); int (*dl_base_compare_function)(int nv,DL a,DL b); int nd_base_ordtype; int nd_dcomp; int nd_rref2; NM _nm_free_list; ND _nd_free_list; ND_pairs _ndp_free_list; NODE nd_hcf; int Nsyz,Nsamesig; Obj nd_top_weight; static NODE nd_subst; static VL nd_vc; static int nd_ntrans; static int nd_nalg; #if 0 static int ndv_alloc; #endif #if 1 static int nd_f4_nsp=0x7fffffff; #else static int nd_f4_nsp=50; #endif static double nd_scale=2; static UINT **nd_bound; static struct order_spec *nd_ord; static EPOS nd_epos; static BlockMask nd_blockmask; static int nd_nvar; static int nd_isrlex; static int nd_epw,nd_bpe,nd_wpd,nd_exporigin; static UINT nd_mask[32]; static UINT nd_mask0,nd_mask1; static NDV *nd_ps; static NDV *nd_ps_trace; static NDV *nd_ps_sym; static NDV *nd_ps_trace_sym; static RHist *nd_psh; static int nd_psn,nd_pslen,nd_nbase; static RHist *nd_red; static int *nd_work_vector; static int **nd_matrix; static int nd_matrix_len; static struct weight_or_block *nd_worb; static int nd_worb_len; static int nd_found,nd_create,nd_notfirst; static int nmv_adv; static int nd_demand; static int nd_module,nd_module_ordtype,nd_mpos,nd_pot_nelim; static int nd_module_rank,nd_poly_weight_len; static int *nd_poly_weight,*nd_module_weight; static NODE nd_tracelist; static NODE nd_alltracelist; static int nd_gentrace,nd_gensyz,nd_nora,nd_newelim,nd_intersect,nd_lf; static int *nd_gbblock; static NODE nd_nzlist,nd_check_splist; static int nd_splist; static int *nd_sugarweight; static int nd_f4red,nd_rank0,nd_last_nonzero; static DL *nd_sba_hm; static NODE *nd_sba_pos; NumberField get_numberfield(); UINT *nd_det_compute_bound(NDV **dm,int n,int j); void nd_det_reconstruct(NDV **dm,int n,int j,NDV d); void nd_heu_nezgcdnpz(VL vl,P *pl,int m,int full,P *pr); int nd_monic(int m,ND *p); NDV plain_vect_to_ndv_q(Z *mat,int col,UINT *s0vect); LIST ndvtopl(int mod,VL vl,VL dvl,NDV p,int rank); NDV pltondv(VL vl,VL dvl,LIST p); void pltozpl(LIST l,Q *cont,LIST *pp); void ndl_max(UINT *d1,unsigned *d2,UINT *d); void nmtodp(int mod,NM m,DP *r); void ndltodp(UINT *d,DP *r); NODE reverse_node(NODE n); P ndc_div(int mod,union oNDC a,union oNDC b); P ndctop(int mod,union oNDC c); void finalize_tracelist(int i,P cont); void conv_ilist(int demand,int trace,NODE g,int **indp); void parse_nd_option(NODE opt); void dltondl(int n,DL dl,UINT *r); DP ndvtodp(int mod,NDV p); DP ndtodp(int mod,ND p); DPM ndvtodpm(int mod,NDV p); NDV dpmtondv(int mod,DPM p); int dpm_getdeg(DPM p,int *rank); void dpm_ptozp(DPM p,Z *cont,DPM *r); int compdmm(int nv,DMM a,DMM b); void Pdp_set_weight(NODE,VECT *); void Pox_cmo_rpc(NODE,Obj *); ND nd_add_lf(ND p1,ND p2); void nd_mul_c_lf(ND p,Z mul); void ndv_mul_c_lf(NDV p,Z mul); NODE nd_f4_red_main(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col, NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred,ND_pairs *nz); NODE nd_f4_red_mod64_main(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col, NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred,ND_pairs *nz); NODE nd_f4_red_lf_main(int m,ND_pairs sp0,int nsp,int trace,UINT *s0vect,int col, NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred); int nd_gauss_elim_lf(mpz_t **mat0,int *sugar,int row,int col,int *colstat); NODE nd_f4_lf_trace_main(int m,int **indp); void nd_f4_lf_trace(LIST f,LIST v,int trace,int homo,struct order_spec *ord,LIST *rp); extern int lf_lazy; extern Z current_mod_lf; extern int Denominator,DP_Multiple,MaxDeg; #define BLEN (8*sizeof(unsigned long)) typedef struct matrix { int row,col; unsigned long **a; } *matrix; void nd_free_private_storage() { _nm_free_list = 0; _ndp_free_list = 0; #if 0 GC_gcollect(); #endif } void _NM_alloc() { NM p; int i; for ( i = 0; i < 1024; i++ ) { p = (NM)MALLOC(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT)); p->next = _nm_free_list; _nm_free_list = p; } } matrix alloc_matrix(int row,int col) { unsigned long **a; int i,len,blen; matrix mat; mat = (matrix)MALLOC(sizeof(struct matrix)); mat->row = row; mat->col = col; mat->a = a = (unsigned long **)MALLOC(row*sizeof(unsigned long *)); return mat; } void _ND_alloc() { ND p; int i; for ( i = 0; i < 1024; i++ ) { p = (ND)MALLOC(sizeof(struct oND)); p->body = (NM)_nd_free_list; _nd_free_list = p; } } void _NDP_alloc() { ND_pairs p; int i; for ( i = 0; i < 1024; i++ ) { p = (ND_pairs)MALLOC(sizeof(struct oND_pairs) +(nd_wpd-1)*sizeof(UINT)); p->next = _ndp_free_list; _ndp_free_list = p; } } INLINE int nd_length(ND p) { NM m; int i; if ( !p ) return 0; else { for ( i = 0, m = BDY(p); m; m = NEXT(m), i++ ); return i; } } extern int dp_negative_weight; INLINE int ndl_reducible(UINT *d1,UINT *d2) { UINT u1,u2; int i,j; if ( nd_module && (MPOS(d1) != MPOS(d2)) ) return 0; if ( !dp_negative_weight && TD(d1) < TD(d2) ) return 0; #if USE_UNROLL switch ( nd_bpe ) { case 3: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; if ( (u1&0x38000000) < (u2&0x38000000) ) return 0; if ( (u1& 0x7000000) < (u2& 0x7000000) ) return 0; if ( (u1& 0xe00000) < (u2& 0xe00000) ) return 0; if ( (u1& 0x1c0000) < (u2& 0x1c0000) ) return 0; if ( (u1& 0x38000) < (u2& 0x38000) ) return 0; if ( (u1& 0x7000) < (u2& 0x7000) ) return 0; if ( (u1& 0xe00) < (u2& 0xe00) ) return 0; if ( (u1& 0x1c0) < (u2& 0x1c0) ) return 0; if ( (u1& 0x38) < (u2& 0x38) ) return 0; if ( (u1& 0x7) < (u2& 0x7) ) return 0; } return 1; break; case 4: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; if ( (u1&0xf0000000) < (u2&0xf0000000) ) return 0; if ( (u1& 0xf000000) < (u2& 0xf000000) ) return 0; if ( (u1& 0xf00000) < (u2& 0xf00000) ) return 0; if ( (u1& 0xf0000) < (u2& 0xf0000) ) return 0; if ( (u1& 0xf000) < (u2& 0xf000) ) return 0; if ( (u1& 0xf00) < (u2& 0xf00) ) return 0; if ( (u1& 0xf0) < (u2& 0xf0) ) return 0; if ( (u1& 0xf) < (u2& 0xf) ) return 0; } return 1; break; case 6: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; if ( (u1&0x3f000000) < (u2&0x3f000000) ) return 0; if ( (u1& 0xfc0000) < (u2& 0xfc0000) ) return 0; if ( (u1& 0x3f000) < (u2& 0x3f000) ) return 0; if ( (u1& 0xfc0) < (u2& 0xfc0) ) return 0; if ( (u1& 0x3f) < (u2& 0x3f) ) return 0; } return 1; break; case 8: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; if ( (u1&0xff000000) < (u2&0xff000000) ) return 0; if ( (u1& 0xff0000) < (u2& 0xff0000) ) return 0; if ( (u1& 0xff00) < (u2& 0xff00) ) return 0; if ( (u1& 0xff) < (u2& 0xff) ) return 0; } return 1; break; case 16: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; if ( (u1&0xffff0000) < (u2&0xffff0000) ) return 0; if ( (u1& 0xffff) < (u2& 0xffff) ) return 0; } return 1; break; case 32: for ( i = nd_exporigin; i < nd_wpd; i++ ) if ( d1[i] < d2[i] ) return 0; return 1; break; default: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; for ( j = 0; j < nd_epw; j++ ) if ( (u1&nd_mask[j]) < (u2&nd_mask[j]) ) return 0; } return 1; } #else for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; for ( j = 0; j < nd_epw; j++ ) if ( (u1&nd_mask[j]) < (u2&nd_mask[j]) ) return 0; } return 1; #endif } /* * If the current order is a block order, * then the last block is length 1 and contains * the homo variable. Otherwise, the original * order is either 0 or 2. */ void ndl_homogenize(UINT *d,UINT *r,int obpe,EPOS oepos,int ompos,int weight) { int w,i,e,n,omask0; omask0 = obpe==32?0xffffffff:((1<>((nd_epw-1)*nd_bpe))&nd_mask0; for ( i = nd_exporigin; i < nd_wpd; i++ ) d[i] = ((d[i]<>((nd_epw-1)*nd_bpe))&nd_mask0):0); TD(d) -= h; } } else { h = GET_EXP(d,nd_nvar-1); XOR_EXP(d,nd_nvar-1,h); TD(d) -= h; } } } void ndl_lcm(UINT *d1,unsigned *d2,UINT *d) { UINT t1,t2,u,u1,u2; int i,j,l; if ( nd_module && (MPOS(d1) != MPOS(d2)) ) error("ndl_lcm : inconsistent monomials"); #if USE_UNROLL switch ( nd_bpe ) { case 3: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; t1 = (u1&0x38000000); t2 = (u2&0x38000000); u = t1>t2?t1:t2; t1 = (u1& 0x7000000); t2 = (u2& 0x7000000); u |= t1>t2?t1:t2; t1 = (u1& 0xe00000); t2 = (u2& 0xe00000); u |= t1>t2?t1:t2; t1 = (u1& 0x1c0000); t2 = (u2& 0x1c0000); u |= t1>t2?t1:t2; t1 = (u1& 0x38000); t2 = (u2& 0x38000); u |= t1>t2?t1:t2; t1 = (u1& 0x7000); t2 = (u2& 0x7000); u |= t1>t2?t1:t2; t1 = (u1& 0xe00); t2 = (u2& 0xe00); u |= t1>t2?t1:t2; t1 = (u1& 0x1c0); t2 = (u2& 0x1c0); u |= t1>t2?t1:t2; t1 = (u1& 0x38); t2 = (u2& 0x38); u |= t1>t2?t1:t2; t1 = (u1& 0x7); t2 = (u2& 0x7); u |= t1>t2?t1:t2; d[i] = u; } break; case 4: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; t1 = (u1&0xf0000000); t2 = (u2&0xf0000000); u = t1>t2?t1:t2; t1 = (u1& 0xf000000); t2 = (u2& 0xf000000); u |= t1>t2?t1:t2; t1 = (u1& 0xf00000); t2 = (u2& 0xf00000); u |= t1>t2?t1:t2; t1 = (u1& 0xf0000); t2 = (u2& 0xf0000); u |= t1>t2?t1:t2; t1 = (u1& 0xf000); t2 = (u2& 0xf000); u |= t1>t2?t1:t2; t1 = (u1& 0xf00); t2 = (u2& 0xf00); u |= t1>t2?t1:t2; t1 = (u1& 0xf0); t2 = (u2& 0xf0); u |= t1>t2?t1:t2; t1 = (u1& 0xf); t2 = (u2& 0xf); u |= t1>t2?t1:t2; d[i] = u; } break; case 6: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; t1 = (u1&0x3f000000); t2 = (u2&0x3f000000); u = t1>t2?t1:t2; t1 = (u1& 0xfc0000); t2 = (u2& 0xfc0000); u |= t1>t2?t1:t2; t1 = (u1& 0x3f000); t2 = (u2& 0x3f000); u |= t1>t2?t1:t2; t1 = (u1& 0xfc0); t2 = (u2& 0xfc0); u |= t1>t2?t1:t2; t1 = (u1& 0x3f); t2 = (u2& 0x3f); u |= t1>t2?t1:t2; d[i] = u; } break; case 8: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; t1 = (u1&0xff000000); t2 = (u2&0xff000000); u = t1>t2?t1:t2; t1 = (u1& 0xff0000); t2 = (u2& 0xff0000); u |= t1>t2?t1:t2; t1 = (u1& 0xff00); t2 = (u2& 0xff00); u |= t1>t2?t1:t2; t1 = (u1& 0xff); t2 = (u2& 0xff); u |= t1>t2?t1:t2; d[i] = u; } break; case 16: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; t1 = (u1&0xffff0000); t2 = (u2&0xffff0000); u = t1>t2?t1:t2; t1 = (u1& 0xffff); t2 = (u2& 0xffff); u |= t1>t2?t1:t2; d[i] = u; } break; case 32: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; d[i] = u1>u2?u1:u2; } break; default: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; for ( j = 0, u = 0; j < nd_epw; j++ ) { t1 = (u1&nd_mask[j]); t2 = (u2&nd_mask[j]); u |= t1>t2?t1:t2; } d[i] = u; } break; } #else for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; for ( j = 0, u = 0; j < nd_epw; j++ ) { t1 = (u1&nd_mask[j]); t2 = (u2&nd_mask[j]); u |= t1>t2?t1:t2; } d[i] = u; } #endif if ( nd_module ) MPOS(d) = MPOS(d1); TD(d) = ndl_weight(d); if ( nd_blockmask ) ndl_weight_mask(d); } void ndl_max(UINT *d1,unsigned *d2,UINT *d) { UINT t1,t2,u,u1,u2; int i,j,l; for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; for ( j = 0, u = 0; j < nd_epw; j++ ) { t1 = (u1&nd_mask[j]); t2 = (u2&nd_mask[j]); u |= t1>t2?t1:t2; } d[i] = u; } } int ndl_weight(UINT *d) { UINT t,u; int i,j; if ( current_dl_weight_vector ) for ( i = 0, t = 0; i < nd_nvar; i++ ) { u = GET_EXP(d,i); t += MUL_WEIGHT(u,i); } else for ( t = 0, i = nd_exporigin; i < nd_wpd; i++ ) { u = d[i]; for ( j = 0; j < nd_epw; j++, u>>=nd_bpe ) t += (u&nd_mask0); } if ( nd_module && nd_module_rank && MPOS(d) ) t += nd_module_weight[MPOS(d)-1]; for ( i = nd_exporigin; i < nd_wpd; i++ ) if ( d[i] && !t ) printf("afo\n"); return t; } /* for sugarweight */ int ndl_weight2(UINT *d) { int t,u; int i,j; for ( i = 0, t = 0; i < nd_nvar; i++ ) { u = GET_EXP(d,i); t += nd_sugarweight[i]*u; } if ( nd_module && nd_module_rank && MPOS(d) ) t += nd_module_weight[MPOS(d)-1]; return t; } void ndl_weight_mask(UINT *d) { UINT t,u; UINT *mask; int i,j,k,l; l = nd_blockmask->n; for ( k = 0; k < l; k++ ) { mask = nd_blockmask->mask[k]; if ( current_dl_weight_vector ) for ( i = 0, t = 0; i < nd_nvar; i++ ) { u = GET_EXP_MASK(d,i,mask); t += MUL_WEIGHT(u,i); } else for ( t = 0, i = nd_exporigin; i < nd_wpd; i++ ) { u = d[i]&mask[i]; for ( j = 0; j < nd_epw; j++, u>>=nd_bpe ) t += (u&nd_mask0); } d[k+1] = t; } } int ndl_glex_compare(UINT *d1,UINT *d2) { if ( TD(d1) > TD(d2) ) return 1; else if ( TD(d1) < TD(d2) ) return -1; else return ndl_lex_compare(d1,d2); } int ndl_lex_compare(UINT *d1,UINT *d2) { int i; d1 += nd_exporigin; d2 += nd_exporigin; for ( i = nd_exporigin; i < nd_wpd; i++, d1++, d2++ ) if ( *d1 > *d2 ) return nd_isrlex ? -1 : 1; else if ( *d1 < *d2 ) return nd_isrlex ? 1 : -1; return 0; } int ndl_block_compare(UINT *d1,UINT *d2) { int i,l,j,ord_o,ord_l; struct order_pair *op; UINT t1,t2,m; UINT *mask; l = nd_blockmask->n; op = nd_blockmask->order_pair; for ( j = 0; j < l; j++ ) { mask = nd_blockmask->mask[j]; ord_o = op[j].order; if ( ord_o < 2 ) { if ( (t1=d1[j+1]) > (t2=d2[j+1]) ) return 1; else if ( t1 < t2 ) return -1; } for ( i = nd_exporigin; i < nd_wpd; i++ ) { m = mask[i]; t1 = d1[i]&m; t2 = d2[i]&m; if ( t1 > t2 ) return !ord_o ? -1 : 1; else if ( t1 < t2 ) return !ord_o ? 1 : -1; } } return 0; } int ndl_matrix_compare(UINT *d1,UINT *d2) { int i,j,s,row; int *v; Z **mat; Z *w; Z t1; Z t,t2; for ( j = 0; j < nd_nvar; j++ ) nd_work_vector[j] = GET_EXP(d1,j)-GET_EXP(d2,j); if ( nd_top_weight ) { if ( OID(nd_top_weight) == O_VECT ) { mat = (Z **)&BDY((VECT)nd_top_weight); row = 1; } else { mat = (Z **)BDY((MAT)nd_top_weight); row = ((MAT)nd_top_weight)->row; } for ( i = 0; i < row; i++ ) { w = mat[i]; for ( j = 0, t = 0; j < nd_nvar; j++ ) { STOZ(nd_work_vector[j],t1); mulz(w[j],t1,&t2); addz(t,t2,&t1); t = t1; } if ( t ) { s = sgnz(t); if ( s > 0 ) return 1; else if ( s < 0 ) return -1; } } } for ( i = 0; i < nd_matrix_len; i++ ) { v = nd_matrix[i]; for ( j = 0, s = 0; j < nd_nvar; j++ ) s += v[j]*nd_work_vector[j]; if ( s > 0 ) return 1; else if ( s < 0 ) return -1; } if ( !ndl_equal(d1,d2) ) error("ndl_matrix_compare : invalid matrix"); return 0; } int ndl_composite_compare(UINT *d1,UINT *d2) { int i,j,s,start,end,len,o; int *v; struct sparse_weight *sw; for ( j = 0; j < nd_nvar; j++ ) nd_work_vector[j] = GET_EXP(d1,j)-GET_EXP(d2,j); for ( i = 0; i < nd_worb_len; i++ ) { len = nd_worb[i].length; switch ( nd_worb[i].type ) { case IS_DENSE_WEIGHT: v = nd_worb[i].body.dense_weight; for ( j = 0, s = 0; j < len; j++ ) s += v[j]*nd_work_vector[j]; if ( s > 0 ) return 1; else if ( s < 0 ) return -1; break; case IS_SPARSE_WEIGHT: sw = nd_worb[i].body.sparse_weight; for ( j = 0, s = 0; j < len; j++ ) s += sw[j].value*nd_work_vector[sw[j].pos]; if ( s > 0 ) return 1; else if ( s < 0 ) return -1; break; case IS_BLOCK: o = nd_worb[i].body.block.order; start = nd_worb[i].body.block.start; switch ( o ) { case 0: end = start+len; for ( j = start, s = 0; j < end; j++ ) s += MUL_WEIGHT(nd_work_vector[j],j); if ( s > 0 ) return 1; else if ( s < 0 ) return -1; for ( j = end-1; j >= start; j-- ) if ( nd_work_vector[j] < 0 ) return 1; else if ( nd_work_vector[j] > 0 ) return -1; break; case 1: end = start+len; for ( j = start, s = 0; j < end; j++ ) s += MUL_WEIGHT(nd_work_vector[j],j); if ( s > 0 ) return 1; else if ( s < 0 ) return -1; for ( j = start; j < end; j++ ) if ( nd_work_vector[j] > 0 ) return 1; else if ( nd_work_vector[j] < 0 ) return -1; break; case 2: end = start+len; for ( j = start; j < end; j++ ) if ( nd_work_vector[j] > 0 ) return 1; else if ( nd_work_vector[j] < 0 ) return -1; break; } break; } } return 0; } /* TDH -> WW -> TD-> RL */ int ndl_ww_lex_compare(UINT *d1,UINT *d2) { int i,m,e1,e2; if ( TD(d1) > TD(d2) ) return 1; else if ( TD(d1) < TD(d2) ) return -1; m = nd_nvar>>1; for ( i = 0, e1 = e2 = 0; i < m; i++ ) { e1 += current_weyl_weight_vector[i]*(GET_EXP(d1,m+i)-GET_EXP(d1,i)); e2 += current_weyl_weight_vector[i]*(GET_EXP(d2,m+i)-GET_EXP(d2,i)); } if ( e1 > e2 ) return 1; else if ( e1 < e2 ) return -1; return ndl_lex_compare(d1,d2); } // common function for module glex and grlex comparison int ndl_module_glex_compare(UINT *d1,UINT *d2) { int c; switch ( nd_module_ordtype ) { case 0: if ( TD(d1) > TD(d2) ) return 1; else if ( TD(d1) < TD(d2) ) return -1; else if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c; else if ( MPOS(d1) < MPOS(d2) ) return 1; else if ( MPOS(d1) > MPOS(d2) ) return -1; else return 0; break; case 1: if ( nd_pot_nelim && MPOS(d1)>=nd_pot_nelim+1 && MPOS(d2) >= nd_pot_nelim+1 ) { if ( TD(d1) > TD(d2) ) return 1; else if ( TD(d1) < TD(d2) ) return -1; if ( (c = ndl_lex_compare(d1,d2)) != 0 ) return c; if ( MPOS(d1) < MPOS(d2) ) return 1; else if ( MPOS(d1) > MPOS(d2) ) return -1; } if ( MPOS(d1) < MPOS(d2) ) return 1; else if ( MPOS(d1) > MPOS(d2) ) return -1; else if ( TD(d1) > TD(d2) ) return 1; else if ( TD(d1) < TD(d2) ) return -1; else return ndl_lex_compare(d1,d2); break; case 2: // weight -> POT if ( TD(d1) > TD(d2) ) return 1; else if ( TD(d1) < TD(d2) ) return -1; else if ( MPOS(d1) < MPOS(d2) ) return 1; else if ( MPOS(d1) > MPOS(d2) ) return -1; else return ndl_lex_compare(d1,d2); break; default: error("ndl_module_glex_compare : invalid module_ordtype"); return 0; } } // common for module comparison int ndl_module_compare(UINT *d1,UINT *d2) { int c; switch ( nd_module_ordtype ) { case 0: if ( (c = (*ndl_base_compare_function)(d1,d2)) != 0 ) return c; else if ( MPOS(d1) > MPOS(d2) ) return -1; else if ( MPOS(d1) < MPOS(d2) ) return 1; else return 0; break; case 1: if ( MPOS(d1) < MPOS(d2) ) return 1; else if ( MPOS(d1) > MPOS(d2) ) return -1; else return (*ndl_base_compare_function)(d1,d2); break; case 2: // weight -> POT if ( TD(d1) > TD(d2) ) return 1; else if ( TD(d1) < TD(d2) ) return -1; else if ( MPOS(d1) < MPOS(d2) ) return 1; else if ( MPOS(d1) > MPOS(d2) ) return -1; else return (*ndl_base_compare_function)(d1,d2); break; default: error("ndl_module_compare : invalid module_ordtype"); return 0; } } extern DMMstack dmm_stack; void _addtodl(int n,DL d1,DL d2); void _adddl(int n,DL d1,DL d2,DL d3); int _eqdl(int n,DL d1,DL d2); int ndl_module_schreyer_compare(UINT *m1,UINT *m2) { int pos1,pos2,t,j; DMM *in; DMMstack s; static DL d1=0; static DL d2=0; static int dlen=0; pos1 = MPOS(m1); pos2 = MPOS(m2); if ( pos1 == pos2 ) return (*ndl_base_compare_function)(m1,m2); if ( nd_nvar > dlen ) { NEWDL(d1,nd_nvar); NEWDL(d2,nd_nvar); dlen = nd_nvar; } d1->td = TD(m1); for ( j = 0; j < nd_nvar; j++ ) d1->d[j] = GET_EXP(m1,j); d2->td = TD(m2); for ( j = 0; j < nd_nvar; j++ ) d2->d[j] = GET_EXP(m2,j); for ( s = dmm_stack; s; s = NEXT(s) ) { in = s->in; _addtodl(nd_nvar,in[pos1]->dl,d1); _addtodl(nd_nvar,in[pos2]->dl,d2); if ( in[pos1]->pos == in[pos2]->pos && _eqdl(nd_nvar,d1,d2)) { if ( pos1 < pos2 ) return 1; else if ( pos1 > pos2 ) return -1; else return 0; } pos1 = in[pos1]->pos; pos2 = in[pos2]->pos; if ( pos1 == pos2 ) return (*dl_base_compare_function)(nd_nvar,d1,d2); } // comparison by the bottom order LAST: switch ( nd_base_ordtype ) { case 0: t = (*dl_base_compare_function)(nd_nvar,d1,d2); if ( t ) return t; else if ( pos1 < pos2 ) return 1; else if ( pos1 > pos2 ) return -1; else return 0; break; case 1: if ( pos1 < pos2 ) return 1; else if ( pos1 > pos2 ) return -1; else return (*dl_base_compare_function)(nd_nvar,d1,d2); break; case 2: if ( d1->td > d2->td ) return 1; else if ( d1->td < d2->td ) return -1; else if ( pos1 < pos2 ) return 1; else if ( pos1 > pos2 ) return -1; else return (*dl_base_compare_function)(nd_nvar,d1,d2); break; default: error("ndl_schreyer_compare : invalid base ordtype"); return 0; } } INLINE int ndl_equal(UINT *d1,UINT *d2) { int i; switch ( nd_wpd ) { case 2: if ( TD(d2) != TD(d1) ) return 0; if ( d2[1] != d1[1] ) return 0; return 1; break; case 3: if ( TD(d2) != TD(d1) ) return 0; if ( d2[1] != d1[1] ) return 0; if ( d2[2] != d1[2] ) return 0; return 1; break; default: for ( i = 0; i < nd_wpd; i++ ) if ( *d1++ != *d2++ ) return 0; return 1; break; } } INLINE void ndl_copy(UINT *d1,UINT *d2) { int i; switch ( nd_wpd ) { case 2: TD(d2) = TD(d1); d2[1] = d1[1]; break; case 3: TD(d2) = TD(d1); d2[1] = d1[1]; d2[2] = d1[2]; break; default: for ( i = 0; i < nd_wpd; i++ ) d2[i] = d1[i]; break; } } INLINE void ndl_zero(UINT *d) { int i; for ( i = 0; i < nd_wpd; i++ ) d[i] = 0; } INLINE void ndl_add(UINT *d1,UINT *d2,UINT *d) { int i; if ( nd_module ) { if ( MPOS(d1) && MPOS(d2) && (MPOS(d1) != MPOS(d2)) ) error("ndl_add : invalid operation"); } #if 1 switch ( nd_wpd ) { case 2: TD(d) = TD(d1)+TD(d2); d[1] = d1[1]+d2[1]; break; case 3: TD(d) = TD(d1)+TD(d2); d[1] = d1[1]+d2[1]; d[2] = d1[2]+d2[2]; break; default: for ( i = 0; i < nd_wpd; i++ ) d[i] = d1[i]+d2[i]; break; } #else for ( i = 0; i < nd_wpd; i++ ) d[i] = d1[i]+d2[i]; #endif } /* d1 += d2 */ INLINE void ndl_addto(UINT *d1,UINT *d2) { int i; if ( nd_module ) { if ( MPOS(d1) && MPOS(d2) && (MPOS(d1) != MPOS(d2)) ) error("ndl_addto : invalid operation"); } #if 1 switch ( nd_wpd ) { case 2: TD(d1) += TD(d2); d1[1] += d2[1]; break; case 3: TD(d1) += TD(d2); d1[1] += d2[1]; d1[2] += d2[2]; break; default: for ( i = 0; i < nd_wpd; i++ ) d1[i] += d2[i]; break; } #else for ( i = 0; i < nd_wpd; i++ ) d1[i] += d2[i]; #endif } INLINE void ndl_sub(UINT *d1,UINT *d2,UINT *d) { int i; for ( i = 0; i < nd_wpd; i++ ) d[i] = d1[i]-d2[i]; } int ndl_disjoint(UINT *d1,UINT *d2) { UINT t1,t2,u,u1,u2; int i,j; if ( nd_module && (MPOS(d1) == MPOS(d2)) ) return 0; #if USE_UNROLL switch ( nd_bpe ) { case 3: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; t1 = u1&0x38000000; t2 = u2&0x38000000; if ( t1&&t2 ) return 0; t1 = u1& 0x7000000; t2 = u2& 0x7000000; if ( t1&&t2 ) return 0; t1 = u1& 0xe00000; t2 = u2& 0xe00000; if ( t1&&t2 ) return 0; t1 = u1& 0x1c0000; t2 = u2& 0x1c0000; if ( t1&&t2 ) return 0; t1 = u1& 0x38000; t2 = u2& 0x38000; if ( t1&&t2 ) return 0; t1 = u1& 0x7000; t2 = u2& 0x7000; if ( t1&&t2 ) return 0; t1 = u1& 0xe00; t2 = u2& 0xe00; if ( t1&&t2 ) return 0; t1 = u1& 0x1c0; t2 = u2& 0x1c0; if ( t1&&t2 ) return 0; t1 = u1& 0x38; t2 = u2& 0x38; if ( t1&&t2 ) return 0; t1 = u1& 0x7; t2 = u2& 0x7; if ( t1&&t2 ) return 0; } return 1; break; case 4: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; t1 = u1&0xf0000000; t2 = u2&0xf0000000; if ( t1&&t2 ) return 0; t1 = u1& 0xf000000; t2 = u2& 0xf000000; if ( t1&&t2 ) return 0; t1 = u1& 0xf00000; t2 = u2& 0xf00000; if ( t1&&t2 ) return 0; t1 = u1& 0xf0000; t2 = u2& 0xf0000; if ( t1&&t2 ) return 0; t1 = u1& 0xf000; t2 = u2& 0xf000; if ( t1&&t2 ) return 0; t1 = u1& 0xf00; t2 = u2& 0xf00; if ( t1&&t2 ) return 0; t1 = u1& 0xf0; t2 = u2& 0xf0; if ( t1&&t2 ) return 0; t1 = u1& 0xf; t2 = u2& 0xf; if ( t1&&t2 ) return 0; } return 1; break; case 6: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; t1 = u1&0x3f000000; t2 = u2&0x3f000000; if ( t1&&t2 ) return 0; t1 = u1& 0xfc0000; t2 = u2& 0xfc0000; if ( t1&&t2 ) return 0; t1 = u1& 0x3f000; t2 = u2& 0x3f000; if ( t1&&t2 ) return 0; t1 = u1& 0xfc0; t2 = u2& 0xfc0; if ( t1&&t2 ) return 0; t1 = u1& 0x3f; t2 = u2& 0x3f; if ( t1&&t2 ) return 0; } return 1; break; case 8: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; t1 = u1&0xff000000; t2 = u2&0xff000000; if ( t1&&t2 ) return 0; t1 = u1& 0xff0000; t2 = u2& 0xff0000; if ( t1&&t2 ) return 0; t1 = u1& 0xff00; t2 = u2& 0xff00; if ( t1&&t2 ) return 0; t1 = u1& 0xff; t2 = u2& 0xff; if ( t1&&t2 ) return 0; } return 1; break; case 16: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; t1 = u1&0xffff0000; t2 = u2&0xffff0000; if ( t1&&t2 ) return 0; t1 = u1& 0xffff; t2 = u2& 0xffff; if ( t1&&t2 ) return 0; } return 1; break; case 32: for ( i = nd_exporigin; i < nd_wpd; i++ ) if ( d1[i] && d2[i] ) return 0; return 1; break; default: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; for ( j = 0; j < nd_epw; j++ ) { if ( (u1&nd_mask0) && (u2&nd_mask0) ) return 0; u1 >>= nd_bpe; u2 >>= nd_bpe; } } return 1; break; } #else for ( i = nd_exporigin; i < nd_wpd; i++ ) { u1 = d1[i]; u2 = d2[i]; for ( j = 0; j < nd_epw; j++ ) { if ( (u1&nd_mask0) && (u2&nd_mask0) ) return 0; u1 >>= nd_bpe; u2 >>= nd_bpe; } } return 1; #endif } int ndl_check_bound(UINT *d1,UINT *d2) { UINT u2; int i,j,ind,k; ind = 0; #if USE_UNROLL switch ( nd_bpe ) { case 3: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u2 = d2[i]; if ( d1[ind++]+((u2>>27)&0x7) >= 0x8 ) return 1; if ( d1[ind++]+((u2>>24)&0x7) >= 0x8 ) return 1; if ( d1[ind++]+((u2>>21)&0x7) >= 0x8 ) return 1; if ( d1[ind++]+((u2>>18)&0x7) >= 0x8 ) return 1; if ( d1[ind++]+((u2>>15)&0x7) >= 0x8 ) return 1; if ( d1[ind++]+((u2>>12)&0x7) >= 0x8 ) return 1; if ( d1[ind++]+((u2>>9)&0x7) >= 0x8 ) return 1; if ( d1[ind++]+((u2>>6)&0x7) >= 0x8 ) return 1; if ( d1[ind++]+((u2>>3)&0x7) >= 0x8 ) return 1; if ( d1[ind++]+(u2&0x7) >= 0x8 ) return 1; } return 0; break; case 4: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u2 = d2[i]; if ( d1[ind++]+((u2>>28)&0xf) >= 0x10 ) return 1; if ( d1[ind++]+((u2>>24)&0xf) >= 0x10 ) return 1; if ( d1[ind++]+((u2>>20)&0xf) >= 0x10 ) return 1; if ( d1[ind++]+((u2>>16)&0xf) >= 0x10 ) return 1; if ( d1[ind++]+((u2>>12)&0xf) >= 0x10 ) return 1; if ( d1[ind++]+((u2>>8)&0xf) >= 0x10 ) return 1; if ( d1[ind++]+((u2>>4)&0xf) >= 0x10 ) return 1; if ( d1[ind++]+(u2&0xf) >= 0x10 ) return 1; } return 0; break; case 6: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u2 = d2[i]; if ( d1[ind++]+((u2>>24)&0x3f) >= 0x40 ) return 1; if ( d1[ind++]+((u2>>18)&0x3f) >= 0x40 ) return 1; if ( d1[ind++]+((u2>>12)&0x3f) >= 0x40 ) return 1; if ( d1[ind++]+((u2>>6)&0x3f) >= 0x40 ) return 1; if ( d1[ind++]+(u2&0x3f) >= 0x40 ) return 1; } return 0; break; case 8: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u2 = d2[i]; if ( d1[ind++]+((u2>>24)&0xff) >= 0x100 ) return 1; if ( d1[ind++]+((u2>>16)&0xff) >= 0x100 ) return 1; if ( d1[ind++]+((u2>>8)&0xff) >= 0x100 ) return 1; if ( d1[ind++]+(u2&0xff) >= 0x100 ) return 1; } return 0; break; case 16: for ( i = nd_exporigin; i < nd_wpd; i++ ) { u2 = d2[i]; if ( d1[ind++]+((u2>>16)&0xffff) > 0x10000 ) return 1; if ( d1[ind++]+(u2&0xffff) > 0x10000 ) return 1; } return 0; break; case 32: for ( i = nd_exporigin; i < nd_wpd; i++ ) if ( d1[i]+d2[i]>k)&nd_mask0) > nd_mask0 ) return 1; } return 0; break; } #else for ( i = nd_exporigin; i < nd_wpd; i++ ) { u2 = d2[i]; k = (nd_epw-1)*nd_bpe; for ( j = 0; j < nd_epw; j++, k -= nd_bpe ) if ( d1[ind++]+((u2>>k)&nd_mask0) > nd_mask0 ) return 1; } return 0; #endif } int ndl_check_bound2(int index,UINT *d2) { return ndl_check_bound(nd_bound[index],d2); } INLINE int ndl_hash_value(UINT *d) { int i; UINT r; r = 0; for ( i = 0; i < nd_wpd; i++ ) r = (r*1511+d[i]); r %= REDTAB_LEN; return r; } INLINE int ndl_find_reducer(UINT *dg) { RHist r; int d,k,i; d = ndl_hash_value(dg); for ( r = nd_red[d], k = 0; r; r = NEXT(r), k++ ) { if ( ndl_equal(dg,DL(r)) ) { if ( k > 0 ) nd_notfirst++; nd_found++; return r->index; } } if ( Reverse ) for ( i = nd_psn-1; i >= 0; i-- ) { r = nd_psh[i]; if ( ndl_reducible(dg,DL(r)) ) { nd_create++; nd_append_red(dg,i); return i; } } else for ( i = 0; i < nd_psn; i++ ) { r = nd_psh[i]; if ( ndl_reducible(dg,DL(r)) ) { nd_create++; nd_append_red(dg,i); return i; } } return -1; } // ret=0,...,nd_psn-1 => reducer found // ret=nd_psn => reducer not found // ret=-1 => singular top reducible int comp_sig(SIG s1,SIG s2); void _ndltodl(UINT *ndl,DL dl); void print_sig(SIG s) { int i; fprintf(asir_out,"<<"); for ( i = 0; i < nd_nvar; i++ ) { fprintf(asir_out,"%d",s->dl->d[i]); if ( i != nd_nvar-1 ) fprintf(asir_out,","); } fprintf(asir_out,">>*e%d",s->pos); } // assuming increasing order wrt signature INLINE int ndl_find_reducer_s(UINT *dg,SIG sig) { RHist r; int i,singular,ret,d,k; static int wpd,nvar; static SIG quo; static UINT *tmp; if ( !quo || nvar != nd_nvar ) NEWSIG(quo); if ( wpd != nd_wpd ) { wpd = nd_wpd; tmp = (UINT *)MALLOC(wpd*sizeof(UINT)); } d = ndl_hash_value(dg); #if 1 for ( r = nd_red[d], k = 0; r; r = NEXT(r), k++ ) { if ( ndl_equal(dg,DL(r)) ) { return r->index; } } #endif singular = 0; for ( i = 0; i < nd_psn; i++ ) { r = nd_psh[i]; if ( ndl_reducible(dg,DL(r)) ) { ndl_sub(dg,DL(r),tmp); _ndltodl(tmp,DL(quo)); _addtodl(nd_nvar,DL(nd_psh[i]->sig),DL(quo)); quo->pos = nd_psh[i]->sig->pos; ret = comp_sig(sig,quo); if ( ret > 0 ) { singular = 0; break; } if ( ret == 0 ) { fprintf(asir_out,"s"); fflush(asir_out); singular = 1; } } } if ( singular ) return -1; else if ( i < nd_psn ) nd_append_red(dg,i); return i; } ND nd_merge(ND p1,ND p2) { int n,c; int t,can,td1,td2; ND r; NM m1,m2,mr0,mr,s; if ( !p1 ) return p2; else if ( !p2 ) return p1; else { can = 0; for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) { c = DL_COMPARE(DL(m1),DL(m2)); switch ( c ) { case 0: s = m1; m1 = NEXT(m1); can++; NEXTNM2(mr0,mr,s); s = m2; m2 = NEXT(m2); FREENM(s); break; case 1: s = m1; m1 = NEXT(m1); NEXTNM2(mr0,mr,s); break; case -1: s = m2; m2 = NEXT(m2); NEXTNM2(mr0,mr,s); break; } } if ( !mr0 ) if ( m1 ) mr0 = m1; else if ( m2 ) mr0 = m2; else return 0; else if ( m1 ) NEXT(mr) = m1; else if ( m2 ) NEXT(mr) = m2; else NEXT(mr) = 0; BDY(p1) = mr0; SG(p1) = MAX(SG(p1),SG(p2)); LEN(p1) = LEN(p1)+LEN(p2)-can; FREEND(p2); return p1; } } ND nd_add(int mod,ND p1,ND p2) { int n,c; int t,can,td1,td2; ND r; NM m1,m2,mr0,mr,s; Nnd_add++; if ( !p1 ) return p2; else if ( !p2 ) return p1; else if ( mod == -1 ) return nd_add_sf(p1,p2); else if ( mod == -2 ) return nd_add_lf(p1,p2); else if ( !mod ) return nd_add_q(p1,p2); else { can = 0; for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) { c = DL_COMPARE(DL(m1),DL(m2)); switch ( c ) { case 0: t = ((CM(m1))+(CM(m2))) - mod; if ( t < 0 ) t += mod; s = m1; m1 = NEXT(m1); if ( t ) { can++; NEXTNM2(mr0,mr,s); CM(mr) = (t); } else { can += 2; FREENM(s); } s = m2; m2 = NEXT(m2); FREENM(s); break; case 1: s = m1; m1 = NEXT(m1); NEXTNM2(mr0,mr,s); break; case -1: s = m2; m2 = NEXT(m2); NEXTNM2(mr0,mr,s); break; } } if ( !mr0 ) if ( m1 ) mr0 = m1; else if ( m2 ) mr0 = m2; else return 0; else if ( m1 ) NEXT(mr) = m1; else if ( m2 ) NEXT(mr) = m2; else NEXT(mr) = 0; BDY(p1) = mr0; SG(p1) = MAX(SG(p1),SG(p2)); LEN(p1) = LEN(p1)+LEN(p2)-can; FREEND(p2); return p1; } } /* XXX on opteron, the inlined manipulation of destructive additon of * two NM seems to make gcc optimizer get confused, so the part is * done in a function. */ int nm_destructive_add_q(NM *m1,NM *m2,NM *mr0,NM *mr) { NM s; P t; int can; addp(nd_vc,CP(*m1),CP(*m2),&t); s = *m1; *m1 = NEXT(*m1); if ( t ) { can = 1; NEXTNM2(*mr0,*mr,s); CP(*mr) = (t); } else { can = 2; FREENM(s); } s = *m2; *m2 = NEXT(*m2); FREENM(s); return can; } ND nd_add_q(ND p1,ND p2) { int n,c,can; ND r; NM m1,m2,mr0,mr,s; P t; if ( !p1 ) return p2; else if ( !p2 ) return p1; else { can = 0; for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) { c = DL_COMPARE(DL(m1),DL(m2)); switch ( c ) { case 0: #if defined(__x86_64__) can += nm_destructive_add_q(&m1,&m2,&mr0,&mr); #else addp(nd_vc,CP(m1),CP(m2),&t); s = m1; m1 = NEXT(m1); if ( t ) { can++; NEXTNM2(mr0,mr,s); CP(mr) = (t); } else { can += 2; FREENM(s); } s = m2; m2 = NEXT(m2); FREENM(s); #endif break; case 1: s = m1; m1 = NEXT(m1); NEXTNM2(mr0,mr,s); break; case -1: s = m2; m2 = NEXT(m2); NEXTNM2(mr0,mr,s); break; } } if ( !mr0 ) if ( m1 ) mr0 = m1; else if ( m2 ) mr0 = m2; else return 0; else if ( m1 ) NEXT(mr) = m1; else if ( m2 ) NEXT(mr) = m2; else NEXT(mr) = 0; BDY(p1) = mr0; SG(p1) = MAX(SG(p1),SG(p2)); LEN(p1) = LEN(p1)+LEN(p2)-can; FREEND(p2); return p1; } } ND nd_add_sf(ND p1,ND p2) { int n,c,can; ND r; NM m1,m2,mr0,mr,s; int t; if ( !p1 ) return p2; else if ( !p2 ) return p1; else { can = 0; for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) { c = DL_COMPARE(DL(m1),DL(m2)); switch ( c ) { case 0: t = _addsf(CM(m1),CM(m2)); s = m1; m1 = NEXT(m1); if ( t ) { can++; NEXTNM2(mr0,mr,s); CM(mr) = (t); } else { can += 2; FREENM(s); } s = m2; m2 = NEXT(m2); FREENM(s); break; case 1: s = m1; m1 = NEXT(m1); NEXTNM2(mr0,mr,s); break; case -1: s = m2; m2 = NEXT(m2); NEXTNM2(mr0,mr,s); break; } } if ( !mr0 ) if ( m1 ) mr0 = m1; else if ( m2 ) mr0 = m2; else return 0; else if ( m1 ) NEXT(mr) = m1; else if ( m2 ) NEXT(mr) = m2; else NEXT(mr) = 0; BDY(p1) = mr0; SG(p1) = MAX(SG(p1),SG(p2)); LEN(p1) = LEN(p1)+LEN(p2)-can; FREEND(p2); return p1; } } ND nd_reduce2(int mod,ND d,ND g,NDV p,NM mul,NDC dn,Obj *divp) { int c,c1,c2; Z cg,cred,gcd,tq; P cgp,credp,gcdp; Obj tr,tr1; if ( mod == -1 ) { CM(mul) = _mulsf(_invsf(HCM(p)),_chsgnsf(HCM(g))); *divp = (Obj)ONE; } else if ( mod == -2 ) { Z inv,t; divlf(ONE,HCZ(p),&inv); chsgnlf(HCZ(g),&t); mullf(inv,t,&CZ(mul)); *divp = (Obj)ONE; } else if ( mod ) { c1 = invm(HCM(p),mod); c2 = mod-HCM(g); DMAR(c1,c2,0,mod,c); CM(mul) = c; *divp = (Obj)ONE; } else if ( nd_vc ) { ezgcdpz(nd_vc,HCP(g),HCP(p),&gcdp); divsp(nd_vc,HCP(g),gcdp,&cgp); divsp(nd_vc,HCP(p),gcdp,&credp); chsgnp(cgp,&CP(mul)); nd_mul_c_q(d,credp); nd_mul_c_q(g,credp); if ( dn ) { mulr(nd_vc,(Obj)dn->r,(Obj)credp,&tr); reductr(nd_vc,tr,&tr1); dn->r = (R)tr1; } *divp = (Obj)credp; } else { igcd_cofactor(HCZ(g),HCZ(p),&gcd,&cg,&cred); chsgnz(cg,&CZ(mul)); nd_mul_c_q(d,(P)cred); nd_mul_c_q(g,(P)cred); if ( dn ) { mulz(dn->z,cred,&tq); dn->z = tq; } *divp = (Obj)cred; } return nd_add(mod,g,ndv_mul_nm(mod,mul,p)); } /* ret=1 : success, ret=0 : overflow */ int nd_nf(int mod,ND d,ND g,NDV *ps,int full,ND *rp) { NM m,mrd,tail; NM mul; int n,sugar,psugar,sugar0,stat,index; int c,c1,c2,dummy; RHist h; NDV p,red; Q cg,cred,gcd,tq,qq; Z iq; DP dmul; NODE node; LIST hist; double hmag; P tp,tp1; Obj tr,tr1,div; union oNDC hg; P cont; if ( !g ) { *rp = d; return 1; } if ( !mod ) hmag = ((double)p_mag(HCP(g)))*nd_scale; sugar0 = sugar = SG(g); n = NV(g); mul = (NM)MALLOC(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT)); if ( d ) for ( tail = BDY(d); NEXT(tail); tail = NEXT(tail) ); for ( ; g; ) { index = ndl_find_reducer(HDL(g)); if ( index >= 0 ) { h = nd_psh[index]; ndl_sub(HDL(g),DL(h),DL(mul)); if ( ndl_check_bound2(index,DL(mul)) ) { nd_free(g); nd_free(d); return 0; } p = nd_demand ? ndv_load(index) : ps[index]; /* d+g -> div*(d+g)+mul*p */ g = nd_reduce2(mod,d,g,p,mul,0,&div); if ( nd_gentrace ) { /* Trace=[div,index,mul,ONE] */ STOZ(index,iq); nmtodp(mod,mul,&dmul); node = mknode(4,div,iq,dmul,ONE); } sugar = MAX(sugar,SG(p)+TD(DL(mul))); if ( !mod && g && !nd_vc && ((double)(p_mag(HCP(g))) > hmag) ) { hg = HCU(g); nd_removecont2(d,g); if ( nd_gentrace ) { /* overwrite cont : Trace=[div,index,mul,cont] */ /* exact division */ cont = ndc_div(mod,hg,HCU(g)); if ( nd_gentrace && !UNIQ(cont) ) ARG3(node) = (pointer)cont; } hmag = ((double)p_mag(HCP(g)))*nd_scale; } MKLIST(hist,node); MKNODE(node,hist,nd_tracelist); nd_tracelist = node; } else if ( !full ) { *rp = g; return 1; } else { m = BDY(g); if ( NEXT(m) ) { BDY(g) = NEXT(m); NEXT(m) = 0; LEN(g)--; } else { FREEND(g); g = 0; } if ( d ) { NEXT(tail)=m; tail=m; LEN(d)++; } else { MKND(n,m,1,d); tail = BDY(d); } } } if ( d ) SG(d) = sugar; *rp = d; return 1; } // ret=1 => success // ret=0 => overflow // ret=-1 => singular top reducible int nd_nf_s(int mod,ND d,ND g,NDV *ps,int full,ND *rp) { NM m,mrd,tail; NM mul; int n,sugar,psugar,sugar0,stat,index; int c,c1,c2,dummy; RHist h; NDV p,red; Q cg,cred,gcd,tq,qq; Z iq; DP dmul; NODE node; LIST hist; double hmag; P tp,tp1; Obj tr,tr1,div; union oNDC hg; P cont; SIG sig; if ( !g ) { *rp = d; return 1; } if ( !mod ) hmag = ((double)p_mag(HCP(g)))*nd_scale; sugar0 = sugar = SG(g); n = NV(g); mul = (NM)MALLOC(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT)); if ( d ) for ( tail = BDY(d); NEXT(tail); tail = NEXT(tail) ); sig = g->sig; for ( ; g; ) { index = ndl_find_reducer_s(HDL(g),sig); if ( index >= 0 && index < nd_psn ) { // reducer found h = nd_psh[index]; ndl_sub(HDL(g),DL(h),DL(mul)); if ( ndl_check_bound2(index,DL(mul)) ) { nd_free(g); nd_free(d); return 0; } p = ps[index]; /* d+g -> div*(d+g)+mul*p */ g = nd_reduce2(mod,d,g,p,mul,0,&div); sugar = MAX(sugar,SG(p)+TD(DL(mul))); if ( !mod && g && ((double)(p_mag(HCP(g))) > hmag) ) { hg = HCU(g); nd_removecont2(d,g); hmag = ((double)p_mag(HCP(g)))*nd_scale; } } else if ( index == -1 ) { // singular top reducible return -1; } else if ( !full ) { *rp = g; g->sig = sig; return 1; } else { m = BDY(g); if ( NEXT(m) ) { BDY(g) = NEXT(m); NEXT(m) = 0; LEN(g)--; } else { FREEND(g); g = 0; } if ( d ) { NEXT(tail)=m; tail=m; LEN(d)++; } else { MKND(n,m,1,d); tail = BDY(d); } } } if ( d ) { SG(d) = sugar; d->sig = sig; } *rp = d; return 1; } int nd_nf_pbucket(int mod,ND g,NDV *ps,int full,ND *rp) { int hindex,index; NDV p; ND u,d,red; NODE l; NM mul,m,mrd,tail; int sugar,psugar,n,h_reducible; PGeoBucket bucket; int c,c1,c2; Z cg,cred,gcd,zzz; RHist h; double hmag,gmag; int count = 0; int hcount = 0; if ( !g ) { *rp = 0; return 1; } sugar = SG(g); n = NV(g); if ( !mod ) hmag = ((double)p_mag((P)HCZ(g)))*nd_scale; bucket = create_pbucket(); add_pbucket(mod,bucket,g); d = 0; mul = (NM)MALLOC(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT)); while ( 1 ) { if ( mod > 0 || mod == -1 ) hindex = head_pbucket(mod,bucket); else if ( mod == -2 ) hindex = head_pbucket_lf(bucket); else hindex = head_pbucket_q(bucket); if ( hindex < 0 ) { if ( DP_Print > 3 ) printf("(%d %d)",count,hcount); if ( d ) SG(d) = sugar; *rp = d; return 1; } g = bucket->body[hindex]; index = ndl_find_reducer(HDL(g)); if ( index >= 0 ) { count++; if ( !d ) hcount++; h = nd_psh[index]; ndl_sub(HDL(g),DL(h),DL(mul)); if ( ndl_check_bound2(index,DL(mul)) ) { nd_free(d); free_pbucket(bucket); *rp = 0; return 0; } p = ps[index]; if ( mod == -1 ) CM(mul) = _mulsf(_invsf(HCM(p)),_chsgnsf(HCM(g))); else if ( mod == -2 ) { Z inv,t; divlf(ONE,HCZ(p),&inv); chsgnlf(HCZ(g),&t); mullf(inv,t,&CZ(mul)); } else if ( mod ) { c1 = invm(HCM(p),mod); c2 = mod-HCM(g); DMAR(c1,c2,0,mod,c); CM(mul) = c; } else { igcd_cofactor(HCZ(g),HCZ(p),&gcd,&cg,&cred); chsgnz(cg,&CZ(mul)); nd_mul_c_q(d,(P)cred); mulq_pbucket(bucket,cred); g = bucket->body[hindex]; gmag = (double)p_mag((P)HCZ(g)); } red = ndv_mul_nm(mod,mul,p); bucket->body[hindex] = nd_remove_head(g); red = nd_remove_head(red); add_pbucket(mod,bucket,red); psugar = SG(p)+TD(DL(mul)); sugar = MAX(sugar,psugar); if ( !mod && hmag && (gmag > hmag) ) { g = normalize_pbucket(mod,bucket); if ( !g ) { if ( d ) SG(d) = sugar; *rp = d; return 1; } nd_removecont2(d,g); hmag = ((double)p_mag((P)HCZ(g)))*nd_scale; add_pbucket(mod,bucket,g); } } else if ( !full ) { g = normalize_pbucket(mod,bucket); if ( g ) SG(g) = sugar; *rp = g; return 1; } else { m = BDY(g); if ( NEXT(m) ) { BDY(g) = NEXT(m); NEXT(m) = 0; LEN(g)--; } else { FREEND(g); g = 0; } bucket->body[hindex] = g; NEXT(m) = 0; if ( d ) { NEXT(tail)=m; tail=m; LEN(d)++; } else { MKND(n,m,1,d); tail = BDY(d); } } } } int nd_nf_pbucket_s(int mod,ND g,NDV *ps,int full,ND *rp) { int hindex,index; NDV p; ND u,d,red; NODE l; NM mul,m,mrd,tail; int sugar,psugar,n,h_reducible; PGeoBucket bucket; int c,c1,c2; Z cg,cred,gcd,zzz; RHist h; double hmag,gmag; int count = 0; int hcount = 0; SIG sig; if ( !g ) { *rp = 0; return 1; } sugar = SG(g); n = NV(g); if ( !mod ) hmag = ((double)p_mag((P)HCZ(g)))*nd_scale; bucket = create_pbucket(); add_pbucket(mod,bucket,g); d = 0; mul = (NM)MALLOC(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT)); sig = g->sig; while ( 1 ) { if ( mod > 0 || mod == -1 ) hindex = head_pbucket(mod,bucket); else if ( mod == -2 ) hindex = head_pbucket_lf(bucket); else hindex = head_pbucket_q(bucket); if ( hindex < 0 ) { if ( DP_Print > 3 ) printf("(%d %d)",count,hcount); if ( d ) { SG(d) = sugar; d->sig = sig; } *rp = d; return 1; } g = bucket->body[hindex]; index = ndl_find_reducer_s(HDL(g),sig); if ( index >= 0 && index < nd_psn ) { count++; if ( !d ) hcount++; h = nd_psh[index]; ndl_sub(HDL(g),DL(h),DL(mul)); if ( ndl_check_bound2(index,DL(mul)) ) { nd_free(d); free_pbucket(bucket); *rp = 0; return 0; } p = ps[index]; if ( mod == -1 ) CM(mul) = _mulsf(_invsf(HCM(p)),_chsgnsf(HCM(g))); else if ( mod == -2 ) { Z inv,t; divlf(ONE,HCZ(p),&inv); chsgnlf(HCZ(g),&t); mullf(inv,t,&CZ(mul)); } else if ( mod ) { c1 = invm(HCM(p),mod); c2 = mod-HCM(g); DMAR(c1,c2,0,mod,c); CM(mul) = c; } else { igcd_cofactor(HCZ(g),HCZ(p),&gcd,&cg,&cred); chsgnz(cg,&CZ(mul)); nd_mul_c_q(d,(P)cred); mulq_pbucket(bucket,cred); g = bucket->body[hindex]; gmag = (double)p_mag((P)HCZ(g)); } red = ndv_mul_nm(mod,mul,p); bucket->body[hindex] = nd_remove_head(g); red = nd_remove_head(red); add_pbucket(mod,bucket,red); psugar = SG(p)+TD(DL(mul)); sugar = MAX(sugar,psugar); if ( !mod && hmag && (gmag > hmag) ) { g = normalize_pbucket(mod,bucket); if ( !g ) { if ( d ) { SG(d) = sugar; d->sig = sig; } *rp = d; return 1; } nd_removecont2(d,g); hmag = ((double)p_mag((P)HCZ(g)))*nd_scale; add_pbucket(mod,bucket,g); } } else if ( index == -1 ) { // singular top reducible return -1; } else if ( !full ) { g = normalize_pbucket(mod,bucket); if ( g ) { SG(g) = sugar; g->sig = sig; } *rp = g; return 1; } else { m = BDY(g); if ( NEXT(m) ) { BDY(g) = NEXT(m); NEXT(m) = 0; LEN(g)--; } else { FREEND(g); g = 0; } bucket->body[hindex] = g; NEXT(m) = 0; if ( d ) { NEXT(tail)=m; tail=m; LEN(d)++; } else { MKND(n,m,1,d); tail = BDY(d); } } } } /* input : list of NDV, cand : list of NDV */ int ndv_check_membership(int m,NODE input,int obpe,int oadv,EPOS oepos,NODE cand) { int n,i,stat; ND nf,d; NDV r; NODE t,s; union oNDC dn; Z q; LIST list; ndv_setup(m,0,cand,nd_gentrace?1:0,1,0); n = length(cand); if ( nd_gentrace ) { nd_alltracelist = 0; nd_tracelist = 0; } /* membercheck : list is a subset of Id(cand) ? */ for ( t = input, i = 0; t; t = NEXT(t), i++ ) { again: nd_tracelist = 0; if ( nd_bpe > obpe ) r = ndv_dup_realloc((NDV)BDY(t),obpe,oadv,oepos); else r = (NDV)BDY(t); #if 0 // moved to nd_f4_lf_trace() if ( m == -2 ) ndv_mod(m,r); #endif d = ndvtond(m,r); stat = nd_nf(m,0,d,nd_ps,0,&nf); if ( !stat ) { nd_reconstruct(0,0); goto again; } else if ( nf ) return 0; if ( nd_gentrace ) { nd_tracelist = reverse_node(nd_tracelist); MKLIST(list,nd_tracelist); STOZ(i,q); s = mknode(2,q,list); MKLIST(list,s); MKNODE(s,list,nd_alltracelist); nd_alltracelist = s; nd_tracelist = 0; } if ( DP_Print ) { printf("."); fflush(stdout); } } if ( DP_Print ) { printf("\n"); } return 1; } ND nd_remove_head(ND p) { NM m; m = BDY(p); if ( !NEXT(m) ) { FREEND(p); p = 0; } else { BDY(p) = NEXT(m); LEN(p)--; } FREENM(m); return p; } ND nd_separate_head(ND p,ND *head) { NM m,m0; ND r; m = BDY(p); if ( !NEXT(m) ) { *head = p; p = 0; } else { m0 = m; BDY(p) = NEXT(m); LEN(p)--; NEXT(m0) = 0; MKND(NV(p),m0,1,r); *head = r; } return p; } PGeoBucket create_pbucket() { PGeoBucket g; g = CALLOC(1,sizeof(struct oPGeoBucket)); g->m = -1; return g; } void free_pbucket(PGeoBucket b) { int i; for ( i = 0; i <= b->m; i++ ) if ( b->body[i] ) { nd_free(b->body[i]); b->body[i] = 0; } GCFREE(b); } void add_pbucket_symbolic(PGeoBucket g,ND d) { int l,i,k,m; if ( !d ) return; l = LEN(d); for ( k = 0, m = 1; l > m; k++, m <<= 1 ); /* 2^(k-1) < l <= 2^k (=m) */ d = nd_merge(g->body[k],d); for ( ; d && LEN(d) > m; k++, m <<= 1 ) { g->body[k] = 0; d = nd_merge(g->body[k+1],d); } g->body[k] = d; g->m = MAX(g->m,k); } void add_pbucket(int mod,PGeoBucket g,ND d) { int l,i,k,m; if ( !d ) return; l = LEN(d); for ( k = 0, m = 1; l > m; k++, m <<= 1 ); /* 2^(k-1) < l <= 2^k (=m) */ d = nd_add(mod,g->body[k],d); for ( ; d && LEN(d) > m; k++, m <<= 1 ) { g->body[k] = 0; d = nd_add(mod,g->body[k+1],d); } g->body[k] = d; g->m = MAX(g->m,k); } void mulq_pbucket(PGeoBucket g,Z c) { int k; for ( k = 0; k <= g->m; k++ ) nd_mul_c_q(g->body[k],(P)c); } NM remove_head_pbucket_symbolic(PGeoBucket g) { int j,i,k,c; NM head; k = g->m; j = -1; for ( i = 0; i <= k; i++ ) { if ( !g->body[i] ) continue; if ( j < 0 ) j = i; else { c = DL_COMPARE(HDL(g->body[i]),HDL(g->body[j])); if ( c > 0 ) j = i; else if ( c == 0 ) g->body[i] = nd_remove_head(g->body[i]); } } if ( j < 0 ) return 0; else { head = BDY(g->body[j]); if ( !NEXT(head) ) { FREEND(g->body[j]); g->body[j] = 0; } else { BDY(g->body[j]) = NEXT(head); LEN(g->body[j])--; } return head; } } int head_pbucket(int mod,PGeoBucket g) { int j,i,c,k,nv,sum; UINT *di,*dj; ND gi,gj; k = g->m; while ( 1 ) { j = -1; for ( i = 0; i <= k; i++ ) { if ( !(gi = g->body[i]) ) continue; if ( j < 0 ) { j = i; gj = g->body[j]; dj = HDL(gj); sum = HCM(gj); } else { c = DL_COMPARE(HDL(gi),dj); if ( c > 0 ) { if ( sum ) HCM(gj) = sum; else g->body[j] = nd_remove_head(gj); j = i; gj = g->body[j]; dj = HDL(gj); sum = HCM(gj); } else if ( c == 0 ) { if ( mod == -1 ) sum = _addsf(sum,HCM(gi)); else { sum = sum+HCM(gi)-mod; if ( sum < 0 ) sum += mod; } g->body[i] = nd_remove_head(gi); } } } if ( j < 0 ) return -1; else if ( sum ) { HCM(gj) = sum; return j; } else g->body[j] = nd_remove_head(gj); } } int head_pbucket_q(PGeoBucket g) { int j,i,c,k,nv; Z sum,t; ND gi,gj; k = g->m; while ( 1 ) { j = -1; for ( i = 0; i <= k; i++ ) { if ( !(gi = g->body[i]) ) continue; if ( j < 0 ) { j = i; gj = g->body[j]; sum = HCZ(gj); } else { nv = NV(gi); c = DL_COMPARE(HDL(gi),HDL(gj)); if ( c > 0 ) { if ( sum ) HCZ(gj) = sum; else g->body[j] = nd_remove_head(gj); j = i; gj = g->body[j]; sum = HCZ(gj); } else if ( c == 0 ) { addz(sum,HCZ(gi),&t); sum = t; g->body[i] = nd_remove_head(gi); } } } if ( j < 0 ) return -1; else if ( sum ) { HCZ(gj) = sum; return j; } else g->body[j] = nd_remove_head(gj); } } int head_pbucket_lf(PGeoBucket g) { int j,i,c,k,nv; Z sum,t; ND gi,gj; k = g->m; while ( 1 ) { j = -1; for ( i = 0; i <= k; i++ ) { if ( !(gi = g->body[i]) ) continue; if ( j < 0 ) { j = i; gj = g->body[j]; sum = HCZ(gj); } else { nv = NV(gi); c = DL_COMPARE(HDL(gi),HDL(gj)); if ( c > 0 ) { if ( sum ) HCZ(gj) = sum; else g->body[j] = nd_remove_head(gj); j = i; gj = g->body[j]; sum = HCZ(gj); } else if ( c == 0 ) { addlf(sum,HCZ(gi),&t); sum = t; g->body[i] = nd_remove_head(gi); } } } if ( j < 0 ) return -1; else if ( sum ) { HCZ(gj) = sum; return j; } else g->body[j] = nd_remove_head(gj); } } ND normalize_pbucket(int mod,PGeoBucket g) { int i; ND r,t; r = 0; for ( i = 0; i <= g->m; i++ ) { r = nd_add(mod,r,g->body[i]); g->body[i] = 0; } g->m = -1; return r; } #if 0 void register_hcf(NDV p) { DCP dc,t; P hc,h; int c; NODE l,l1,prev; hc = p->body->c.p; if ( !nd_vc || NUM(hc) ) return; fctrp(nd_vc,hc,&dc); for ( t = dc; t; t = NEXT(t) ) { h = t->c; if ( NUM(h) ) continue; for ( prev = 0, l = nd_hcf; l; prev = l, l = NEXT(l) ) { c = compp(nd_vc,h,(P)BDY(l)); if ( c >= 0 ) break; } if ( !l || c > 0 ) { MKNODE(l1,h,l); if ( !prev ) nd_hcf = l1; else NEXT(prev) = l1; } } } #else void register_hcf(NDV p) { DCP dc,t; P hc,h,q; Q dmy; int c; NODE l,l1,prev; hc = p->body->c.p; if ( NUM(hc) ) return; ptozp(hc,1,&dmy,&h); #if 1 for ( l = nd_hcf; l; l = NEXT(l) ) { while ( 1 ) { if ( divtpz(nd_vc,h,(P)BDY(l),&q) ) h = q; else break; } } if ( NUM(h) ) return; #endif for ( prev = 0, l = nd_hcf; l; prev = l, l = NEXT(l) ) { c = compp(nd_vc,h,(P)BDY(l)); if ( c >= 0 ) break; } if ( !l || c > 0 ) { MKNODE(l1,h,l); if ( !prev ) nd_hcf = l1; else NEXT(prev) = l1; } } #endif int do_diagonalize(int sugar,int m) { int i,nh,stat; NODE r,g,t; ND h,nf,s,head; NDV nfv; Q q; P nm,nmp,dn,mnp,dnp,cont,cont1; union oNDC hc; NODE node; LIST l; Z iq; for ( i = nd_psn-1; i >= 0 && SG(nd_psh[i]) == sugar; i-- ) { if ( nd_gentrace ) { /* Trace = [1,index,1,1] */ STOZ(i,iq); node = mknode(4,ONE,iq,ONE,ONE); MKLIST(l,node); MKNODE(nd_tracelist,l,0); } if ( nd_demand ) nfv = ndv_load(i); else nfv = nd_ps[i]; s = ndvtond(m,nfv); s = nd_separate_head(s,&head); stat = nd_nf(m,head,s,nd_ps,1,&nf); if ( !stat ) return 0; ndv_free(nfv); hc = HCU(nf); nd_removecont(m,nf); /* exact division */ cont = ndc_div(m,hc,HCU(nf)); if ( nd_gentrace ) finalize_tracelist(i,cont); nfv = ndtondv(m,nf); nd_free(nf); nd_bound[i] = ndv_compute_bound(nfv); if ( !m ) register_hcf(nfv); if ( nd_demand ) { ndv_save(nfv,i); ndv_free(nfv); } else nd_ps[i] = nfv; } return 1; } LIST compute_splist() { NODE g,tn0,tn,node; LIST l0; ND_pairs d,t; int i; Z i1,i2; g = 0; d = 0; for ( i = 0; i < nd_psn; i++ ) { d = update_pairs(d,g,i,0); g = update_base(g,i); } for ( t = d, tn0 = 0; t; t = NEXT(t) ) { NEXTNODE(tn0,tn); STOZ(t->i1,i1); STOZ(t->i2,i2); node = mknode(2,i1,i2); MKLIST(l0,node); BDY(tn) = l0; } if ( tn0 ) NEXT(tn) = 0; MKLIST(l0,tn0); return l0; } /* return value = 0 => input is not a GB */ NODE nd_gb(int m,int ishomo,int checkonly,int gensyz,int **indp) { int i,nh,sugar,stat; NODE r,g,t; ND_pairs d; ND_pairs l; ND h,nf,s,head,nf1; NDV nfv; Z q; union oNDC dn,hc; int diag_count = 0; P cont; LIST list; struct oEGT eg1,eg2,eg_update; init_eg(&eg_update); Nnd_add = 0; g = 0; d = 0; for ( i = 0; i < nd_psn; i++ ) { d = update_pairs(d,g,i,gensyz); g = update_base(g,i); } sugar = 0; while ( d ) { again: l = nd_minp(d,&d); if ( MaxDeg > 0 && SG(l) > MaxDeg ) break; if ( SG(l) != sugar ) { if ( ishomo ) { diag_count = 0; stat = do_diagonalize(sugar,m); if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(0,d); goto again; } } sugar = SG(l); if ( DP_Print ) fprintf(asir_out,"%d",sugar); } stat = nd_sp(m,0,l,&h); if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(0,d); goto again; } #if USE_GEOBUCKET stat = (m&&!nd_gentrace)?nd_nf_pbucket(m,h,nd_ps,!Top,&nf) :nd_nf(m,0,h,nd_ps,!Top,&nf); #else stat = nd_nf(m,0,h,nd_ps,!Top,&nf); #endif if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(0,d); goto again; } else if ( nf ) { if ( checkonly || gensyz ) return 0; if ( nd_newelim ) { if ( nd_module ) { if ( MPOS(HDL(nf)) > 1 ) return 0; } else if ( !(HDL(nf)[nd_exporigin] & nd_mask[0]) ) return 0; } if ( DP_Print ) { printf("+"); fflush(stdout); } hc = HCU(nf); nd_removecont(m,nf); if ( !m && nd_nalg ) { nd_monic(0,&nf); nd_removecont(m,nf); } if ( nd_gentrace ) { /* exact division */ cont = ndc_div(m,hc,HCU(nf)); if ( m || !UNIQ(cont) ) { t = mknode(4,NULLP,NULLP,NULLP,cont); MKLIST(list,t); MKNODE(t,list,nd_tracelist); nd_tracelist = t; } } nfv = ndtondv(m,nf); nd_free(nf); nh = ndv_newps(m,nfv,0); if ( !m && (ishomo && ++diag_count == diag_period) ) { diag_count = 0; stat = do_diagonalize(sugar,m); if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(1,d); goto again; } } get_eg(&eg1); d = update_pairs(d,g,nh,0); get_eg(&eg2); add_eg(&eg_update,&eg1,&eg2); g = update_base(g,nh); FREENDP(l); } else { if ( nd_gentrace && gensyz ) { nd_tracelist = reverse_node(nd_tracelist); MKLIST(list,nd_tracelist); STOZ(-1,q); t = mknode(2,q,list); MKLIST(list,t); MKNODE(t,list,nd_alltracelist); nd_alltracelist = t; nd_tracelist = 0; } if ( DP_Print ) { printf("."); fflush(stdout); } FREENDP(l); } } conv_ilist(nd_demand,0,g,indp); if ( !checkonly && DP_Print ) { printf("nd_gb done. Number of nd_add=%d\n",Nnd_add); fflush(stdout); } if ( DP_Print ) print_eg("update",&eg_update); return g; } ND_pairs update_pairs_s(ND_pairs d,int t,NODE *syz); ND_pairs nd_newpairs_s(int t ,NODE *syz); int nd_nf_pbucket_s(int mod,ND g,NDV *ps,int full,ND *nf); int nd_nf_s(int mod,ND d,ND g,NDV *ps,int full,ND *nf); void _copydl(int n,DL d1,DL d2); void _subfromdl(int n,DL d1,DL d2); extern int (*cmpdl)(int n,DL d1,DL d2); NODE insert_sig(NODE l,SIG s) { int pos; DL sig; struct oNODE root; NODE p,prev,r; SIG t; pos = s->pos; sig = DL(s); root.next = l; prev = &root; for ( p = l; p; p = p->next ) { t = (SIG)p->body; if ( t->pos == pos ) { if ( _dl_redble(DL(t),sig,nd_nvar) ) return root.next; else if ( _dl_redble(sig,DL(t),nd_nvar) ) // remove p prev->next = p->next; } else prev = p; } NEWNODE(r); r->body = (pointer)s; r->next = 0; for ( p = &root; p->next; p = p->next ); p->next = r; // r->next = root.next; // return r; return root.next; } ND_pairs remove_spair_s(ND_pairs d,SIG sig) { struct oND_pairs root; ND_pairs prev,p; SIG spsig; root.next = d; prev = &root; p = d; while ( p ) { spsig = p->sig; if ( sig->pos == spsig->pos && _dl_redble(DL(sig),DL(spsig),nd_nvar) ) { // remove p prev->next = p->next; Nsyz++; } else prev = p; p = p->next; } return (ND_pairs)root.next; } int _dl_redble_ext(DL,DL,DL,int); int small_lcm(ND_pairs l) { SIG sig; int i; NODE t; static DL lcm,mul,quo; static int nvar; if ( nvar < nd_nvar ) { nvar = nd_nvar; NEWDL(lcm,nvar); NEWDL(quo,nvar); NEWDL(mul,nvar); } sig = l->sig; _ndltodl(l->lcm,lcm); #if 0 for ( i = 0; i < nd_psn; i++ ) { if ( sig->pos == nd_psh[i]->sig->pos && _dl_redble_ext(DL(nd_psh[i]->sig),DL(sig),quo,nd_nvar) ) { _ndltodl(DL(nd_psh[i]),mul); _addtodl(nd_nvar,quo,mul); if ( (*cmpdl)(nd_nvar,lcm,mul) > 0 ) break; } } if ( i < nd_psn ) return 1; else return 0; #else for ( t = nd_sba_pos[sig->pos]; t; t = t->next ) { i = (long)BDY(t); if ( _dl_redble_ext(DL(nd_psh[i]->sig),DL(sig),quo,nd_nvar) ) { _ndltodl(DL(nd_psh[i]),mul); _addtodl(nd_nvar,quo,mul); if ( (*cmpdl)(nd_nvar,lcm,mul) > 0 ) break; } } if ( t ) return 1; else return 0; #endif } ND_pairs remove_large_lcm(ND_pairs d) { struct oND_pairs root; ND_pairs prev,p; root.next = d; prev = &root; p = d; while ( p ) { if ( small_lcm(p) ) { // remove p prev->next = p->next; } else prev = p; p = p->next; } return (ND_pairs)root.next; } struct oEGT eg_create,eg_newpairs,eg_merge; NODE conv_ilist_s(int demand,int trace,int **indp); NODE nd_sba_buch(int m,int ishomo,int **indp) { int i,j,nh,sugar,stat; NODE r,t,g; ND_pairs d; ND_pairs l; ND h,nf,s,head,nf1; NDV nfv; Z q; union oNDC dn,hc; P cont; LIST list; SIG sig; NODE *syzlist; int Nredundant; DL lcm,quo,mul; struct oEGT eg1,eg2,eg_update,eg_remove,eg_large,eg_nf,eg_nfzero; init_eg(&eg_remove); syzlist = (NODE *)MALLOC(nd_psn*sizeof(NODE)); Nsyz = 0; Nnd_add = 0; Nredundant = 0; d = 0; for ( i = 0; i < nd_psn; i++ ) { d = update_pairs_s(d,i,syzlist); } for ( i = 0; i < nd_psn; i++ ) for ( j = i+1; j < nd_psn; j++ ) { NEWSIG(sig); sig->pos = j; _copydl(nd_nvar,nd_sba_hm[i],sig->dl); syzlist[sig->pos] = insert_sig(syzlist[sig->pos],sig); } sugar = 0; NEWDL(lcm,nd_nvar); NEWDL(quo,nd_nvar); NEWDL(mul,nd_nvar); init_eg(&eg_create); init_eg(&eg_merge); init_eg(&eg_large); init_eg(&eg_nf); init_eg(&eg_nfzero); while ( d ) { again: if ( DP_Print ) { int len; ND_pairs td; for ( td = d, len=0; td; td = td->next, len++) ; if ( !(len%100) ) fprintf(asir_out,"(%d)",len); } l = d; d = d->next; if ( small_lcm(l) ) { if ( DP_Print ) fprintf(asir_out,"M"); Nredundant++; continue; } if ( SG(l) != sugar ) { sugar = SG(l); if ( DP_Print ) fprintf(asir_out,"%d",sugar); } sig = l->sig; stat = nd_sp(m,0,l,&h); if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(0,d); goto again; } get_eg(&eg1); #if USE_GEOBUCKET stat = m?nd_nf_pbucket_s(m,h,nd_ps,!Top,&nf):nd_nf_s(m,0,h,nd_ps,!Top,&nf); #else stat = nd_nf_s(m,0,h,nd_ps,!Top,&nf); #endif get_eg(&eg2); if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(0,d); goto again; } else if ( stat == -1 ) { if ( DP_Print ) { printf("S"); fflush(stdout); } FREENDP(l); } else if ( nf ) { if ( DP_Print ) { printf("+"); fflush(stdout); } add_eg(&eg_nf,&eg1,&eg2); hc = HCU(nf); nd_removecont(m,nf); nfv = ndtondv(m,nf); nd_free(nf); nh = ndv_newps(m,nfv,0); d = update_pairs_s(d,nh,syzlist); nd_sba_pos[sig->pos] = append_one(nd_sba_pos[sig->pos],nh); FREENDP(l); } else { add_eg(&eg_nfzero,&eg1,&eg2); // syzygy get_eg(&eg1); d = remove_spair_s(d,sig); get_eg(&eg2); add_eg(&eg_remove,&eg1,&eg2); syzlist[sig->pos] = insert_sig(syzlist[sig->pos],sig); if ( DP_Print ) { printf("."); fflush(stdout); } FREENDP(l); } } g = conv_ilist_s(nd_demand,0,indp); if ( DP_Print ) { printf("\nnd_sba done. nd_add=%d,Nsyz=%d,Nsamesig=%d,Nredundant=%d\n",Nnd_add,Nsyz,Nsamesig,Nredundant); fflush(stdout); print_eg("create",&eg_create); print_eg("merge",&eg_merge); print_eg("remove",&eg_remove); print_eg("nf",&eg_nf); print_eg("nfzero",&eg_nfzero); printf("\n"); } return g; } /* splist = [[i1,i2],...] */ int check_splist(int m,NODE splist) { NODE t,p; ND_pairs d,r,l; int stat; ND h,nf; for ( d = 0, t = splist; t; t = NEXT(t) ) { p = BDY((LIST)BDY(t)); NEXTND_pairs(d,r); r->i1 = ZTOS((Q)ARG0(p)); r->i2 = ZTOS((Q)ARG1(p)); ndl_lcm(DL(nd_psh[r->i1]),DL(nd_psh[r->i2]),r->lcm); SG(r) = TD(LCM(r)); /* XXX */ } if ( d ) NEXT(r) = 0; while ( d ) { again: l = nd_minp(d,&d); stat = nd_sp(m,0,l,&h); if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(0,d); goto again; } stat = nd_nf(m,0,h,nd_ps,!Top,&nf); if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(0,d); goto again; } else if ( nf ) return 0; if ( DP_Print) { printf("."); fflush(stdout); } } if ( DP_Print) { printf("done.\n"); fflush(stdout); } return 1; } int check_splist_f4(int m,NODE splist) { UINT *s0vect; PGeoBucket bucket; NODE p,rp0,t; ND_pairs d,r,l,ll; int col,stat; for ( d = 0, t = splist; t; t = NEXT(t) ) { p = BDY((LIST)BDY(t)); NEXTND_pairs(d,r); r->i1 = ZTOS((Q)ARG0(p)); r->i2 = ZTOS((Q)ARG1(p)); ndl_lcm(DL(nd_psh[r->i1]),DL(nd_psh[r->i2]),r->lcm); SG(r) = TD(LCM(r)); /* XXX */ } if ( d ) NEXT(r) = 0; while ( d ) { l = nd_minsugarp(d,&d); bucket = create_pbucket(); stat = nd_sp_f4(m,0,l,bucket); if ( !stat ) { for ( ll = l; NEXT(ll); ll = NEXT(ll) ); NEXT(ll) = d; d = l; d = nd_reconstruct(0,d); continue; } if ( bucket->m < 0 ) continue; col = nd_symbolic_preproc(bucket,0,&s0vect,&rp0); if ( !col ) { for ( ll = l; NEXT(ll); ll = NEXT(ll) ); NEXT(ll) = d; d = l; d = nd_reconstruct(0,d); continue; } if ( nd_f4_red(m,l,0,s0vect,col,rp0,0) ) return 0; } return 1; } int do_diagonalize_trace(int sugar,int m) { int i,nh,stat; NODE r,g,t; ND h,nf,nfq,s,head; NDV nfv,nfqv; Q q,den,num; union oNDC hc; NODE node; LIST l; Z iq; P cont,cont1; for ( i = nd_psn-1; i >= 0 && SG(nd_psh[i]) == sugar; i-- ) { if ( nd_gentrace ) { /* Trace = [1,index,1,1] */ STOZ(i,iq); node = mknode(4,ONE,iq,ONE,ONE); MKLIST(l,node); MKNODE(nd_tracelist,l,0); } /* for nd_ps */ s = ndvtond(m,nd_ps[i]); s = nd_separate_head(s,&head); stat = nd_nf_pbucket(m,s,nd_ps,1,&nf); if ( !stat ) return 0; nf = nd_add(m,head,nf); ndv_free(nd_ps[i]); nd_ps[i] = ndtondv(m,nf); nd_free(nf); /* for nd_ps_trace */ if ( nd_demand ) nfv = ndv_load(i); else nfv = nd_ps_trace[i]; s = ndvtond(0,nfv); s = nd_separate_head(s,&head); stat = nd_nf(0,head,s,nd_ps_trace,1,&nf); if ( !stat ) return 0; ndv_free(nfv); hc = HCU(nf); nd_removecont(0,nf); /* exact division */ cont = ndc_div(0,hc,HCU(nf)); if ( nd_gentrace ) finalize_tracelist(i,cont); nfv = ndtondv(0,nf); nd_free(nf); nd_bound[i] = ndv_compute_bound(nfv); register_hcf(nfv); if ( nd_demand ) { ndv_save(nfv,i); ndv_free(nfv); } else nd_ps_trace[i] = nfv; } return 1; } static struct oEGT eg_invdalg; struct oEGT eg_le; void nd_subst_vector(VL vl,P p,NODE subst,P *r) { NODE tn; P p1; for ( tn = subst; tn; tn = NEXT(NEXT(tn)) ) { substp(vl,p,BDY(tn),BDY(NEXT(tn)),&p1); p = p1; } *r = p; } NODE nd_gb_trace(int m,int ishomo,int **indp) { int i,nh,sugar,stat; NODE r,g,t; ND_pairs d; ND_pairs l; ND h,nf,nfq,s,head; NDV nfv,nfqv; Z q,den,num; P hc; union oNDC dn,hnfq; struct oEGT eg_monic,egm0,egm1; int diag_count = 0; P cont; LIST list; init_eg(&eg_monic); init_eg(&eg_invdalg); init_eg(&eg_le); g = 0; d = 0; for ( i = 0; i < nd_psn; i++ ) { d = update_pairs(d,g,i,0); g = update_base(g,i); } sugar = 0; while ( d ) { again: l = nd_minp(d,&d); if ( MaxDeg > 0 && SG(l) > MaxDeg ) break; if ( SG(l) != sugar ) { #if 1 if ( ishomo ) { if ( DP_Print > 2 ) fprintf(asir_out,"|"); stat = do_diagonalize_trace(sugar,m); if ( DP_Print > 2 ) fprintf(asir_out,"|"); diag_count = 0; if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(1,d); goto again; } } #endif sugar = SG(l); if ( DP_Print ) fprintf(asir_out,"%d",sugar); } stat = nd_sp(m,0,l,&h); if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(1,d); goto again; } #if USE_GEOBUCKET stat = nd_nf_pbucket(m,h,nd_ps,!Top,&nf); #else stat = nd_nf(m,0,h,nd_ps,!Top,&nf); #endif if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(1,d); goto again; } else if ( nf ) { if ( nd_demand ) { nfqv = ndv_load(nd_psn); nfq = ndvtond(0,nfqv); } else nfq = 0; if ( !nfq ) { if ( !nd_sp(0,1,l,&h) || !nd_nf(0,0,h,nd_ps_trace,!Top,&nfq) ) { NEXT(l) = d; d = l; d = nd_reconstruct(1,d); goto again; } } if ( nfq ) { /* m|HC(nfq) => failure */ if ( nd_vc ) { nd_subst_vector(nd_vc,HCP(nfq),nd_subst,&hc); q = (Z)hc; } else q = HCZ(nfq); if ( !remqi((Q)q,m) ) return 0; if ( DP_Print ) { printf("+"); fflush(stdout); } hnfq = HCU(nfq); if ( nd_nalg ) { /* m|DN(HC(nf)^(-1)) => failure */ get_eg(&egm0); if ( !nd_monic(m,&nfq) ) return 0; get_eg(&egm1); add_eg(&eg_monic,&egm0,&egm1); nd_removecont(0,nfq); nfqv = ndtondv(0,nfq); nd_free(nfq); nfv = ndv_dup(0,nfqv); ndv_mod(m,nfv); nd_free(nf); } else { nd_removecont(0,nfq); nfqv = ndtondv(0,nfq); nd_free(nfq); nd_removecont(m,nf); nfv = ndtondv(m,nf); nd_free(nf); } if ( nd_gentrace ) { /* exact division */ cont = ndc_div(0,hnfq,HCU(nfqv)); if ( !UNIQ(cont) ) { t = mknode(4,NULLP,NULLP,NULLP,cont); MKLIST(list,t); MKNODE(t,list,nd_tracelist); nd_tracelist = t; } } nh = ndv_newps(0,nfv,nfqv); if ( ishomo && ++diag_count == diag_period ) { diag_count = 0; if ( DP_Print > 2 ) fprintf(asir_out,"|"); stat = do_diagonalize_trace(sugar,m); if ( DP_Print > 2 ) fprintf(asir_out,"|"); if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(1,d); goto again; } } d = update_pairs(d,g,nh,0); g = update_base(g,nh); } else { if ( DP_Print ) { printf("*"); fflush(stdout); } } } else { if ( DP_Print ) { printf("."); fflush(stdout); } } FREENDP(l); } if ( nd_nalg ) { if ( DP_Print ) { print_eg("monic",&eg_monic); print_eg("invdalg",&eg_invdalg); print_eg("le",&eg_le); } } conv_ilist(nd_demand,1,g,indp); if ( DP_Print ) { printf("nd_gb_trace done.\n"); fflush(stdout); } return g; } int ndv_compare(NDV *p1,NDV *p2) { return DL_COMPARE(HDL(*p1),HDL(*p2)); } int ndv_compare_rev(NDV *p1,NDV *p2) { return -DL_COMPARE(HDL(*p1),HDL(*p2)); } int ndvi_compare(NDVI p1,NDVI p2) { return DL_COMPARE(HDL(p1->p),HDL(p2->p)); } int ndvi_compare_rev(NDVI p1,NDVI p2) { return -DL_COMPARE(HDL(p1->p),HDL(p2->p)); } NODE ndv_reduceall(int m,NODE f) { int i,j,n,stat; ND nf,g,head; NODE t,a0,a; union oNDC dn; Q q,num,den; NODE node; LIST l; Z iq,jq; int *perm; union oNDC hc; P cont,cont1; if ( nd_nora ) return f; n = length(f); ndv_setup(m,0,f,0,1,0); perm = (int *)MALLOC(n*sizeof(int)); if ( nd_gentrace ) { for ( t = nd_tracelist, i = 0; i < n; i++, t = NEXT(t) ) perm[i] = ZTOS((Q)ARG1(BDY((LIST)BDY(t)))); } for ( i = 0; i < n; ) { if ( nd_gentrace ) { /* Trace = [1,index,1,1] */ STOZ(i,iq); node = mknode(4,ONE,iq,ONE,ONE); MKLIST(l,node); MKNODE(nd_tracelist,l,0); } g = ndvtond(m,nd_ps[i]); g = nd_separate_head(g,&head); stat = nd_nf(m,head,g,nd_ps,1,&nf); if ( !stat ) nd_reconstruct(0,0); else { if ( DP_Print ) { printf("."); fflush(stdout); } ndv_free(nd_ps[i]); hc = HCU(nf); nd_removecont(m,nf); if ( nd_gentrace ) { for ( t = nd_tracelist; t; t = NEXT(t) ) { jq = ARG1(BDY((LIST)BDY(t))); j = ZTOS(jq); STOZ(perm[j],jq); ARG1(BDY((LIST)BDY(t))) = jq; } /* exact division */ cont = ndc_div(m,hc,HCU(nf)); finalize_tracelist(perm[i],cont); } nd_ps[i] = ndtondv(m,nf); nd_free(nf); nd_bound[i] = ndv_compute_bound(nd_ps[i]); i++; } } if ( DP_Print ) { printf("\n"); } for ( a0 = 0, i = 0; i < n; i++ ) { NEXTNODE(a0,a); if ( !nd_gentrace ) BDY(a) = (pointer)nd_ps[i]; else { for ( j = 0; j < n; j++ ) if ( perm[j] == i ) break; BDY(a) = (pointer)nd_ps[j]; } } NEXT(a) = 0; return a0; } ND_pairs update_pairs( ND_pairs d, NODE /* of index */ g, int t, int gensyz) { ND_pairs d1,nd,cur,head,prev,remove; if ( !g ) return d; /* for testing */ if ( gensyz && nd_gensyz == 2 ) { d1 = nd_newpairs(g,t); if ( !d ) return d1; else { nd = d; while ( NEXT(nd) ) nd = NEXT(nd); NEXT(nd) = d1; return d; } } d = crit_B(d,t); d1 = nd_newpairs(g,t); d1 = crit_M(d1); d1 = crit_F(d1); if ( gensyz || do_weyl ) head = d1; else { prev = 0; cur = head = d1; while ( cur ) { if ( crit_2( cur->i1,cur->i2 ) ) { remove = cur; if ( !prev ) head = cur = NEXT(cur); else cur = NEXT(prev) = NEXT(cur); FREENDP(remove); } else { prev = cur; cur = NEXT(cur); } } } if ( !d ) return head; else { nd = d; while ( NEXT(nd) ) nd = NEXT(nd); NEXT(nd) = head; return d; } } ND_pairs merge_pairs_s(ND_pairs d,ND_pairs d1); ND_pairs update_pairs_s( ND_pairs d, int t,NODE *syz) { ND_pairs d1; struct oEGT eg1,eg2,eg3; if ( !t ) return d; get_eg(&eg1); d1 = nd_newpairs_s(t,syz); get_eg(&eg2); add_eg(&eg_create,&eg1,&eg2); d = merge_pairs_s(d,d1); get_eg(&eg3); add_eg(&eg_merge,&eg2,&eg3); return d; } ND_pairs nd_newpairs( NODE g, int t ) { NODE h; UINT *dl; int ts,s,i,t0,min,max; ND_pairs r,r0; dl = DL(nd_psh[t]); ts = SG(nd_psh[t]) - TD(dl); if ( nd_module && nd_intersect && (MPOS(dl) > nd_intersect) ) return 0; for ( r0 = 0, h = g; h; h = NEXT(h) ) { if ( nd_module && (MPOS(DL(nd_psh[(long)BDY(h)])) != MPOS(dl)) ) continue; if ( nd_gbblock ) { t0 = (long)BDY(h); for ( i = 0; nd_gbblock[i] >= 0; i += 2 ) { min = nd_gbblock[i]; max = nd_gbblock[i+1]; if ( t0 >= min && t0 <= max && t >= min && t <= max ) break; } if ( nd_gbblock[i] >= 0 ) continue; } NEXTND_pairs(r0,r); r->i1 = (long)BDY(h); r->i2 = t; ndl_lcm(DL(nd_psh[r->i1]),dl,r->lcm); s = SG(nd_psh[r->i1])-TD(DL(nd_psh[r->i1])); SG(r) = MAX(s,ts) + TD(LCM(r)); /* experimental */ if ( nd_sugarweight ) r->sugar2 = ndl_weight2(r->lcm); } if ( r0 ) NEXT(r) = 0; return r0; } int comp_sig(SIG s1,SIG s2) { #if 0 if ( s1->pos > s2->pos ) return 1; else if ( s1->pos < s2->pos ) return -1; else return (*cmpdl)(nd_nvar,s1->dl,s2->dl); #else static DL m1,m2; static int nvar; int ret; if ( nvar != nd_nvar ) { nvar = nd_nvar; NEWDL(m1,nvar); NEWDL(m2,nvar); } #if 0 _copydl(nd_nvar,nd_sba_hm[s1->pos],m1); _copydl(nd_nvar,nd_sba_hm[s2->pos],m2); _addtodl(nd_nvar,s1->dl,m1); _addtodl(nd_nvar,s2->dl,m2); #else _adddl(nd_nvar,s1->dl,nd_sba_hm[s1->pos],m1); _adddl(nd_nvar,s2->dl,nd_sba_hm[s2->pos],m2); #endif ret = (*cmpdl)(nd_nvar,m1,m2); if ( ret != 0 ) return ret; else if ( s1->pos > s2->pos ) return 1; else if ( s1->pos < s2->pos ) return -1; else return 0; #endif } int _create_spair_s(int i1,int i2,ND_pairs sp,SIG sig1,SIG sig2) { int ret,s1,s2; RHist p1,p2; static int wpd; static UINT *lcm; sp->i1 = i1; sp->i2 = i2; p1 = nd_psh[i1]; p2 = nd_psh[i2]; ndl_lcm(DL(p1),DL(p2),sp->lcm); s1 = SG(p1)-TD(DL(p1)); s2 = SG(p2)-TD(DL(p2)); SG(sp) = MAX(s1,s2) + TD(sp->lcm); if ( wpd != nd_wpd ) { wpd = nd_wpd; lcm = (UINT *)MALLOC(wpd*sizeof(UINT)); } // DL(sig1) <- sp->lcm // DL(sig1) -= DL(p1) // DL(sig1) += DL(p1->sig) ndl_sub(sp->lcm,DL(p1),lcm); _ndltodl(lcm,DL(sig1)); _addtodl(nd_nvar,DL(p1->sig),DL(sig1)); sig1->pos = p1->sig->pos; // DL(sig2) <- sp->lcm // DL(sig2) -= DL(p2) // DL(sig2) += DL(p2->sig) ndl_sub(sp->lcm,DL(p2),lcm); _ndltodl(lcm,DL(sig2)); _addtodl(nd_nvar,DL(p2->sig),DL(sig2)); sig2->pos = p2->sig->pos; ret = comp_sig(sig1,sig2); if ( ret == 0 ) return 0; else if ( ret > 0 ) sp->sig = sig1; else sp->sig = sig2; return 1; } SIG dup_sig(SIG sig) { SIG r; if ( !sig ) return 0; else { NEWSIG(r); _copydl(nd_nvar,DL(sig),DL(r)); r->pos = sig->pos; return r; } } void dup_ND_pairs(ND_pairs to,ND_pairs from) { to->i1 = from->i1; to->i2 = from->i2; to->sugar = from->sugar; to->sugar2 = from->sugar2; ndl_copy(from->lcm,to->lcm); to->sig = dup_sig(from->sig); } ND_pairs merge_pairs_s(ND_pairs p1,ND_pairs p2) { struct oND_pairs root; ND_pairs q1,q2,r0,r; int ret; r = &root; for ( q1 = p1, q2 = p2; q1 != 0 && q2 != 0; ) { ret = comp_sig(q1->sig,q2->sig); if ( ret < 0 ) { r->next = q1; r = q1; q1 = q1->next; } else if ( ret > 0 ) { r->next = q2; r = q2; q2 = q2->next; } else { ret = DL_COMPARE(q1->lcm,q2->lcm); Nsamesig++; if ( ret < 0 ) { r->next = q1; r = q1; q1 = q1->next; q2 = q2->next; } else { r->next = q2; r = q2; q2 = q2->next; q1 = q1->next; } } } if ( q1 ) { r->next = q1; } else { r->next = q2; } return root.next; } ND_pairs insert_pair_s(ND_pairs l,ND_pairs s) { ND_pairs p,prev; int ret; for ( p = l, prev = 0; p != 0; prev = p, p = p->next ) { if ( (ret = comp_sig(s->sig,p->sig)) <= 0 ) break; } if ( ret == 0 ) { ret = DL_COMPARE(s->lcm,p->lcm); if ( ret < 0 ) { // replace p with s s->next = p->next; if ( prev == 0 ) { return s; } else { prev->next = s; return l; } } else return l; } else { // insert s between prev and p s->next = p; if ( prev == 0 ) { return s; } else { prev->next = s; return l; } } } INLINE int __dl_redble(DL d1,DL d2,int nvar) { int i; if ( d1->td > d2->td ) return 0; for ( i = nvar-1; i >= 0; i-- ) if ( d1->d[i] > d2->d[i] ) break; if ( i >= 0 ) return 0; else return 1; } ND_pairs nd_newpairs_s(int t, NODE *syz) { NODE h,s; UINT *dl; int ts,ret,i; ND_pairs r,r0,_sp,sp; SIG spsig,tsig; static int nvar; static SIG _sig1,_sig2; struct oEGT eg1,eg2,eg3,eg4; NEWND_pairs(_sp); if ( !_sig1 || nvar != nd_nvar ) { nvar = nd_nvar; NEWSIG(_sig1); NEWSIG(_sig2); } r0 = 0; for ( i = 0; i < t; i++ ) { ret = _create_spair_s(i,t,_sp,_sig1,_sig2); if ( ret ) { spsig = _sp->sig; for ( s = syz[spsig->pos]; s; s = s->next ) { tsig = (SIG)s->body; if ( _dl_redble(DL(tsig),DL(spsig),nd_nvar) ) break; } if ( s == 0 ) { NEWND_pairs(sp); dup_ND_pairs(sp,_sp); r0 = insert_pair_s(r0,sp); } else Nsyz++; } } return r0; } /* ipair = [i1,i2],[i1,i2],... */ ND_pairs nd_ipairtospair(NODE ipair) { int s1,s2; NODE tn,t; ND_pairs r,r0; for ( r0 = 0, t = ipair; t; t = NEXT(t) ) { NEXTND_pairs(r0,r); tn = BDY((LIST)BDY(t)); r->i1 = ZTOS((Q)ARG0(tn)); r->i2 = ZTOS((Q)ARG1(tn)); ndl_lcm(DL(nd_psh[r->i1]),DL(nd_psh[r->i2]),r->lcm); s1 = SG(nd_psh[r->i1])-TD(DL(nd_psh[r->i1])); s2 = SG(nd_psh[r->i2])-TD(DL(nd_psh[r->i2])); SG(r) = MAX(s1,s2) + TD(LCM(r)); /* experimental */ if ( nd_sugarweight ) r->sugar2 = ndl_weight2(r->lcm); } if ( r0 ) NEXT(r) = 0; return r0; } /* kokokara */ ND_pairs crit_B( ND_pairs d, int s ) { ND_pairs cur,head,prev,remove; UINT *t,*tl,*lcm; int td,tdl; if ( !d ) return 0; t = DL(nd_psh[s]); prev = 0; head = cur = d; lcm = (UINT *)MALLOC(nd_wpd*sizeof(UINT)); while ( cur ) { tl = cur->lcm; if ( ndl_reducible(tl,t) ) { ndl_lcm(DL(nd_psh[cur->i1]),t,lcm); if ( !ndl_equal(lcm,tl) ) { ndl_lcm(DL(nd_psh[cur->i2]),t,lcm); if (!ndl_equal(lcm,tl)) { remove = cur; if ( !prev ) { head = cur = NEXT(cur); } else { cur = NEXT(prev) = NEXT(cur); } FREENDP(remove); } else { prev = cur; cur = NEXT(cur); } } else { prev = cur; cur = NEXT(cur); } } else { prev = cur; cur = NEXT(cur); } } return head; } ND_pairs crit_M( ND_pairs d1 ) { ND_pairs e,d2,d3,dd,p; UINT *id,*jd; if ( !d1 ) return d1; for ( dd = 0, e = d1; e; e = d3 ) { if ( !(d2 = NEXT(e)) ) { NEXT(e) = dd; return e; } id = LCM(e); for ( d3 = 0; d2; d2 = p ) { p = NEXT(d2); jd = LCM(d2); if ( ndl_equal(jd,id) ) ; else if ( TD(jd) > TD(id) ) if ( ndl_reducible(jd,id) ) continue; else ; else if ( ndl_reducible(id,jd) ) goto delit; NEXT(d2) = d3; d3 = d2; } NEXT(e) = dd; dd = e; continue; /**/ delit: NEXT(d2) = d3; d3 = d2; for ( ; p; p = d2 ) { d2 = NEXT(p); NEXT(p) = d3; d3 = p; } FREENDP(e); } return dd; } ND_pairs crit_F( ND_pairs d1 ) { ND_pairs rest, head,remove; ND_pairs last, p, r, w; int s; if ( !d1 ) return d1; for ( head = last = 0, p = d1; NEXT(p); ) { r = w = equivalent_pairs(p,&rest); s = SG(r); w = NEXT(w); while ( w ) { if ( crit_2(w->i1,w->i2) ) { r = w; w = NEXT(w); while ( w ) { remove = w; w = NEXT(w); FREENDP(remove); } break; } else if ( SG(w) < s ) { FREENDP(r); r = w; s = SG(r); w = NEXT(w); } else { remove = w; w = NEXT(w); FREENDP(remove); } } if ( last ) NEXT(last) = r; else head = r; NEXT(last = r) = 0; p = rest; if ( !p ) return head; } if ( !last ) return p; NEXT(last) = p; return head; } int crit_2( int dp1, int dp2 ) { return ndl_disjoint(DL(nd_psh[dp1]),DL(nd_psh[dp2])); } ND_pairs equivalent_pairs( ND_pairs d1, ND_pairs *prest ) { ND_pairs w,p,r,s; UINT *d; w = d1; d = LCM(w); s = NEXT(w); NEXT(w) = 0; for ( r = 0; s; s = p ) { p = NEXT(s); if ( ndl_equal(d,LCM(s)) ) { NEXT(s) = w; w = s; } else { NEXT(s) = r; r = s; } } *prest = r; return w; } NODE update_base(NODE nd,int ndp) { UINT *dl, *dln; NODE last, p, head; dl = DL(nd_psh[ndp]); for ( head = last = 0, p = nd; p; ) { dln = DL(nd_psh[(long)BDY(p)]); if ( ndl_reducible( dln, dl ) ) { p = NEXT(p); if ( last ) NEXT(last) = p; } else { if ( !last ) head = p; p = NEXT(last = p); } } head = append_one(head,ndp); return head; } ND_pairs nd_minp( ND_pairs d, ND_pairs *prest ) { ND_pairs m,ml,p,l; UINT *lcm; int s,td,len,tlen,c,c1; if ( !(p = NEXT(m = d)) ) { *prest = p; NEXT(m) = 0; return m; } if ( !NoSugar ) { if ( nd_sugarweight ) { s = m->sugar2; for ( ml = 0, l = m; p; p = NEXT(l = p) ) if ( (p->sugar2 < s) || ((p->sugar2 == s) && (DL_COMPARE(LCM(p),LCM(m)) < 0)) ) { ml = l; m = p; s = m->sugar2; } } else { s = SG(m); for ( ml = 0, l = m; p; p = NEXT(l = p) ) if ( (SG(p) < s) || ((SG(p) == s) && (DL_COMPARE(LCM(p),LCM(m)) < 0)) ) { ml = l; m = p; s = SG(m); } } } else { for ( ml = 0, l = m; p; p = NEXT(l = p) ) if ( DL_COMPARE(LCM(p),LCM(m)) < 0 ) { ml = l; m = p; s = SG(m); } } if ( !ml ) *prest = NEXT(m); else { NEXT(ml) = NEXT(m); *prest = d; } NEXT(m) = 0; return m; } ND_pairs nd_minsugarp( ND_pairs d, ND_pairs *prest ) { int msugar,i; ND_pairs t,dm0,dm,dr0,dr; if ( nd_sugarweight ) { for ( msugar = d->sugar2, t = NEXT(d); t; t = NEXT(t) ) if ( t->sugar2 < msugar ) msugar = t->sugar2; dm0 = 0; dr0 = 0; for ( i = 0, t = d; t; t = NEXT(t) ) if ( i < nd_f4_nsp && t->sugar2 == msugar ) { if ( dm0 ) NEXT(dm) = t; else dm0 = t; dm = t; i++; } else { if ( dr0 ) NEXT(dr) = t; else dr0 = t; dr = t; } } else { for ( msugar = SG(d), t = NEXT(d); t; t = NEXT(t) ) if ( SG(t) < msugar ) msugar = SG(t); dm0 = 0; dr0 = 0; for ( i = 0, t = d; t; t = NEXT(t) ) if ( i < nd_f4_nsp && SG(t) == msugar ) { if ( dm0 ) NEXT(dm) = t; else dm0 = t; dm = t; i++; } else { if ( dr0 ) NEXT(dr) = t; else dr0 = t; dr = t; } } NEXT(dm) = 0; if ( dr0 ) NEXT(dr) = 0; *prest = dr0; return dm0; } ND_pairs nd_minsugarp_s( ND_pairs d, ND_pairs *prest ) { int msugar; ND_pairs t,last; for ( msugar = SG(d), t = d; t; t = NEXT(t) ) if ( SG(t) == msugar ) last = t; *prest = last->next; last->next = 0; return d; } int nd_tdeg(NDV c) { int wmax = 0; int i,len; NMV a; len = LEN(c); for ( a = BDY(c), i = 0; i < len; i++, NMV_ADV(a) ) wmax = MAX(TD(DL(a)),wmax); return wmax; } int ndv_newps(int m,NDV a,NDV aq) { int len; RHist r; NDV b; NODE tn; LIST l; Z iq; if ( nd_psn == nd_pslen ) { nd_pslen *= 2; nd_ps = (NDV *)REALLOC((char *)nd_ps,nd_pslen*sizeof(NDV)); nd_ps_trace = (NDV *)REALLOC((char *)nd_ps_trace,nd_pslen*sizeof(NDV)); nd_psh = (RHist *)REALLOC((char *)nd_psh,nd_pslen*sizeof(RHist)); nd_bound = (UINT **) REALLOC((char *)nd_bound,nd_pslen*sizeof(UINT *)); nd_ps_sym = (NDV *)REALLOC((char *)nd_ps_sym,nd_pslen*sizeof(NDV)); nd_ps_trace_sym = (NDV *)REALLOC((char *)nd_ps_trace_sym,nd_pslen*sizeof(NDV)); } NEWRHist(r); nd_psh[nd_psn] = r; nd_ps[nd_psn] = a; if ( aq ) { nd_ps_trace[nd_psn] = aq; if ( !m ) { register_hcf(aq); } else if ( m == -2 ) { /* do nothing */ } else error("ndv_newps : invalud modulus"); nd_bound[nd_psn] = ndv_compute_bound(aq); #if 1 SG(r) = SG(aq); #else SG(r) = nd_tdeg(aq); #endif ndl_copy(HDL(aq),DL(r)); r->sig = dup_sig(aq->sig); } else { if ( !m ) register_hcf(a); nd_bound[nd_psn] = ndv_compute_bound(a); #if 1 SG(r) = SG(a); #else SG(r) = nd_tdeg(a); #endif ndl_copy(HDL(a),DL(r)); r->sig = dup_sig(a->sig); } if ( nd_demand ) { if ( aq ) { ndv_save(nd_ps_trace[nd_psn],nd_psn); nd_ps_sym[nd_psn] = ndv_symbolic(m,nd_ps_trace[nd_psn]); nd_ps_trace_sym[nd_psn] = ndv_symbolic(m,nd_ps_trace[nd_psn]); nd_ps_trace[nd_psn] = 0; } else { ndv_save(nd_ps[nd_psn],nd_psn); nd_ps_sym[nd_psn] = ndv_symbolic(m,nd_ps[nd_psn]); nd_ps[nd_psn] = 0; } } if ( nd_gentrace ) { /* reverse the tracelist and append it to alltracelist */ nd_tracelist = reverse_node(nd_tracelist); MKLIST(l,nd_tracelist); STOZ(nd_psn,iq); tn = mknode(2,iq,l); MKLIST(l,tn); MKNODE(tn,l,nd_alltracelist); nd_alltracelist = tn; nd_tracelist = 0; } return nd_psn++; } /* nd_tracelist = [[0,index,div],...,[nd_psn-1,index,div]] */ /* return 1 if success, 0 if failure (HC(a mod p)) */ int ndv_setup(int mod,int trace,NODE f,int dont_sort,int dont_removecont,int sba) { int i,j,td,len,max; NODE s,s0,f0,tn; UINT *d; RHist r; NDVI w; NDV a,am; union oNDC hc; NODE node; P hcp; Z iq,jq; LIST l; nd_found = 0; nd_notfirst = 0; nd_create = 0; /* initialize the tracelist */ nd_tracelist = 0; for ( nd_psn = 0, s = f; s; s = NEXT(s) ) if ( BDY(s) ) nd_psn++; w = (NDVI)MALLOC(nd_psn*sizeof(struct oNDVI)); for ( i = j = 0, s = f; s; s = NEXT(s), j++ ) if ( BDY(s) ) { w[i].p = BDY(s); w[i].i = j; i++; } if ( !dont_sort ) { /* XXX heuristic */ if ( !sba && !nd_ord->id && (nd_ord->ord.simple<2) ) qsort(w,nd_psn,sizeof(struct oNDVI), (int (*)(const void *,const void *))ndvi_compare_rev); else qsort(w,nd_psn,sizeof(struct oNDVI), (int (*)(const void *,const void *))ndvi_compare); } nd_pslen = 2*nd_psn; nd_ps = (NDV *)MALLOC(nd_pslen*sizeof(NDV)); nd_ps_trace = (NDV *)MALLOC(nd_pslen*sizeof(NDV)); nd_ps_sym = (NDV *)MALLOC(nd_pslen*sizeof(NDV)); nd_ps_trace_sym = (NDV *)MALLOC(nd_pslen*sizeof(NDV)); nd_psh = (RHist *)MALLOC(nd_pslen*sizeof(RHist)); nd_bound = (UINT **)MALLOC(nd_pslen*sizeof(UINT *)); nd_hcf = 0; if ( trace && nd_vc ) makesubst(nd_vc,&nd_subst); else nd_subst = 0; if ( !nd_red ) nd_red = (RHist *)MALLOC(REDTAB_LEN*sizeof(RHist)); for ( i = 0; i < REDTAB_LEN; i++ ) nd_red[i] = 0; for ( i = 0; i < nd_psn; i++ ) { hc = HCU(w[i].p); if ( trace ) { if ( mod == -2 ) { /* over a large finite field */ /* trace = small modulus */ a = nd_ps_trace[i] = ndv_dup(-2,w[i].p); ndv_mod(-2,a); if ( !dont_removecont) ndv_removecont(-2,a); am = nd_ps[i] = ndv_dup(trace,w[i].p); ndv_mod(trace,am); if ( DL_COMPARE(HDL(am),HDL(a)) ) return 0; ndv_removecont(trace,am); } else { a = nd_ps_trace[i] = ndv_dup(0,w[i].p); if ( !dont_removecont) ndv_removecont(0,a); register_hcf(a); am = nd_ps[i] = ndv_dup(mod,a); ndv_mod(mod,am); if ( DL_COMPARE(HDL(am),HDL(a)) ) return 0; ndv_removecont(mod,am); } } else { a = nd_ps[i] = ndv_dup(mod,w[i].p); if ( mod || !dont_removecont ) ndv_removecont(mod,a); if ( !mod ) register_hcf(a); } if ( nd_gentrace ) { STOZ(i,iq); STOZ(w[i].i,jq); node = mknode(3,iq,jq,ONE); /* exact division */ if ( !dont_removecont ) ARG2(node) = (pointer)ndc_div(trace?0:mod,hc,HCU(a)); MKLIST(l,node); NEXTNODE(nd_tracelist,tn); BDY(tn) = l; } NEWRHist(r); SG(r) = HTD(a); ndl_copy(HDL(a),DL(r)); nd_bound[i] = ndv_compute_bound(a); nd_psh[i] = r; if ( nd_demand ) { if ( trace ) { ndv_save(nd_ps_trace[i],i); nd_ps_sym[i] = ndv_symbolic(mod,nd_ps_trace[i]); nd_ps_trace_sym[i] = ndv_symbolic(mod,nd_ps_trace[i]); nd_ps_trace[i] = 0; } else { ndv_save(nd_ps[i],i); nd_ps_sym[i] = ndv_symbolic(mod,nd_ps[i]); nd_ps[i] = 0; } } } if ( sba ) { nd_sba_hm = (DL *)MALLOC(nd_psn*sizeof(DL)); // setup signatures for ( i = 0; i < nd_psn; i++ ) { SIG sig; NEWSIG(sig); sig->pos = i; nd_ps[i]->sig = sig; if ( nd_demand ) nd_ps_sym[i]->sig = sig; nd_psh[i]->sig = sig; if ( trace ) { nd_ps_trace[i]->sig = sig; if ( nd_demand ) nd_ps_trace_sym[i]->sig = sig; } NEWDL(nd_sba_hm[i],nd_nvar); _ndltodl(DL(nd_psh[i]),nd_sba_hm[i]); } nd_sba_pos = (NODE *)MALLOC(nd_psn*sizeof(NODE)); for ( i = 0; i < nd_psn; i++ ) { j = nd_psh[i]->sig->pos; nd_sba_pos[j] = append_one(nd_sba_pos[j],i); } } if ( nd_gentrace && nd_tracelist ) NEXT(tn) = 0; return 1; } struct order_spec *append_block(struct order_spec *spec, int nv,int nalg,int ord); extern VECT current_dl_weight_vector_obj; static VECT prev_weight_vector_obj; void preprocess_algcoef(VL vv,VL av,struct order_spec *ord,LIST f, struct order_spec **ord1p,LIST *f1p,NODE *alistp) { NODE alist,t,s,r0,r,arg; VL tv; P poly; DP d; Alg alpha,dp; DAlg inv,da,hc; MP m; int i,nvar,nalg,n; NumberField nf; LIST f1,f2; struct order_spec *current_spec; VECT obj,obj0; VECT tmp; for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++); for ( nalg = 0, tv = av; tv; tv = NEXT(tv), nalg++); for ( alist = 0, tv = av; tv; tv = NEXT(tv) ) { NEXTNODE(alist,t); MKV(tv->v,poly); MKAlg(poly,alpha); BDY(t) = (pointer)alpha; tv->v = tv->v->priv; } NEXT(t) = 0; /* simplification, making polynomials monic */ setfield_dalg(alist); obj_algtodalg((Obj)f,(Obj *)&f1); for ( t = BDY(f); t; t = NEXT(t) ) { initd(ord); ptod(vv,vv,(P)BDY(t),&d); hc = (DAlg)BDY(d)->c; if ( NID(hc) == N_DA ) { invdalg(hc,&inv); for ( m = BDY(d); m; m = NEXT(m) ) { muldalg(inv,(DAlg)m->c,&da); m->c = (Obj)da; } } initd(ord); dtop(vv,vv,d,(Obj *)&poly); BDY(f) = (pointer)poly; } obj_dalgtoalg((Obj)f1,(Obj *)&f); /* append alg vars to the var list */ for ( tv = vv; NEXT(tv); tv = NEXT(tv) ); NEXT(tv) = av; /* append a block to ord */ *ord1p = append_block(ord,nvar,nalg,2); /* create generator list */ nf = get_numberfield(); for ( i = nalg-1, t = BDY(f); i >= 0; i-- ) { MKAlg(nf->defpoly[i],dp); MKNODE(s,dp,t); t = s; } MKLIST(f1,t); *alistp = alist; algobjtorat((Obj)f1,(Obj *)f1p); /* creating a new weight vector */ prev_weight_vector_obj = obj0 = current_dl_weight_vector_obj; n = nvar+nalg+1; MKVECT(obj,n); if ( obj0 && obj0->len == nvar ) for ( i = 0; i < nvar; i++ ) BDY(obj)[i] = BDY(obj0)[i]; else for ( i = 0; i < nvar; i++ ) BDY(obj)[i] = (pointer)ONE; for ( i = 0; i < nalg; i++ ) BDY(obj)[i+nvar] = 0; BDY(obj)[n-1] = (pointer)ONE; arg = mknode(1,obj); Pdp_set_weight(arg,&tmp); } NODE postprocess_algcoef(VL av,NODE alist,NODE r) { NODE s,t,u0,u; P p; VL tv; Obj obj; VECT tmp; NODE arg; u0 = 0; for ( t = r; t; t = NEXT(t) ) { p = (P)BDY(t); for ( tv = av, s = alist; tv; tv = NEXT(tv), s = NEXT(s) ) { substr(CO,0,(Obj)p,tv->v,(Obj)BDY(s),&obj); p = (P)obj; } if ( OID(p) == O_P || (OID(p) == O_N && NID((Num)p) != N_A) ) { NEXTNODE(u0,u); BDY(u) = (pointer)p; } } arg = mknode(1,prev_weight_vector_obj); Pdp_set_weight(arg,&tmp); return u0; } void nd_gr(LIST f,LIST v,int m,int homo,int retdp,int f4,struct order_spec *ord,LIST *rp) { VL tv,fv,vv,vc,av; NODE fd,fd0,r,r0,t,x,s,xx,alist; int e,max,nvar,i; NDV b; int ishomo,nalg,mrank,trank,wmax,len; NMV a; Alg alpha,dp; P p,zp; Q dmy; LIST f1,f2,zpl; Obj obj; NumberField nf; struct order_spec *ord1; NODE tr,tl1,tl2,tl3,tl4,nzlist; LIST l1,l2,l3,l4,l5; int j; Z jq,bpe,last_nonzero; int *perm; EPOS oepos; int obpe,oadv,ompos,cbpe; VECT hvect; nd_module = 0; if ( !m && Demand ) nd_demand = 1; else nd_demand = 0; parse_nd_option(current_option); if ( DP_Multiple ) nd_scale = ((double)DP_Multiple)/(double)(Denominator?Denominator:1); #if 0 ndv_alloc = 0; #endif get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc); if ( m && nd_vc ) error("nd_{gr,f4} : computation over Fp(X) is unsupported. Use dp_gr_mod_main()."); for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ ); switch ( ord->id ) { case 1: if ( ord->nv != nvar ) error("nd_{gr,f4} : invalid order specification"); break; default: break; } nd_nalg = 0; av = 0; if ( !m ) { get_algtree((Obj)f,&av); for ( nalg = 0, tv = av; tv; tv = NEXT(tv), nalg++ ); nd_ntrans = nvar; nd_nalg = nalg; /* #i -> t#i */ if ( nalg ) { preprocess_algcoef(vv,av,ord,f,&ord1,&f1,&alist); ord = ord1; f = f1; } nvar += nalg; } nd_init_ord(ord); mrank = 0; for ( t = BDY(f), max = 1; t; t = NEXT(t) ) for ( tv = vv; tv; tv = NEXT(tv) ) { if ( nd_module ) { if ( OID(BDY(t)) == O_DPM ) { e = dpm_getdeg((DPM)BDY(t),&trank); max = MAX(e,max); mrank = MAX(mrank,trank); } else { s = BDY((LIST)BDY(t)); trank = length(s); mrank = MAX(mrank,trank); for ( ; s; s = NEXT(s) ) { e = getdeg(tv->v,(P)BDY(s)); max = MAX(e,max); } } } else { e = getdeg(tv->v,(P)BDY(t)); max = MAX(e,max); } } nd_setup_parameters(nvar,nd_nzlist?0:max); obpe = nd_bpe; oadv = nmv_adv; oepos = nd_epos; ompos = nd_mpos; ishomo = 1; for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) { if ( nd_module ) { if ( OID(BDY(t)) == O_DPM ) { Z cont; DPM zdpm; if ( !m && !nd_gentrace ) dpm_ptozp((DPM)BDY(t),&cont,&zdpm); else zdpm = (DPM)BDY(t); b = (pointer)dpmtondv(m,zdpm); } else { if ( !m && !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl); else zpl = (LIST)BDY(t); b = (pointer)pltondv(CO,vv,zpl); } } else { if ( !m && !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp); else zp = (P)BDY(t); b = (pointer)ptondv(CO,vv,zp); } if ( ishomo ) ishomo = ishomo && ndv_ishomo(b); if ( m ) ndv_mod(m,b); if ( b ) { NEXTNODE(fd0,fd); BDY(fd) = (pointer)b; } } if ( fd0 ) NEXT(fd) = 0; if ( !ishomo && homo ) { for ( t = fd0, wmax = max; t; t = NEXT(t) ) { b = (NDV)BDY(t); len = LEN(b); for ( a = BDY(b), i = 0; i < len; i++, NMV_ADV(a) ) wmax = MAX(TD(DL(a)),wmax); } homogenize_order(ord,nvar,&ord1); nd_init_ord(ord1); nd_setup_parameters(nvar+1,nd_nzlist?0:wmax); for ( t = fd0; t; t = NEXT(t) ) ndv_homogenize((NDV)BDY(t),obpe,oadv,oepos,ompos); } ndv_setup(m,0,fd0,(nd_gbblock||nd_splist||nd_check_splist)?1:0,0,0); if ( nd_gentrace ) { MKLIST(l1,nd_tracelist); MKNODE(nd_alltracelist,l1,0); } if ( nd_splist ) { *rp = compute_splist(); return; } if ( nd_check_splist ) { if ( f4 ) { if ( check_splist_f4(m,nd_check_splist) ) *rp = (LIST)ONE; else *rp = 0; } else { if ( check_splist(m,nd_check_splist) ) *rp = (LIST)ONE; else *rp = 0; } return; } x = f4?nd_f4(m,0,&perm):nd_gb(m,ishomo || homo,0,0,&perm); if ( !x ) { *rp = 0; return; } if ( nd_gentrace ) { MKVECT(hvect,nd_psn); for ( i = 0; i < nd_psn; i++ ) ndltodp(nd_psh[i]->dl,(DP *)&BDY(hvect)[i]); } if ( !ishomo && homo ) { /* dehomogenization */ for ( t = x; t; t = NEXT(t) ) ndv_dehomogenize((NDV)BDY(t),ord); nd_init_ord(ord); nd_setup_parameters(nvar,0); } nd_demand = 0; if ( nd_module && nd_intersect ) { for ( j = nd_psn-1, x = 0; j >= 0; j-- ) if ( MPOS(DL(nd_psh[j])) > nd_intersect ) { MKNODE(xx,(pointer)((unsigned long)j),x); x = xx; } conv_ilist(nd_demand,0,x,0); goto FINAL; } if ( nd_gentrace && f4 ) { nzlist = nd_alltracelist; } x = ndv_reducebase(x,perm); if ( nd_gentrace && !f4 ) { tl1 = nd_alltracelist; nd_alltracelist = 0; } x = ndv_reduceall(m,x); cbpe = nd_bpe; if ( nd_gentrace && !f4 ) { tl2 = nd_alltracelist; nd_alltracelist = 0; ndv_check_membership(m,fd0,obpe,oadv,oepos,x); tl3 = nd_alltracelist; nd_alltracelist = 0; if ( nd_gensyz ) { nd_gb(m,0,1,1,0); tl4 = nd_alltracelist; nd_alltracelist = 0; } else tl4 = 0; } nd_bpe = cbpe; nd_setup_parameters(nd_nvar,0); FINAL: for ( r0 = 0, t = x; t; t = NEXT(t) ) { NEXTNODE(r0,r); if ( nd_module ) { if ( retdp ) BDY(r) = ndvtodpm(m,BDY(t)); else BDY(r) = ndvtopl(m,CO,vv,BDY(t),mrank); } else if ( retdp ) BDY(r) = ndvtodp(m,BDY(t)); else BDY(r) = ndvtop(m,CO,vv,BDY(t)); } if ( r0 ) NEXT(r) = 0; if ( !m && nd_nalg ) r0 = postprocess_algcoef(av,alist,r0); MKLIST(*rp,r0); if ( nd_gentrace ) { if ( f4 ) { STOZ(16,bpe); STOZ(nd_last_nonzero,last_nonzero); tr = mknode(6,*rp,(!ishomo&&homo)?ONE:0,BDY(nzlist),bpe,last_nonzero,hvect); MKLIST(*rp,tr); } else { tl1 = reverse_node(tl1); tl2 = reverse_node(tl2); tl3 = reverse_node(tl3); /* tl2 = [[i,[[*,j,*,*],...]],...] */ for ( t = tl2; t; t = NEXT(t) ) { /* s = [i,[*,j,*,*],...] */ s = BDY((LIST)BDY(t)); j = perm[ZTOS((Q)ARG0(s))]; STOZ(j,jq); ARG0(s) = (pointer)jq; for ( s = BDY((LIST)ARG1(s)); s; s = NEXT(s) ) { j = perm[ZTOS((Q)ARG1(BDY((LIST)BDY(s))))]; STOZ(j,jq); ARG1(BDY((LIST)BDY(s))) = (pointer)jq; } } for ( j = length(x)-1, t = 0; j >= 0; j-- ) { STOZ(perm[j],jq); MKNODE(s,jq,t); t = s; } MKLIST(l1,tl1); MKLIST(l2,tl2); MKLIST(l3,t); MKLIST(l4,tl3); MKLIST(l5,tl4); STOZ(nd_bpe,bpe); tr = mknode(9,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe,hvect); MKLIST(*rp,tr); } } #if 0 fprintf(asir_out,"ndv_alloc=%d\n",ndv_alloc); #endif } NODE nd_sba_f4(int m,int **indp); void nd_sba(LIST f,LIST v,int m,int homo,int retdp,int f4,struct order_spec *ord,LIST *rp) { VL tv,fv,vv,vc,av; NODE fd,fd0,r,r0,t,x,s,xx; int e,max,nvar,i; NDV b; int ishomo,nalg,wmax,len; NMV a; P p,zp; Q dmy; struct order_spec *ord1; int j; int *perm; EPOS oepos; int obpe,oadv,ompos,cbpe; struct oEGT eg0,eg1,egconv; nd_module = 0; nd_demand = 0; parse_nd_option(current_option); Nsamesig = 0; if ( DP_Multiple ) nd_scale = ((double)DP_Multiple)/(double)(Denominator?Denominator:1); get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc); if ( m && nd_vc ) error("nd_sba : computation over Fp(X) is unsupported. Use dp_gr_mod_main()."); for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ ); switch ( ord->id ) { case 1: if ( ord->nv != nvar ) error("nd_sba : invalid order specification"); break; default: break; } nd_nalg = 0; nd_init_ord(ord); // for SIG comparison initd(ord); for ( t = BDY(f), max = 1; t; t = NEXT(t) ) { for ( tv = vv; tv; tv = NEXT(tv) ) { e = getdeg(tv->v,(P)BDY(t)); max = MAX(e,max); } } nd_setup_parameters(nvar,max); obpe = nd_bpe; oadv = nmv_adv; oepos = nd_epos; ompos = nd_mpos; ishomo = 1; for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) { if ( !m ) ptozp((P)BDY(t),1,&dmy,&zp); else zp = (P)BDY(t); b = (pointer)ptondv(CO,vv,zp); if ( ishomo ) ishomo = ishomo && ndv_ishomo(b); if ( m ) ndv_mod(m,b); if ( b ) { NEXTNODE(fd0,fd); BDY(fd) = (pointer)b; } } if ( fd0 ) NEXT(fd) = 0; if ( !ishomo && homo ) { for ( t = fd0, wmax = max; t; t = NEXT(t) ) { b = (NDV)BDY(t); len = LEN(b); for ( a = BDY(b), i = 0; i < len; i++, NMV_ADV(a) ) wmax = MAX(TD(DL(a)),wmax); } homogenize_order(ord,nvar,&ord1); nd_init_ord(ord1); nd_setup_parameters(nvar+1,nd_nzlist?0:wmax); for ( t = fd0; t; t = NEXT(t) ) ndv_homogenize((NDV)BDY(t),obpe,oadv,oepos,ompos); } ndv_setup(m,0,fd0,0,0,1); x = f4 ? nd_sba_f4(m,&perm) : nd_sba_buch(m,ishomo || homo,&perm); if ( !x ) { *rp = 0; return; } if ( !ishomo && homo ) { /* dehomogenization */ for ( t = x; t; t = NEXT(t) ) ndv_dehomogenize((NDV)BDY(t),ord); nd_init_ord(ord); nd_setup_parameters(nvar,0); } nd_demand = 0; x = ndv_reducebase(x,perm); x = ndv_reduceall(m,x); nd_setup_parameters(nd_nvar,0); get_eg(&eg0); for ( r0 = 0, t = x; t; t = NEXT(t) ) { NEXTNODE(r0,r); if ( retdp ) BDY(r) = ndvtodp(m,BDY(t)); else BDY(r) = ndvtop(m,CO,vv,BDY(t)); } if ( r0 ) NEXT(r) = 0; MKLIST(*rp,r0); get_eg(&eg1); init_eg(&egconv); add_eg(&egconv,&eg0,&eg1); print_eg("conv",&egconv); fprintf(asir_out,"\n"); } void nd_gr_postproc(LIST f,LIST v,int m,struct order_spec *ord,int do_check,LIST *rp) { VL tv,fv,vv,vc,av; NODE fd,fd0,r,r0,t,x,s,xx,alist; int e,max,nvar,i; NDV b; int ishomo,nalg; Alg alpha,dp; P p,zp; Q dmy; LIST f1,f2; Obj obj; NumberField nf; struct order_spec *ord1; int *perm; parse_nd_option(current_option); get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc); for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ ); switch ( ord->id ) { case 1: if ( ord->nv != nvar ) error("nd_check : invalid order specification"); break; default: break; } nd_nalg = 0; av = 0; if ( !m ) { get_algtree((Obj)f,&av); for ( nalg = 0, tv = av; tv; tv = NEXT(tv), nalg++ ); nd_ntrans = nvar; nd_nalg = nalg; /* #i -> t#i */ if ( nalg ) { preprocess_algcoef(vv,av,ord,f,&ord1,&f1,&alist); ord = ord1; f = f1; } nvar += nalg; } nd_init_ord(ord); for ( t = BDY(f), max = 1; t; t = NEXT(t) ) for ( tv = vv; tv; tv = NEXT(tv) ) { e = getdeg(tv->v,(P)BDY(t)); max = MAX(e,max); } nd_setup_parameters(nvar,max); ishomo = 1; for ( fd0 = 0, t = BDY(f); t; t = NEXT(t) ) { ptozp((P)BDY(t),1,&dmy,&zp); b = (pointer)ptondv(CO,vv,zp); if ( ishomo ) ishomo = ishomo && ndv_ishomo(b); if ( m ) ndv_mod(m,b); if ( b ) { NEXTNODE(fd0,fd); BDY(fd) = (pointer)b; } } if ( fd0 ) NEXT(fd) = 0; ndv_setup(m,0,fd0,0,1,0); for ( x = 0, i = 0; i < nd_psn; i++ ) x = update_base(x,i); if ( do_check ) { x = nd_gb(m,ishomo,1,0,&perm); if ( !x ) { *rp = 0; return; } } else { #if 0 /* bug ? */ for ( t = x; t; t = NEXT(t) ) BDY(t) = (pointer)nd_ps[(long)BDY(t)]; #else conv_ilist(0,0,x,&perm); #endif } x = ndv_reducebase(x,perm); x = ndv_reduceall(m,x); for ( r0 = 0, t = x; t; t = NEXT(t) ) { NEXTNODE(r0,r); BDY(r) = ndvtop(m,CO,vv,BDY(t)); } if ( r0 ) NEXT(r) = 0; if ( !m && nd_nalg ) r0 = postprocess_algcoef(av,alist,r0); MKLIST(*rp,r0); } NDV recompute_trace(NODE trace,NDV *p,int m); void nd_gr_recompute_trace(LIST f,LIST v,int m,struct order_spec *ord,LIST tlist,LIST *rp); NDV recompute_trace(NODE ti,NDV *p,int mod) { int c,c1,c2,i; NM mul,m,tail; ND d,r,rm; NODE sj; NDV red; Obj mj; mul = (NM)MALLOC(sizeof(struct oNM)+(nd_wpd-1)*sizeof(UINT)); CM(mul) = 1; tail = 0; for ( i = 0, d = r = 0; ti; ti = NEXT(ti), i++ ) { sj = BDY((LIST)BDY(ti)); if ( ARG0(sj) ) { red = p[ZTOS((Q)ARG1(sj))]; mj = (Obj)ARG2(sj); if ( OID(mj) != O_DP ) ndl_zero(DL(mul)); else dltondl(nd_nvar,BDY((DP)mj)->dl,DL(mul)); rm = ndv_mul_nm(mod,mul,red); if ( !r ) r = rm; else { for ( m = BDY(r); m && !ndl_equal(m->dl,BDY(rm)->dl); m = NEXT(m), LEN(r)-- ) { if ( d ) { NEXT(tail) = m; tail = m; LEN(d)++; } else { MKND(nd_nvar,m,1,d); tail = BDY(d); } } if ( !m ) return 0; /* failure */ else { BDY(r) = m; if ( mod > 0 || mod == -1 ) { c1 = invm(HCM(rm),mod); c2 = mod-HCM(r); DMAR(c1,c2,0,mod,c); nd_mul_c(mod,rm,c); } else { Z t,u; chsgnlf(HCZ(r),&t); divlf(t,HCZ(rm),&u); nd_mul_c_lf(rm,u); } r = nd_add(mod,r,rm); } } } } if ( tail ) NEXT(tail) = 0; d = nd_add(mod,d,r); nd_mul_c(mod,d,invm(HCM(d),mod)); return ndtondv(mod,d); } void nd_gr_recompute_trace(LIST f,LIST v,int m,struct order_spec *ord,LIST tlist,LIST *rp) { VL tv,fv,vv,vc,av; NODE fd,fd0,r,r0,t,x,s,xx,alist; int e,max,nvar,i; NDV b; int ishomo,nalg; Alg alpha,dp; P p,zp; Q dmy; LIST f1,f2; Obj obj; NumberField nf; struct order_spec *ord1; NODE permtrace,intred,ind,perm,trace,ti; int len,n,j; NDV *db,*pb; parse_nd_option(current_option); get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc); for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ ); switch ( ord->id ) { case 1: if ( ord->nv != nvar ) error("nd_check : invalid order specification"); break; default: break; } nd_init_ord(ord); nd_bpe = ZTOS((Q)ARG7(BDY(tlist))); nd_setup_parameters(nvar,0); len = length(BDY(f)); db = (NDV *)MALLOC(len*sizeof(NDV *)); for ( i = 0, t = BDY(f); t; i++, t = NEXT(t) ) { ptozp((P)BDY(t),1,&dmy,&zp); b = ptondv(CO,vv,zp); ndv_mod(m,b); ndv_mul_c(m,b,invm(HCM(b),m)); db[i] = b; } permtrace = BDY((LIST)ARG2(BDY(tlist))); intred = BDY((LIST)ARG3(BDY(tlist))); ind = BDY((LIST)ARG4(BDY(tlist))); perm = BDY((LIST)ARG0(permtrace)); trace = NEXT(permtrace); for ( i = length(perm)-1, t = trace; t; t = NEXT(t) ) { j = ZTOS((Q)ARG0(BDY((LIST)BDY(t)))); if ( j > i ) i = j; } n = i+1; pb = (NDV *)MALLOC(n*sizeof(NDV *)); for ( t = perm, i = 0; t; t = NEXT(t), i++ ) { ti = BDY((LIST)BDY(t)); pb[ZTOS((Q)ARG0(ti))] = db[ZTOS((Q)ARG1(ti))]; } for ( t = trace; t; t = NEXT(t) ) { ti = BDY((LIST)BDY(t)); pb[ZTOS((Q)ARG0(ti))] = recompute_trace(BDY((LIST)ARG1(ti)),pb,m); if ( !pb[ZTOS((Q)ARG0(ti))] ) { *rp = 0; return; } if ( DP_Print ) { fprintf(asir_out,"."); fflush(asir_out); } } for ( t = intred; t; t = NEXT(t) ) { ti = BDY((LIST)BDY(t)); pb[ZTOS((Q)ARG0(ti))] = recompute_trace(BDY((LIST)ARG1(ti)),pb,m); if ( !pb[ZTOS((Q)ARG0(ti))] ) { *rp = 0; return; } if ( DP_Print ) { fprintf(asir_out,"*"); fflush(asir_out); } } for ( r0 = 0, t = ind; t; t = NEXT(t) ) { NEXTNODE(r0,r); b = pb[ZTOS((Q)BDY(t))]; ndv_mul_c(m,b,invm(HCM(b),m)); #if 0 BDY(r) = ndvtop(m,CO,vv,pb[ZTOS((Q)BDY(t))]); #else BDY(r) = ndvtodp(m,pb[ZTOS((Q)BDY(t))]); #endif } if ( r0 ) NEXT(r) = 0; MKLIST(*rp,r0); if ( DP_Print ) fprintf(asir_out,"\n"); } void nd_gr_trace(LIST f,LIST v,int trace,int homo,int retdp,int f4,struct order_spec *ord,LIST *rp) { VL tv,fv,vv,vc,av; NODE fd,fd0,in0,in,r,r0,t,s,cand,alist; int m,nocheck,nvar,mindex,e,max; NDV c; NMV a; P p,zp; Q dmy; EPOS oepos; int obpe,oadv,wmax,i,len,cbpe,ishomo,nalg,mrank,trank,ompos; Alg alpha,dp; P poly; LIST f1,f2,zpl; Obj obj; NumberField nf; struct order_spec *ord1; struct oEGT eg_check,eg0,eg1; NODE tr,tl1,tl2,tl3,tl4; LIST l1,l2,l3,l4,l5; int *perm; int j,ret; Z jq,bpe; VECT hvect; nd_module = 0; nd_lf = 0; parse_nd_option(current_option); if ( nd_lf ) { if ( f4 ) nd_f4_lf_trace(f,v,trace,homo,ord,rp); else error("nd_gr_trace is not implemented yet over a large finite field"); return; } if ( DP_Multiple ) nd_scale = ((double)DP_Multiple)/(double)(Denominator?Denominator:1); get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc); for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ ); switch ( ord->id ) { case 1: if ( ord->nv != nvar ) error("nd_gr_trace : invalid order specification"); break; default: break; } get_algtree((Obj)f,&av); for ( nalg = 0, tv = av; tv; tv = NEXT(tv), nalg++ ); nd_ntrans = nvar; nd_nalg = nalg; /* #i -> t#i */ if ( nalg ) { preprocess_algcoef(vv,av,ord,f,&ord1,&f1,&alist); ord = ord1; f = f1; } nvar += nalg; nocheck = 0; mindex = 0; if ( Demand ) nd_demand = 1; else nd_demand = 0; /* setup modulus */ if ( trace < 0 ) { trace = -trace; nocheck = 1; } m = trace > 1 ? trace : get_lprime(mindex); nd_init_ord(ord); mrank = 0; for ( t = BDY(f), max = 1; t; t = NEXT(t) ) for ( tv = vv; tv; tv = NEXT(tv) ) { if ( nd_module ) { if ( OID(BDY(t)) == O_DPM ) { e = dpm_getdeg((DPM)BDY(t),&trank); max = MAX(e,max); mrank = MAX(mrank,trank); } else { s = BDY((LIST)BDY(t)); trank = length(s); mrank = MAX(mrank,trank); for ( ; s; s = NEXT(s) ) { e = getdeg(tv->v,(P)BDY(s)); max = MAX(e,max); } } } else { e = getdeg(tv->v,(P)BDY(t)); max = MAX(e,max); } } nd_setup_parameters(nvar,max); obpe = nd_bpe; oadv = nmv_adv; oepos = nd_epos; ompos = nd_mpos; ishomo = 1; for ( in0 = 0, fd0 = 0, t = BDY(f); t; t = NEXT(t) ) { if ( nd_module ) { if ( OID(BDY(t)) == O_DPM ) { Z cont; DPM zdpm; if ( !nd_gentrace ) dpm_ptozp((DPM)BDY(t),&cont,&zdpm); else zdpm = (DPM)BDY(t); c = (pointer)dpmtondv(m,zdpm); } else { if ( !nd_gentrace ) pltozpl((LIST)BDY(t),&dmy,&zpl); else zpl = (LIST)BDY(t); c = (pointer)pltondv(CO,vv,zpl); } } else { if ( !nd_gentrace ) ptozp((P)BDY(t),1,&dmy,&zp); else zp = (P)BDY(t); c = (pointer)ptondv(CO,vv,zp); } if ( ishomo ) ishomo = ishomo && ndv_ishomo(c); if ( c ) { NEXTNODE(in0,in); BDY(in) = (pointer)c; NEXTNODE(fd0,fd); BDY(fd) = (pointer)ndv_dup(0,c); } } if ( in0 ) NEXT(in) = 0; if ( fd0 ) NEXT(fd) = 0; if ( !ishomo && homo ) { for ( t = in0, wmax = max; t; t = NEXT(t) ) { c = (NDV)BDY(t); len = LEN(c); for ( a = BDY(c), i = 0; i < len; i++, NMV_ADV(a) ) wmax = MAX(TD(DL(a)),wmax); } homogenize_order(ord,nvar,&ord1); nd_init_ord(ord1); nd_setup_parameters(nvar+1,wmax); for ( t = fd0; t; t = NEXT(t) ) ndv_homogenize((NDV)BDY(t),obpe,oadv,oepos,ompos); } if ( MaxDeg > 0 ) nocheck = 1; while ( 1 ) { tl1 = tl2 = tl3 = tl4 = 0; if ( Demand ) nd_demand = 1; ret = ndv_setup(m,1,fd0,nd_gbblock?1:0,0,0); if ( nd_gentrace ) { MKLIST(l1,nd_tracelist); MKNODE(nd_alltracelist,l1,0); } if ( ret ) cand = f4?nd_f4_trace(m,&perm):nd_gb_trace(m,ishomo || homo,&perm); if ( !ret || !cand ) { /* failure */ if ( trace > 1 ) { *rp = 0; return; } else m = get_lprime(++mindex); continue; } if ( nd_gentrace ) { MKVECT(hvect,nd_psn); for ( i = 0; i < nd_psn; i++ ) ndltodp(nd_psh[i]->dl,(DP *)&BDY(hvect)[i]); } if ( !ishomo && homo ) { /* dehomogenization */ for ( t = cand; t; t = NEXT(t) ) ndv_dehomogenize((NDV)BDY(t),ord); nd_init_ord(ord); nd_setup_parameters(nvar,0); } nd_demand = 0; cand = ndv_reducebase(cand,perm); if ( nd_gentrace ) { tl1 = nd_alltracelist; nd_alltracelist = 0; } cand = ndv_reduceall(0,cand); cbpe = nd_bpe; if ( nd_gentrace ) { tl2 = nd_alltracelist; nd_alltracelist = 0; } get_eg(&eg0); if ( nocheck ) break; if ( (ret = ndv_check_membership(0,in0,obpe,oadv,oepos,cand)) != 0 ) { if ( nd_gentrace ) { tl3 = nd_alltracelist; nd_alltracelist = 0; } else tl3 = 0; /* gbcheck : cand is a GB of Id(cand) ? */ if ( nd_vc || nd_gentrace || nd_gensyz ) ret = nd_gb(0,0,1,nd_gensyz?1:0,0)!=0; else ret = nd_f4(0,1,0)!=0; if ( nd_gentrace && nd_gensyz ) { tl4 = nd_alltracelist; nd_alltracelist = 0; } else tl4 = 0; } if ( ret ) break; else if ( trace > 1 ) { /* failure */ *rp = 0; return; } else { /* try the next modulus */ m = get_lprime(++mindex); /* reset the parameters */ if ( !ishomo && homo ) { nd_init_ord(ord1); nd_setup_parameters(nvar+1,wmax); } else { nd_init_ord(ord); nd_setup_parameters(nvar,max); } } } get_eg(&eg1); init_eg(&eg_check); add_eg(&eg_check,&eg0,&eg1); if ( DP_Print ) fprintf(asir_out,"check=%.3fsec\n",eg_check.exectime); /* dp->p */ nd_bpe = cbpe; nd_setup_parameters(nd_nvar,0); for ( r = cand; r; r = NEXT(r) ) { if ( nd_module ) { if ( retdp ) BDY(r) = ndvtodpm(0,BDY(r)); else BDY(r) = ndvtopl(0,CO,vv,BDY(r),mrank); } else if ( retdp ) BDY(r) = ndvtodp(0,BDY(r)); else BDY(r) = (pointer)ndvtop(0,CO,vv,BDY(r)); } if ( nd_nalg ) cand = postprocess_algcoef(av,alist,cand); MKLIST(*rp,cand); if ( nd_gentrace ) { tl1 = reverse_node(tl1); tl2 = reverse_node(tl2); tl3 = reverse_node(tl3); /* tl2 = [[i,[[*,j,*,*],...]],...] */ for ( t = tl2; t; t = NEXT(t) ) { /* s = [i,[*,j,*,*],...] */ s = BDY((LIST)BDY(t)); j = perm[ZTOS((Q)ARG0(s))]; STOZ(j,jq); ARG0(s) = (pointer)jq; for ( s = BDY((LIST)ARG1(s)); s; s = NEXT(s) ) { j = perm[ZTOS((Q)ARG1(BDY((LIST)BDY(s))))]; STOZ(j,jq); ARG1(BDY((LIST)BDY(s))) = (pointer)jq; } } for ( j = length(cand)-1, t = 0; j >= 0; j-- ) { STOZ(perm[j],jq); MKNODE(s,jq,t); t = s; } MKLIST(l1,tl1); MKLIST(l2,tl2); MKLIST(l3,t); MKLIST(l4,tl3); MKLIST(l5,tl4); STOZ(nd_bpe,bpe); tr = mknode(9,*rp,(!ishomo&&homo)?ONE:0,l1,l2,l3,l4,l5,bpe,hvect); MKLIST(*rp,tr); } } /* XXX : module element is not considered */ void dltondl(int n,DL dl,UINT *r) { UINT *d; int i,j,l,s,ord_l; struct order_pair *op; d = (unsigned int *)dl->d; for ( i = 0; i < nd_wpd; i++ ) r[i] = 0; if ( nd_blockmask ) { l = nd_blockmask->n; op = nd_blockmask->order_pair; for ( j = 0, s = 0; j < l; j++ ) { ord_l = op[j].length; for ( i = 0; i < ord_l; i++, s++ ) PUT_EXP(r,s,d[s]); } TD(r) = ndl_weight(r); ndl_weight_mask(r); } else { for ( i = 0; i < n; i++ ) PUT_EXP(r,i,d[i]); TD(r) = ndl_weight(r); } } DL ndltodl(int n,UINT *ndl) { DL dl; int *d; int i,j,l,s,ord_l; struct order_pair *op; NEWDL_NOINIT(dl,n); dl->td = TD(ndl); d = dl->d; if ( nd_blockmask ) { l = nd_blockmask->n; op = nd_blockmask->order_pair; for ( j = 0, s = 0; j < l; j++ ) { ord_l = op[j].length; for ( i = 0; i < ord_l; i++, s++ ) d[s] = GET_EXP(ndl,s); } } else { for ( i = 0; i < n; i++ ) d[i] = GET_EXP(ndl,i); } return dl; } void _ndltodl(UINT *ndl,DL dl) { int *d; int i,j,l,s,ord_l,n; struct order_pair *op; n = nd_nvar; dl->td = TD(ndl); d = dl->d; if ( nd_blockmask ) { l = nd_blockmask->n; op = nd_blockmask->order_pair; for ( j = 0, s = 0; j < l; j++ ) { ord_l = op[j].length; for ( i = 0; i < ord_l; i++, s++ ) d[s] = GET_EXP(ndl,s); } } else { for ( i = 0; i < n; i++ ) d[i] = GET_EXP(ndl,i); } } void nmtodp(int mod,NM m,DP *r) { DP dp; MP mr; NEWMP(mr); mr->dl = ndltodl(nd_nvar,DL(m)); mr->c = (Obj)ndctop(mod,m->c); NEXT(mr) = 0; MKDP(nd_nvar,mr,dp); dp->sugar = mr->dl->td; *r = dp; } void ndltodp(UINT *d,DP *r) { DP dp; MP mr; NEWMP(mr); mr->dl = ndltodl(nd_nvar,d); mr->c = (Obj)ONE; NEXT(mr) = 0; MKDP(nd_nvar,mr,dp); dp->sugar = mr->dl->td; *r = dp; } void ndl_print(UINT *dl) { int n; int i,j,l,ord_l,s,s0; struct order_pair *op; n = nd_nvar; printf("<<"); if ( nd_blockmask ) { l = nd_blockmask->n; op = nd_blockmask->order_pair; for ( j = 0, s = s0 = 0; j < l; j++ ) { ord_l = op[j].length; for ( i = 0; i < ord_l; i++, s++ ) printf(s==n-1?"%d":"%d,",GET_EXP(dl,s)); } } else { for ( i = 0; i < n; i++ ) printf(i==n-1?"%d":"%d,",GET_EXP(dl,i)); } printf(">>"); if ( nd_module && MPOS(dl) ) printf("*e%d",MPOS(dl)); } void nd_print(ND p) { NM m; if ( !p ) printf("0\n"); else { for ( m = BDY(p); m; m = NEXT(m) ) { if ( CM(m) & 0x80000000 ) printf("+@_%d*",IFTOF(CM(m))); else printf("+%ld*",CM(m)); ndl_print(DL(m)); } printf("\n"); } } void nd_print_q(ND p) { NM m; if ( !p ) printf("0\n"); else { for ( m = BDY(p); m; m = NEXT(m) ) { printf("+"); printexpr(CO,(Obj)CZ(m)); printf("*"); ndl_print(DL(m)); } printf("\n"); } } void ndp_print(ND_pairs d) { ND_pairs t; for ( t = d; t; t = NEXT(t) ) printf("%d,%d ",t->i1,t->i2); printf("\n"); } void nd_removecont(int mod,ND p) { int i,n; Z *w; NM m; struct oVECT v; if ( mod == -1 ) nd_mul_c(mod,p,_invsf(HCM(p))); else if ( mod == -2 ) { Z inv; divlf(ONE,HCZ(p),&inv); nd_mul_c_lf(p,inv); } else if ( mod ) nd_mul_c(mod,p,invm(HCM(p),mod)); else { for ( m = BDY(p), n = 0; m; m = NEXT(m), n++ ); w = (Z *)MALLOC(n*sizeof(Q)); v.len = n; v.body = (pointer *)w; for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) w[i] = CZ(m); removecont_array((P *)w,n,1); for ( m = BDY(p), i = 0; i < n; m = NEXT(m), i++ ) CZ(m) = w[i]; } } void nd_removecont2(ND p1,ND p2) { int i,n1,n2,n; Z *w; NM m; struct oVECT v; n1 = nd_length(p1); n2 = nd_length(p2); n = n1+n2; w = (Z *)MALLOC(n*sizeof(Q)); v.len = n; v.body = (pointer *)w; i = 0; if ( p1 ) for ( m = BDY(p1); i < n1; m = NEXT(m), i++ ) w[i] = CZ(m); if ( p2 ) for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) w[i] = CZ(m); removecont_array((P *)w,n,1); i = 0; if ( p1 ) for ( m = BDY(p1); i < n1; m = NEXT(m), i++ ) CZ(m) = w[i]; if ( p2 ) for ( m = BDY(p2); i < n; m = NEXT(m), i++ ) CZ(m) = w[i]; } void ndv_removecont(int mod,NDV p) { int i,len,all_p; Z *c; P *w; Z dvr,t; P g,cont,tp; NMV m; if ( mod == -1 ) ndv_mul_c(mod,p,_invsf(HCM(p))); else if ( mod == -2 ) { Z inv; divlf(ONE,HCZ(p),&inv); ndv_mul_c_lf(p,inv); } else if ( mod ) ndv_mul_c(mod,p,invm(HCM(p),mod)); else { len = p->len; w = (P *)MALLOC(len*sizeof(P)); c = (Z *)MALLOC(len*sizeof(Q)); for ( m = BDY(p), all_p = 1, i = 0; i < len; NMV_ADV(m), i++ ) { ptozp(CP(m),1,(Q *)&c[i],&w[i]); all_p = all_p && !NUM(w[i]); } if ( all_p ) { qltozl((Q *)c,len,&dvr); nd_heu_nezgcdnpz(nd_vc,w,len,1,&g); mulp(nd_vc,(P)dvr,g,&cont); for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ ) { divsp(nd_vc,CP(m),cont,&tp); CP(m) = tp; } } else { sortbynm((Q *)c,len); qltozl((Q *)c,len,&dvr); for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ ) { divsp(nd_vc,CP(m),(P)dvr,&tp); CP(m) = tp; } } } } /* koko */ void ndv_homogenize(NDV p,int obpe,int oadv,EPOS oepos,int ompos) { int len,i,max; NMV m,mr0,mr,t; len = p->len; for ( m = BDY(p), i = 0, max = 0; i < len; NMV_OADV(m), i++ ) max = MAX(max,TD(DL(m))); mr0 = nmv_adv>oadv?(NMV)REALLOC(BDY(p),len*nmv_adv):BDY(p); m = (NMV)((char *)mr0+(len-1)*oadv); mr = (NMV)((char *)mr0+(len-1)*nmv_adv); t = (NMV)MALLOC(nmv_adv); for ( i = 0; i < len; i++, NMV_OPREV(m), NMV_PREV(mr) ) { ndl_homogenize(DL(m),DL(t),obpe,oepos,ompos,max); CZ(mr) = CZ(m); ndl_copy(DL(t),DL(mr)); } NV(p)++; BDY(p) = mr0; } void ndv_dehomogenize(NDV p,struct order_spec *ord) { int i,j,adj,len,newnvar,newwpd,newadv,newexporigin,newmpos; int pos; Q *w; Q dvr,t; NMV m,r; len = p->len; newnvar = nd_nvar-1; newexporigin = nd_get_exporigin(ord); if ( nd_module ) newmpos = newexporigin-1; newwpd = newnvar/nd_epw+(newnvar%nd_epw?1:0)+newexporigin; for ( m = BDY(p), i = 0; i < len; NMV_ADV(m), i++ ) ndl_dehomogenize(DL(m)); if ( newwpd != nd_wpd ) { newadv = ROUND_FOR_ALIGN(sizeof(struct oNMV)+(newwpd-1)*sizeof(UINT)); for ( m = r = BDY(p), i = 0; i < len; NMV_ADV(m), NDV_NADV(r), i++ ) { CZ(r) = CZ(m); if ( nd_module ) pos = MPOS(DL(m)); for ( j = 0; j < newexporigin; j++ ) DL(r)[j] = DL(m)[j]; adj = nd_exporigin-newexporigin; for ( ; j < newwpd; j++ ) DL(r)[j] = DL(m)[j+adj]; if ( nd_module ) { DL(r)[newmpos] = pos; } } } NV(p)--; } void nd_heu_nezgcdnpz(VL vl,P *pl,int m,int full,P *pr) { int i; P *tpl,*tpl1; NODE l; P h,gcd,t; tpl = (P *)MALLOC(m*sizeof(P)); tpl1 = (P *)MALLOC(m*sizeof(P)); bcopy(pl,tpl,m*sizeof(P)); gcd = (P)ONE; for ( l = nd_hcf; l; l = NEXT(l) ) { h = (P)BDY(l); while ( 1 ) { for ( i = 0; i < m; i++ ) if ( !divtpz(vl,tpl[i],h,&tpl1[i]) ) break; if ( i == m ) { bcopy(tpl1,tpl,m*sizeof(P)); mulp(vl,gcd,h,&t); gcd = t; } else break; } } if ( DP_Print > 2 ){fprintf(asir_out,"[%d]",nmonop(gcd)); fflush(asir_out);} if ( full ) { heu_nezgcdnpz(vl,tpl,m,&t); mulp(vl,gcd,t,pr); } else *pr = gcd; } void removecont_array(P *p,int n,int full) { int all_p,all_q,i; Z *c; P *w; P t,s; for ( all_q = 1, i = 0; i < n; i++ ) all_q = all_q && NUM(p[i]); if ( all_q ) { removecont_array_q((Z *)p,n); } else { c = (Z *)MALLOC(n*sizeof(Z)); w = (P *)MALLOC(n*sizeof(P)); for ( i = 0; i < n; i++ ) { ptozp(p[i],1,(Q *)&c[i],&w[i]); } removecont_array_q(c,n); nd_heu_nezgcdnpz(nd_vc,w,n,full,&t); for ( i = 0; i < n; i++ ) { divsp(nd_vc,w[i],t,&s); mulp(nd_vc,s,(P)c[i],&p[i]); } } } /* c is an int array */ void removecont_array_q(Z *c,int n) { struct oVECT v; Z d0,d1,a,u,u1,gcd; int i,j; Z *q,*r; q = (Z *)MALLOC(n*sizeof(Z)); r = (Z *)MALLOC(n*sizeof(Z)); v.id = O_VECT; v.len = n; v.body = (pointer *)c; gcdvz_estimate(&v,&d0); for ( i = 0; i < n; i++ ) { divqrz(c[i],d0,&q[i],&r[i]); } for ( i = 0; i < n; i++ ) if ( r[i] ) break; if ( i < n ) { v.id = O_VECT; v.len = n; v.body = (pointer *)r; gcdvz(&v,&d1); gcdz(d0,d1,&gcd); /* exact division */ divsz(d0,gcd,&a); for ( i = 0; i < n; i++ ) { mulz(a,q[i],&u); if ( r[i] ) { /* exact division */ divsz(r[i],gcd,&u1); addz(u,u1,&q[i]); } else q[i] = u; } } for ( i = 0; i < n; i++ ) c[i] = q[i]; } void gcdv_mpz_estimate(mpz_t d0,mpz_t *c,int n); void mpz_removecont_array(mpz_t *c,int n) { mpz_t d0,a,u,u1,gcd; int i,j; static mpz_t *q,*r; static int c_len = 0; for ( i = 0; i < n; i++ ) if ( mpz_sgn(c[i]) ) break; if ( i == n ) return; gcdv_mpz_estimate(d0,c,n); if ( n > c_len ) { q = (mpz_t *)MALLOC(n*sizeof(mpz_t)); r = (mpz_t *)MALLOC(n*sizeof(mpz_t)); c_len = n; } for ( i = 0; i < n; i++ ) { mpz_init(q[i]); mpz_init(r[i]); mpz_fdiv_qr(q[i],r[i],c[i],d0); } for ( i = 0; i < n; i++ ) if ( mpz_sgn(r[i]) ) break; mpz_init(gcd); mpz_init(a); mpz_init(u); mpz_init(u1); if ( i < n ) { mpz_gcd(gcd,d0,r[i]); for ( j = i+1; j < n; j++ ) mpz_gcd(gcd,gcd,r[j]); mpz_div(a,d0,gcd); for ( i = 0; i < n; i++ ) { mpz_mul(u,a,q[i]); if ( mpz_sgn(r[i]) ) { mpz_div(u1,r[i],gcd); mpz_add(q[i],u,u1); } else mpz_set(q[i],u); } } for ( i = 0; i < n; i++ ) mpz_set(c[i],q[i]); } void nd_mul_c(int mod,ND p,int mul) { NM m; int c,c1; if ( !p ) return; if ( mul == 1 ) return; if ( mod == -1 ) for ( m = BDY(p); m; m = NEXT(m) ) CM(m) = _mulsf(CM(m),mul); else for ( m = BDY(p); m; m = NEXT(m) ) { c1 = CM(m); DMAR(c1,mul,0,mod,c); CM(m) = c; } } void nd_mul_c_lf(ND p,Z mul) { NM m; Z c; if ( !p ) return; if ( UNIZ(mul) ) return; for ( m = BDY(p); m; m = NEXT(m) ) { mullf(CZ(m),mul,&c); CZ(m) = c; } } void nd_mul_c_q(ND p,P mul) { NM m; P c; if ( !p ) return; if ( UNIQ(mul) ) return; for ( m = BDY(p); m; m = NEXT(m) ) { mulp(nd_vc,CP(m),mul,&c); CP(m) = c; } } void nd_mul_c_p(VL vl,ND p,P mul) { NM m; P c; if ( !p ) return; for ( m = BDY(p); m; m = NEXT(m) ) { mulp(vl,CP(m),mul,&c); CP(m) = c; } } void nd_free(ND p) { NM t,s; if ( !p ) return; t = BDY(p); while ( t ) { s = NEXT(t); FREENM(t); t = s; } FREEND(p); } void ndv_free(NDV p) { GCFREE(BDY(p)); } void nd_append_red(UINT *d,int i) { RHist m,m0; int h; NEWRHist(m); h = ndl_hash_value(d); m->index = i; ndl_copy(d,DL(m)); NEXT(m) = nd_red[h]; nd_red[h] = m; } UINT *ndv_compute_bound(NDV p) { UINT *d1,*d2,*t; UINT u; int i,j,k,l,len,ind; NMV m; if ( !p ) return 0; d1 = (UINT *)MALLOC(nd_wpd*sizeof(UINT)); d2 = (UINT *)MALLOC(nd_wpd*sizeof(UINT)); len = LEN(p); m = BDY(p); ndl_copy(DL(m),d1); NMV_ADV(m); for ( i = 1; i < len; i++, NMV_ADV(m) ) { ndl_max(DL(m),d1,d2); t = d1; d1 = d2; d2 = t; } l = nd_nvar+31; t = (UINT *)MALLOC_ATOMIC(l*sizeof(UINT)); for ( i = nd_exporigin, ind = 0; i < nd_wpd; i++ ) { u = d1[i]; k = (nd_epw-1)*nd_bpe; for ( j = 0; j < nd_epw; j++, k -= nd_bpe, ind++ ) t[ind] = (u>>k)&nd_mask0; } for ( ; ind < l; ind++ ) t[ind] = 0; return t; } UINT *nd_compute_bound(ND p) { UINT *d1,*d2,*t; UINT u; int i,j,k,l,len,ind; NM m; if ( !p ) return 0; d1 = (UINT *)MALLOC(nd_wpd*sizeof(UINT)); d2 = (UINT *)MALLOC(nd_wpd*sizeof(UINT)); len = LEN(p); m = BDY(p); ndl_copy(DL(m),d1); m = NEXT(m); for ( m = NEXT(m); m; m = NEXT(m) ) { ndl_lcm(DL(m),d1,d2); t = d1; d1 = d2; d2 = t; } l = nd_nvar+31; t = (UINT *)MALLOC_ATOMIC(l*sizeof(UINT)); for ( i = nd_exporigin, ind = 0; i < nd_wpd; i++ ) { u = d1[i]; k = (nd_epw-1)*nd_bpe; for ( j = 0; j < nd_epw; j++, k -= nd_bpe, ind++ ) t[ind] = (u>>k)&nd_mask0; } for ( ; ind < l; ind++ ) t[ind] = 0; return t; } /* if nd_module == 1 then d[nd_exporigin-1] indicates the position */ /* of a term. In this case we need additional 1 word. */ int nd_get_exporigin(struct order_spec *ord) { switch ( ord->id ) { case 0: case 2: case 256: case 258: case 300: return 1+nd_module; case 1: case 257: /* block order */ /* poly ring d[0]:weight d[1]:w0,...,d[nd_exporigin-1]:w(n-1) */ /* module d[0]:weight d[1]:w0,...,d[nd_exporigin-2]:w(n-1) */ return ord->ord.block.length+1+nd_module; case 3: case 259: #if 0 error("nd_get_exporigin : composite order is not supported yet."); #else return 1+nd_module; #endif default: error("nd_get_exporigin : ivalid argument."); return 0; } } void nd_setup_parameters(int nvar,int max) { int i,j,n,elen,ord_o,ord_l,l,s,wpd; struct order_pair *op; nd_nvar = nvar; if ( max ) { /* XXX */ if ( do_weyl ) nd_bpe = 32; else if ( max < 2 ) nd_bpe = 1; else if ( max < 4 ) nd_bpe = 2; else if ( max < 8 ) nd_bpe = 3; else if ( max < 16 ) nd_bpe = 4; else if ( max < 32 ) nd_bpe = 5; else if ( max < 64 ) nd_bpe = 6; else if ( max < 256 ) nd_bpe = 8; else if ( max < 1024 ) nd_bpe = 10; else if ( max < 65536 ) nd_bpe = 16; else nd_bpe = 32; } if ( !do_weyl && weight_check && (current_dl_weight_vector || nd_matrix) ) { UINT t; int st; int *v; /* t = max(weights) */ t = 0; if ( current_dl_weight_vector ) for ( i = 0, t = 0; i < nd_nvar; i++ ) { if ( (st=current_dl_weight_vector[i]) < 0 ) st = -st; if ( t < st ) t = st; } if ( nd_matrix ) for ( i = 0; i < nd_matrix_len; i++ ) for ( j = 0, v = nd_matrix[i]; j < nd_nvar; j++ ) { if ( (st=v[j]) < 0 ) st = -st; if ( t < st ) t = st; } /* i = bitsize of t */ for ( i = 0; t; t >>=1, i++ ); /* i += bitsize of nd_nvar */ for ( t = nd_nvar; t; t >>=1, i++); /* nd_bpe+i = bitsize of max(weights)*max(exp)*nd_nvar */ if ( (nd_bpe+i) >= 31 ) error("nd_setup_parameters : too large weight"); } nd_epw = (sizeof(UINT)*8)/nd_bpe; elen = nd_nvar/nd_epw+(nd_nvar%nd_epw?1:0); nd_exporigin = nd_get_exporigin(nd_ord); wpd = nd_exporigin+elen; if ( nd_module ) nd_mpos = nd_exporigin-1; else nd_mpos = -1; if ( wpd != nd_wpd ) { nd_free_private_storage(); nd_wpd = wpd; } if ( nd_bpe < 32 ) { nd_mask0 = (1<= 0; i-- ) { ndv_realloc(nd_ps[i],obpe,oadv,oepos); ndv_realloc(nd_ps_sym[i],obpe,oadv,oepos); } if ( trace ) for ( i = nd_psn-1; i >= 0; i-- ) { ndv_realloc(nd_ps_trace[i],obpe,oadv,oepos); ndv_realloc(nd_ps_trace_sym[i],obpe,oadv,oepos); } s0 = 0; for ( t = d; t; t = NEXT(t) ) { NEXTND_pairs(s0,s); s->i1 = t->i1; s->i2 = t->i2; s->sig = t->sig; SG(s) = SG(t); ndl_reconstruct(LCM(t),LCM(s),obpe,oepos); } old_red = (RHist *)MALLOC(REDTAB_LEN*sizeof(RHist)); for ( i = 0; i < REDTAB_LEN; i++ ) { old_red[i] = nd_red[i]; nd_red[i] = 0; } for ( i = 0; i < REDTAB_LEN; i++ ) for ( r = old_red[i]; r; r = NEXT(r) ) { NEWRHist(mr); mr->index = r->index; SG(mr) = SG(r); ndl_reconstruct(DL(r),DL(mr),obpe,oepos); h = ndl_hash_value(DL(mr)); NEXT(mr) = nd_red[h]; nd_red[h] = mr; mr->sig = r->sig; } for ( i = 0; i < REDTAB_LEN; i++ ) old_red[i] = 0; old_red = 0; for ( i = 0; i < nd_psn; i++ ) { NEWRHist(r); SG(r) = SG(nd_psh[i]); ndl_reconstruct(DL(nd_psh[i]),DL(r),obpe,oepos); r->sig = nd_psh[i]->sig; nd_psh[i] = r; } if ( s0 ) NEXT(s) = 0; prev_nm_free_list = 0; prev_ndp_free_list = 0; #if 0 GC_gcollect(); #endif return s0; } void nd_reconstruct_s(int trace,ND_pairs *d) { int i,obpe,oadv,h; static NM prev_nm_free_list; static ND_pairs prev_ndp_free_list; RHist mr0,mr; RHist r; RHist *old_red; ND_pairs s0,s,t; EPOS oepos; obpe = nd_bpe; oadv = nmv_adv; oepos = nd_epos; if ( obpe < 2 ) nd_bpe = 2; else if ( obpe < 3 ) nd_bpe = 3; else if ( obpe < 4 ) nd_bpe = 4; else if ( obpe < 5 ) nd_bpe = 5; else if ( obpe < 6 ) nd_bpe = 6; else if ( obpe < 8 ) nd_bpe = 8; else if ( obpe < 10 ) nd_bpe = 10; else if ( obpe < 16 ) nd_bpe = 16; else if ( obpe < 32 ) nd_bpe = 32; else error("nd_reconstruct_s : exponent too large"); nd_setup_parameters(nd_nvar,0); prev_nm_free_list = _nm_free_list; prev_ndp_free_list = _ndp_free_list; _nm_free_list = 0; _ndp_free_list = 0; for ( i = nd_psn-1; i >= 0; i-- ) { ndv_realloc(nd_ps[i],obpe,oadv,oepos); ndv_realloc(nd_ps_sym[i],obpe,oadv,oepos); } if ( trace ) for ( i = nd_psn-1; i >= 0; i-- ) { ndv_realloc(nd_ps_trace[i],obpe,oadv,oepos); ndv_realloc(nd_ps_trace_sym[i],obpe,oadv,oepos); } for ( i = 0; i < nd_nbase; i++ ) { s0 = 0; for ( t = d[i]; t; t = NEXT(t) ) { NEXTND_pairs(s0,s); s->i1 = t->i1; s->i2 = t->i2; s->sig = t->sig; SG(s) = SG(t); ndl_reconstruct(LCM(t),LCM(s),obpe,oepos); } d[i] = s0; } old_red = (RHist *)MALLOC(REDTAB_LEN*sizeof(RHist)); for ( i = 0; i < REDTAB_LEN; i++ ) { old_red[i] = nd_red[i]; nd_red[i] = 0; } for ( i = 0; i < REDTAB_LEN; i++ ) for ( r = old_red[i]; r; r = NEXT(r) ) { NEWRHist(mr); mr->index = r->index; SG(mr) = SG(r); ndl_reconstruct(DL(r),DL(mr),obpe,oepos); h = ndl_hash_value(DL(mr)); NEXT(mr) = nd_red[h]; nd_red[h] = mr; mr->sig = r->sig; } for ( i = 0; i < REDTAB_LEN; i++ ) old_red[i] = 0; old_red = 0; for ( i = 0; i < nd_psn; i++ ) { NEWRHist(r); SG(r) = SG(nd_psh[i]); ndl_reconstruct(DL(nd_psh[i]),DL(r),obpe,oepos); r->sig = nd_psh[i]->sig; nd_psh[i] = r; } if ( s0 ) NEXT(s) = 0; prev_nm_free_list = 0; prev_ndp_free_list = 0; #if 0 GC_gcollect(); #endif } void ndl_reconstruct(UINT *d,UINT *r,int obpe,EPOS oepos) { int n,i,ei,oepw,omask0,j,s,ord_l,l; struct order_pair *op; n = nd_nvar; oepw = (sizeof(UINT)*8)/obpe; omask0 = (1<n; op = nd_blockmask->order_pair; for ( i = 1; i < nd_exporigin; i++ ) r[i] = d[i]; for ( j = 0, s = 0; j < l; j++ ) { ord_l = op[j].length; for ( i = 0; i < ord_l; i++, s++ ) { ei = GET_EXP_OLD(d,s); PUT_EXP(r,s,ei); } } } else { for ( i = 0; i < n; i++ ) { ei = GET_EXP_OLD(d,i); PUT_EXP(r,i,ei); } } if ( nd_module ) MPOS(r) = MPOS(d); } ND nd_copy(ND p) { NM m,mr,mr0; int c,n; ND r; if ( !p ) return 0; else { for ( mr0 = 0, m = BDY(p); m; m = NEXT(m) ) { NEXTNM(mr0,mr); CM(mr) = CM(m); ndl_copy(DL(m),DL(mr)); } NEXT(mr) = 0; MKND(NV(p),mr0,LEN(p),r); SG(r) = SG(p); return r; } } int nd_sp(int mod,int trace,ND_pairs p,ND *rp) { NM m1,m2; NDV p1,p2; ND t1,t2; UINT *lcm; P gp,tp; Z g,t; Z iq; int td; LIST hist; NODE node; DP d; if ( !mod && nd_demand ) { p1 = ndv_load(p->i1); p2 = ndv_load(p->i2); } else { if ( trace ) { p1 = nd_ps_trace[p->i1]; p2 = nd_ps_trace[p->i2]; } else { p1 = nd_ps[p->i1]; p2 = nd_ps[p->i2]; } } lcm = LCM(p); NEWNM(m1); ndl_sub(lcm,HDL(p1),DL(m1)); if ( ndl_check_bound2(p->i1,DL(m1)) ) { FREENM(m1); return 0; } NEWNM(m2); ndl_sub(lcm,HDL(p2),DL(m2)); if ( ndl_check_bound2(p->i2,DL(m2)) ) { FREENM(m1); FREENM(m2); return 0; } if ( mod == -1 ) { CM(m1) = HCM(p2); CM(m2) = _chsgnsf(HCM(p1)); } else if ( mod > 0 ) { CM(m1) = HCM(p2); CM(m2) = mod-HCM(p1); } else if ( mod == -2 ) { CZ(m1) = HCZ(p2); chsgnlf(HCZ(p1),&CZ(m2)); } else if ( nd_vc ) { ezgcdpz(nd_vc,HCP(p1),HCP(p2),&gp); divsp(nd_vc,HCP(p2),gp,&CP(m1)); divsp(nd_vc,HCP(p1),gp,&tp); chsgnp(tp,&CP(m2)); } else { igcd_cofactor(HCZ(p1),HCZ(p2),&g,&t,&CZ(m1)); chsgnz(t,&CZ(m2)); } t1 = ndv_mul_nm(mod,m1,p1); t2 = ndv_mul_nm(mod,m2,p2); *rp = nd_add(mod,t1,t2); if ( nd_gentrace ) { /* nd_tracelist is initialized */ STOZ(p->i1,iq); nmtodp(mod,m1,&d); node = mknode(4,ONE,iq,d,ONE); MKLIST(hist,node); MKNODE(nd_tracelist,hist,0); STOZ(p->i2,iq); nmtodp(mod,m2,&d); node = mknode(4,ONE,iq,d,ONE); MKLIST(hist,node); MKNODE(node,hist,nd_tracelist); nd_tracelist = node; } if ( *rp ) (*rp)->sig = p->sig; FREENM(m1); FREENM(m2); return 1; } void ndv_mul_c(int mod,NDV p,int mul) { NMV m; int c,c1,len,i; if ( !p ) return; len = LEN(p); if ( mod == -1 ) for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) CM(m) = _mulsf(CM(m),mul); else for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) { c1 = CM(m); DMAR(c1,mul,0,mod,c); CM(m) = c; } } void ndv_mul_c_lf(NDV p,Z mul) { NMV m; Z c; int len,i; if ( !p ) return; len = LEN(p); for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) { mullf(CZ(m),mul,&c); CZ(m) = c; } } /* for nd_det */ void ndv_mul_c_q(NDV p,Z mul) { NMV m; Z c; int len,i; if ( !p ) return; len = LEN(p); for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) { mulz(CZ(m),mul,&c); CZ(m) = c; } } ND weyl_ndv_mul_nm(int mod,NM m0,NDV p) { int n2,i,j,l,n,tlen; UINT *d0; NM *tab,*psum; ND s,r; NM t; NMV m1; if ( !p ) return 0; n = NV(p); n2 = n>>1; d0 = DL(m0); l = LEN(p); for ( i = 0, tlen = 1; i < n2; i++ ) tlen *= (GET_EXP(d0,n2+i)+1); tab = (NM *)MALLOC(tlen*sizeof(NM)); psum = (NM *)MALLOC(tlen*sizeof(NM)); for ( i = 0; i < tlen; i++ ) psum[i] = 0; m1 = (NMV)(((char *)BDY(p))+nmv_adv*(l-1)); for ( i = l-1; i >= 0; i--, NMV_PREV(m1) ) { /* m0(NM) * m1(NMV) => tab(NM) */ weyl_mul_nm_nmv(n,mod,m0,m1,tab,tlen); for ( j = 0; j < tlen; j++ ) { if ( tab[j] ) { NEXT(tab[j]) = psum[j]; psum[j] = tab[j]; } } } for ( i = tlen-1, r = 0; i >= 0; i-- ) if ( psum[i] ) { for ( j = 0, t = psum[i]; t; t = NEXT(t), j++ ); MKND(n,psum[i],j,s); r = nd_add(mod,r,s); } if ( r ) SG(r) = SG(p)+TD(d0); return r; } /* product of monomials */ /* XXX block order is not handled correctly */ void weyl_mul_nm_nmv(int n,int mod,NM m0,NMV m1,NM *tab,int tlen) { int i,n2,j,s,curlen,homo,h,a,b,k,l,u,min; UINT *d0,*d1,*d,*dt,*ctab; Z *ctab_q; Z q,q1; UINT c0,c1,c; NM *p; NM m,t; int mpos; for ( i = 0; i < tlen; i++ ) tab[i] = 0; if ( !m0 || !m1 ) return; d0 = DL(m0); d1 = DL(m1); n2 = n>>1; if ( nd_module ) if ( MPOS(d0) ) error("weyl_mul_nm_nmv : invalid operation"); NEWNM(m); d = DL(m); if ( mod ) { c0 = CM(m0); c1 = CM(m1); DMAR(c0,c1,0,mod,c); CM(m) = c; } else if ( nd_vc ) mulp(nd_vc,CP(m0),CP(m1),&CP(m)); else mulz(CZ(m0),CZ(m1),&CZ(m)); for ( i = 0; i < nd_wpd; i++ ) d[i] = 0; homo = n&1 ? 1 : 0; if ( homo ) { /* offset of h-degree */ h = GET_EXP(d0,n-1)+GET_EXP(d1,n-1); PUT_EXP(DL(m),n-1,h); TD(DL(m)) = h; if ( nd_blockmask ) ndl_weight_mask(DL(m)); } tab[0] = m; NEWNM(m); d = DL(m); for ( i = 0, curlen = 1; i < n2; i++ ) { a = GET_EXP(d0,i); b = GET_EXP(d1,n2+i); k = GET_EXP(d0,n2+i); l = GET_EXP(d1,i); /* 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; j < curlen; j++ ) if ( (t = tab[j]) != 0 ) { dt = DL(t); PUT_EXP(dt,i,a); PUT_EXP(dt,n2+i,b); TD(dt) += s; if ( nd_blockmask ) ndl_weight_mask(dt); } curlen *= k+1; continue; } min = MIN(k,l); if ( mod ) { ctab = (UINT *)MALLOC((min+1)*sizeof(UINT)); mkwcm(k,l,mod,(int *)ctab); } else { ctab_q = (Z *)MALLOC((min+1)*sizeof(Z)); mkwc(k,l,ctab_q); } for ( j = min; j >= 0; j-- ) { for ( u = 0; u < nd_wpd; u++ ) d[u] = 0; PUT_EXP(d,i,a-j); PUT_EXP(d,n2+i,b-j); h = MUL_WEIGHT(a-j,i)+MUL_WEIGHT(b-j,n2+i); if ( homo ) { TD(d) = s; PUT_EXP(d,n-1,s-h); } else TD(d) = h; if ( nd_blockmask ) ndl_weight_mask(d); if ( mod ) c = ctab[j]; else q = ctab_q[j]; p = tab+curlen*j; if ( j == 0 ) { for ( u = 0; u < curlen; u++, p++ ) { if ( tab[u] ) { ndl_addto(DL(tab[u]),d); if ( mod ) { c0 = CM(tab[u]); DMAR(c0,c,0,mod,c1); CM(tab[u]) = c1; } else if ( nd_vc ) mulp(nd_vc,CP(tab[u]),(P)q,&CP(tab[u])); else { mulz(CZ(tab[u]),q,&q1); CZ(tab[u]) = q1; } } } } else { for ( u = 0; u < curlen; u++, p++ ) { if ( tab[u] ) { NEWNM(t); ndl_add(DL(tab[u]),d,DL(t)); if ( mod ) { c0 = CM(tab[u]); DMAR(c0,c,0,mod,c1); CM(t) = c1; } else if ( nd_vc ) mulp(nd_vc,CP(tab[u]),(P)q,&CP(t)); else mulz(CZ(tab[u]),q,&CZ(t)); *p = t; } } } } curlen *= k+1; } FREENM(m); if ( nd_module ) { mpos = MPOS(d1); for ( i = 0; i < tlen; i++ ) if ( tab[i] ) { d = DL(tab[i]); MPOS(d) = mpos; TD(d) = ndl_weight(d); } } } ND ndv_mul_nm_symbolic(NM m0,NDV p) { NM mr,mr0; NMV m; UINT *d,*dt,*dm; int c,n,td,i,c1,c2,len; Q q; ND r; if ( !p ) return 0; else { n = NV(p); m = BDY(p); d = DL(m0); len = LEN(p); mr0 = 0; td = TD(d); c = CM(m0); for ( i = 0; i < len; i++, NMV_ADV(m) ) { NEXTNM(mr0,mr); CM(mr) = 1; ndl_add(DL(m),d,DL(mr)); } NEXT(mr) = 0; MKND(NV(p),mr0,len,r); SG(r) = SG(p) + TD(d); return r; } } ND ndv_mul_nm(int mod,NM m0,NDV p) { NM mr,mr0; NMV m; UINT *d,*dt,*dm; int c,n,td,i,c1,c2,len; P q; ND r; if ( !p ) return 0; else if ( do_weyl ) { if ( mod < 0 ) { error("ndv_mul_nm : not implemented (weyl)"); return 0; } else return weyl_ndv_mul_nm(mod,m0,p); } else { n = NV(p); m = BDY(p); d = DL(m0); len = LEN(p); mr0 = 0; td = TD(d); if ( mod == -1 ) { c = CM(m0); for ( i = 0; i < len; i++, NMV_ADV(m) ) { NEXTNM(mr0,mr); CM(mr) = _mulsf(CM(m),c); ndl_add(DL(m),d,DL(mr)); } } else if ( mod == -2 ) { Z cl; cl = CZ(m0); for ( i = 0; i < len; i++, NMV_ADV(m) ) { NEXTNM(mr0,mr); mullf(CZ(m),cl,&CZ(mr)); ndl_add(DL(m),d,DL(mr)); } } else if ( mod ) { c = CM(m0); for ( i = 0; i < len; i++, NMV_ADV(m) ) { NEXTNM(mr0,mr); c1 = CM(m); DMAR(c1,c,0,mod,c2); CM(mr) = c2; ndl_add(DL(m),d,DL(mr)); } } else { q = CP(m0); for ( i = 0; i < len; i++, NMV_ADV(m) ) { NEXTNM(mr0,mr); mulp(nd_vc,CP(m),q,&CP(mr)); ndl_add(DL(m),d,DL(mr)); } } NEXT(mr) = 0; MKND(NV(p),mr0,len,r); SG(r) = SG(p) + TD(d); return r; } } ND nd_quo(int mod,PGeoBucket bucket,NDV d) { NM mq0,mq; NMV tm; Q q; int i,nv,sg,c,c1,c2,hindex; ND p,t,r; if ( bucket->m < 0 ) return 0; else { nv = NV(d); mq0 = 0; tm = (NMV)MALLOC(nmv_adv); while ( 1 ) { if ( mod > 0 || mod == -1 ) hindex = head_pbucket(mod,bucket); else if ( mod == -2 ) hindex = head_pbucket_lf(bucket); else hindex = head_pbucket_q(bucket); if ( hindex < 0 ) break; p = bucket->body[hindex]; NEXTNM(mq0,mq); ndl_sub(HDL(p),HDL(d),DL(mq)); ndl_copy(DL(mq),DL(tm)); if ( mod ) { c1 = invm(HCM(d),mod); c2 = HCM(p); DMAR(c1,c2,0,mod,c); CM(mq) = c; CM(tm) = mod-c; } else { divsz(HCZ(p),HCZ(d),&CZ(mq)); chsgnz(CZ(mq),&CZ(tm)); } t = ndv_mul_nmv_trunc(mod,tm,d,HDL(d)); bucket->body[hindex] = nd_remove_head(p); t = nd_remove_head(t); add_pbucket(mod,bucket,t); } if ( !mq0 ) r = 0; else { NEXT(mq) = 0; for ( i = 0, mq = mq0; mq; mq = NEXT(mq), i++ ); MKND(nv,mq0,i,r); /* XXX */ SG(r) = HTD(r); } return r; } } void ndv_realloc(NDV p,int obpe,int oadv,EPOS oepos) { NMV m,mr,mr0,t; int len,i,k; if ( !p ) return; m = BDY(p); len = LEN(p); mr0 = nmv_adv>oadv?(NMV)REALLOC(BDY(p),len*nmv_adv):BDY(p); m = (NMV)((char *)mr0+(len-1)*oadv); mr = (NMV)((char *)mr0+(len-1)*nmv_adv); t = (NMV)MALLOC(nmv_adv); for ( i = 0; i < len; i++, NMV_OPREV(m), NMV_PREV(mr) ) { CZ(t) = CZ(m); for ( k = 0; k < nd_wpd; k++ ) DL(t)[k] = 0; ndl_reconstruct(DL(m),DL(t),obpe,oepos); CZ(mr) = CZ(t); ndl_copy(DL(t),DL(mr)); } BDY(p) = mr0; } NDV ndv_dup_realloc(NDV p,int obpe,int oadv,EPOS oepos) { NMV m,mr,mr0; int len,i; NDV r; if ( !p ) return 0; m = BDY(p); len = LEN(p); mr0 = mr = (NMV)MALLOC(len*nmv_adv); for ( i = 0; i < len; i++, NMV_OADV(m), NMV_ADV(mr) ) { ndl_zero(DL(mr)); ndl_reconstruct(DL(m),DL(mr),obpe,oepos); CZ(mr) = CZ(m); } MKNDV(NV(p),mr0,len,r); SG(r) = SG(p); r->sig = p->sig; return r; } /* duplicate p */ NDV ndv_dup(int mod,NDV p) { NDV d; NMV t,m,m0; int i,len; if ( !p ) return 0; len = LEN(p); m0 = m = (NMV)((mod>0 || mod==-1)?MALLOC_ATOMIC(len*nmv_adv):MALLOC(len*nmv_adv)); for ( t = BDY(p), i = 0; i < len; i++, NMV_ADV(t), NMV_ADV(m) ) { ndl_copy(DL(t),DL(m)); CZ(m) = CZ(t); } MKNDV(NV(p),m0,len,d); SG(d) = SG(p); return d; } NDV ndv_symbolic(int mod,NDV p) { NDV d; NMV t,m,m0; int i,len; if ( !p ) return 0; len = LEN(p); m0 = m = (NMV)((mod>0||mod==-1)?MALLOC_ATOMIC(len*nmv_adv):MALLOC(len*nmv_adv)); for ( t = BDY(p), i = 0; i < len; i++, NMV_ADV(t), NMV_ADV(m) ) { ndl_copy(DL(t),DL(m)); CZ(m) = ONE; } MKNDV(NV(p),m0,len,d); SG(d) = SG(p); return d; } ND nd_dup(ND p) { ND d; NM t,m,m0; if ( !p ) return 0; for ( m0 = 0, t = BDY(p); t; t = NEXT(t) ) { NEXTNM(m0,m); ndl_copy(DL(t),DL(m)); CZ(m) = CZ(t); } if ( m0 ) NEXT(m) = 0; MKND(NV(p),m0,LEN(p),d); SG(d) = SG(p); return d; } /* XXX if p->len == 0 then it represents 0 */ void ndv_mod(int mod,NDV p) { NMV t,d; int r,s,u; int i,len,dlen; P cp; Z c; Obj gfs; if ( !p ) return; len = LEN(p); dlen = 0; if ( mod == -1 ) for ( t = d = BDY(p), i = 0; i < len; i++, NMV_ADV(t) ) { simp_ff((Obj)CP(t),&gfs); if ( gfs ) { r = FTOIF(CONT((GFS)gfs)); CM(d) = r; ndl_copy(DL(t),DL(d)); NMV_ADV(d); dlen++; } } else if ( mod == -2 ) for ( t = d = BDY(p), i = 0; i < len; i++, NMV_ADV(t) ) { simp_ff((Obj)CP(t),&gfs); if ( gfs ) { lmtolf((LM)gfs,&CZ(d)); ndl_copy(DL(t),DL(d)); NMV_ADV(d); dlen++; } } else for ( t = d = BDY(p), i = 0; i < len; i++, NMV_ADV(t) ) { if ( nd_vc ) { nd_subst_vector(nd_vc,CP(t),nd_subst,&cp); c = (Z)cp; } else c = CZ(t); r = remqi((Q)c,mod); if ( r ) { CM(d) = r; ndl_copy(DL(t),DL(d)); NMV_ADV(d); dlen++; } } LEN(p) = dlen; } NDV ptondv(VL vl,VL dvl,P p) { ND nd; nd = ptond(vl,dvl,p); return ndtondv(0,nd); } void pltozpl(LIST l,Q *cont,LIST *pp) { NODE nd,nd1; int n; P *pl; Q *cl; int i; P dmy; Z dvr,inv; LIST r; nd = BDY(l); n = length(nd); pl = (P *)MALLOC(n*sizeof(P)); cl = (Q *)MALLOC(n*sizeof(Q)); for ( i = 0; i < n; i++, nd = NEXT(nd) ) { ptozp((P)BDY(nd),1,&cl[i],&dmy); } qltozl(cl,n,&dvr); divz(ONE,dvr,&inv); nd = BDY(l); for ( i = 0; i < n; i++, nd = NEXT(nd) ) divsp(CO,(P)BDY(nd),(P)dvr,&pl[i]); nd = 0; for ( i = n-1; i >= 0; i-- ) { MKNODE(nd1,pl[i],nd); nd = nd1; } MKLIST(r,nd); *pp = r; } /* (a1,a2,...,an) -> a1*e(1)+...+an*e(n) */ NDV pltondv(VL vl,VL dvl,LIST p) { int i; NODE t; ND r,ri; NM m; if ( !nd_module ) error("pltond : module order must be set"); r = 0; for ( i = 1, t = BDY(p); t; t = NEXT(t), i++ ) { ri = ptond(vl,dvl,(P)BDY(t)); if ( ri ) for ( m = BDY(ri); m; m = NEXT(m) ) { MPOS(DL(m)) = i; TD(DL(m)) = ndl_weight(DL(m)); if ( nd_blockmask ) ndl_weight_mask(DL(m)); } r = nd_add(0,r,ri); } return ndtondv(0,r); } ND ptond(VL vl,VL dvl,P p) { int n,i,j,k,e; VL tvl; V v; DCP dc; DCP *w; ND r,s,t,u; P x; int c; UINT *d; NM m,m0; if ( !p ) return 0; else if ( NUM(p) ) { NEWNM(m); ndl_zero(DL(m)); if ( !INT((Q)p) ) error("ptond : input must be integer-coefficient"); CZ(m) = (Z)p; NEXT(m) = 0; MKND(nd_nvar,m,1,r); SG(r) = 0; return r; } else { for ( dc = DC(p), k = 0; dc; dc = NEXT(dc), k++ ); w = (DCP *)MALLOC(k*sizeof(DCP)); for ( dc = DC(p), j = 0; j < k; dc = NEXT(dc), j++ ) w[j] = dc; for ( i = 0, tvl = dvl, v = VR(p); tvl && tvl->v != v; tvl = NEXT(tvl), i++ ); if ( !tvl ) { for ( j = k-1, s = 0, MKV(v,x); j >= 0; j-- ) { t = ptond(vl,dvl,COEF(w[j])); pwrp(vl,x,DEG(w[j]),&p); nd_mul_c_p(CO,t,p); s = nd_add(0,s,t); } return s; } else { NEWNM(m0); d = DL(m0); for ( j = k-1, s = 0; j >= 0; j-- ) { ndl_zero(d); e = ZTOS(DEG(w[j])); PUT_EXP(d,i,e); TD(d) = MUL_WEIGHT(e,i); if ( nd_blockmask) ndl_weight_mask(d); if ( nd_module ) MPOS(d) = 0; t = ptond(vl,dvl,COEF(w[j])); for ( m = BDY(t); m; m = NEXT(m) ) ndl_addto(DL(m),d); SG(t) += TD(d); s = nd_add(0,s,t); } FREENM(m0); return s; } } } P ndvtop(int mod,VL vl,VL dvl,NDV p) { VL tvl; int len,n,j,i,e; NMV m; Z q; P c; UINT *d; P s,r,u,t,w; GFS gfs; if ( !p ) return 0; else { len = LEN(p); n = NV(p); m = (NMV)(((char *)BDY(p))+nmv_adv*(len-1)); for ( j = len-1, s = 0; j >= 0; j--, NMV_PREV(m) ) { if ( mod == -1 ) { e = IFTOF(CM(m)); MKGFS(e,gfs); c = (P)gfs; } else if ( mod == -2 ) { c = (P)CZ(m); } else if ( mod > 0 ) { STOZ(CM(m),q); c = (P)q; } else c = CP(m); d = DL(m); for ( i = 0, t = c, tvl = dvl; i < n; tvl = NEXT(tvl), i++ ) { MKV(tvl->v,r); e = GET_EXP(d,i); STOZ(e,q); pwrp(vl,r,q,&u); mulp(vl,t,u,&w); t = w; } addp(vl,s,t,&u); s = u; } return s; } } LIST ndvtopl(int mod,VL vl,VL dvl,NDV p,int rank) { VL tvl; int len,n,j,i,e; NMV m; Z q; P c; UINT *d; P s,r,u,t,w; GFS gfs; P *a; LIST l; NODE nd,nd1; if ( !p ) return 0; else { a = (P *)MALLOC((rank+1)*sizeof(P)); for ( i = 0; i <= rank; i++ ) a[i] = 0; len = LEN(p); n = NV(p); m = (NMV)(((char *)BDY(p))+nmv_adv*(len-1)); for ( j = len-1; j >= 0; j--, NMV_PREV(m) ) { if ( mod == -1 ) { e = IFTOF(CM(m)); MKGFS(e,gfs); c = (P)gfs; } else if ( mod ) { STOZ(CM(m),q); c = (P)q; } else c = CP(m); d = DL(m); for ( i = 0, t = c, tvl = dvl; i < n; tvl = NEXT(tvl), i++ ) { MKV(tvl->v,r); e = GET_EXP(d,i); STOZ(e,q); pwrp(vl,r,q,&u); mulp(vl,t,u,&w); t = w; } addp(vl,a[MPOS(d)],t,&u); a[MPOS(d)] = u; } nd = 0; for ( i = rank; i > 0; i-- ) { MKNODE(nd1,a[i],nd); nd = nd1; } MKLIST(l,nd); return l; } } NDV ndtondv(int mod,ND p) { NDV d; NMV m,m0; NM t; int i,len; if ( !p ) return 0; len = LEN(p); if ( mod > 0 || mod == -1 ) m0 = m = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(len*nmv_adv); else m0 = m = MALLOC(len*nmv_adv); #if 0 ndv_alloc += nmv_adv*len; #endif for ( t = BDY(p), i = 0; t; t = NEXT(t), i++, NMV_ADV(m) ) { ndl_copy(DL(t),DL(m)); CZ(m) = CZ(t); } MKNDV(NV(p),m0,len,d); SG(d) = SG(p); d->sig = p->sig; return d; } static int dmm_comp_nv; int dmm_comp(DMM *a,DMM *b) { return -compdmm(dmm_comp_nv,*a,*b); } void dmm_sort_by_ord(DMM *a,int len,int nv) { dmm_comp_nv = nv; qsort(a,len,sizeof(DMM),(int (*)(const void *,const void *))dmm_comp); } void dpm_sort(DPM p,DPM *rp) { DMM t,t1; int len,i,n; DMM *a; DPM d; if ( !p ) *rp = 0; for ( t = BDY(p), len = 0; t; t = NEXT(t), len++ ); a = (DMM *)MALLOC(len*sizeof(DMM)); for ( i = 0, t = BDY(p); i < len; i++, t = NEXT(t) ) a[i] = t; n = p->nv; dmm_sort_by_ord(a,len,n); t = 0; for ( i = len-1; i >= 0; i-- ) { NEWDMM(t1); t1->c = a[i]->c; t1->dl = a[i]->dl; t1->pos = a[i]->pos; t1->next = t; t = t1; } MKDPM(n,t,d); SG(d) = SG(p); *rp = d; } int dpm_comp(DPM *a,DPM *b) { return -compdpm(CO,*a,*b); } NODE dpm_sort_list(NODE l) { int i,len; NODE t,t1; DPM *a; len = length(l); a = (DPM *)MALLOC(len*sizeof(DPM)); for ( t = l, i = 0; i < len; i++, t = NEXT(t) ) a[i] = (DPM)BDY(t); qsort(a,len,sizeof(DPM),(int (*)(const void *,const void *))dpm_comp); t = 0; for ( i = len-1; i >= 0; i-- ) { MKNODE(t1,(pointer)a[i],t); t = t1; } return t; } int nmv_comp(NMV a,NMV b) { int t; t = DL_COMPARE(a->dl,b->dl); return -t; } NDV dpmtondv(int mod,DPM p) { NDV d; NMV m,m0; DMM t; DMM *a; int i,len,n; if ( !p ) return 0; for ( t = BDY(p), len = 0; t; t = NEXT(t), len++ ); a = (DMM *)MALLOC(len*sizeof(DMM)); for ( i = 0, t = BDY(p); i < len; i++, t = NEXT(t) ) a[i] = t; n = p->nv; dmm_sort_by_ord(a,len,n); if ( mod > 0 || mod == -1 ) m0 = m = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(len*nmv_adv); else m0 = m = MALLOC(len*nmv_adv); #if 0 ndv_alloc += nmv_adv*len; #endif for ( i = 0; i < len; i++, NMV_ADV(m) ) { dltondl(n,a[i]->dl,DL(m)); MPOS(DL(m)) = a[i]->pos; TD(DL(m)) = ndl_weight(DL(m)); CZ(m) = (Z)a[i]->c; } qsort(m0,len,nmv_adv,(int (*)(const void *,const void *))nmv_comp); MKNDV(NV(p),m0,len,d); SG(d) = SG(p); return d; } ND ndvtond(int mod,NDV p) { ND d; NM m,m0; NMV t; int i,len; if ( !p ) return 0; m0 = 0; len = p->len; for ( t = BDY(p), i = 0; i < len; NMV_ADV(t), i++ ) { NEXTNM(m0,m); ndl_copy(DL(t),DL(m)); CZ(m) = CZ(t); } NEXT(m) = 0; MKND(NV(p),m0,len,d); SG(d) = SG(p); d->sig = p->sig; return d; } DP ndvtodp(int mod,NDV p) { MP m,m0; DP d; NMV t; int i,len; if ( !p ) return 0; m0 = 0; len = p->len; for ( t = BDY(p), i = 0; i < len; NMV_ADV(t), i++ ) { NEXTMP(m0,m); m->dl = ndltodl(nd_nvar,DL(t)); m->c = (Obj)ndctop(mod,t->c); } NEXT(m) = 0; MKDP(nd_nvar,m0,d); SG(d) = SG(p); return d; } DPM ndvtodpm(int mod,NDV p) { DMM m,m0; DPM d; NMV t; int i,len; if ( !p ) return 0; m0 = 0; len = p->len; for ( t = BDY(p), i = 0; i < len; NMV_ADV(t), i++ ) { NEXTDMM(m0,m); m->dl = ndltodl(nd_nvar,DL(t)); m->c = (Obj)ndctop(mod,t->c); m->pos = MPOS(DL(t)); } NEXT(m) = 0; MKDPM(nd_nvar,m0,d); SG(d) = SG(p); return d; } DP ndtodp(int mod,ND p) { MP m,m0; DP d; NM t; int i,len; if ( !p ) return 0; m0 = 0; len = p->len; for ( t = BDY(p); t; t = NEXT(t) ) { NEXTMP(m0,m); m->dl = ndltodl(nd_nvar,DL(t)); m->c = (Obj)ndctop(mod,t->c); } NEXT(m) = 0; MKDP(nd_nvar,m0,d); SG(d) = SG(p); return d; } void ndv_print(NDV p) { NMV m; int i,len; if ( !p ) printf("0\n"); else { len = LEN(p); for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) { if ( CM(m) & 0x80000000 ) printf("+@_%d*",IFTOF(CM(m))); else printf("+%ld*",CM(m)); ndl_print(DL(m)); } printf("\n"); } } void ndv_print_q(NDV p) { NMV m; int i,len; if ( !p ) printf("0\n"); else { len = LEN(p); for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) { printf("+"); printexpr(CO,(Obj)CZ(m)); printf("*"); ndl_print(DL(m)); } printf("\n"); } } NODE ndv_reducebase(NODE x,int *perm) { int len,i,j; NDVI w; NODE t,t0; len = length(x); w = (NDVI)MALLOC(len*sizeof(struct oNDVI)); for ( i = 0, t = x; i < len; i++, t = NEXT(t) ) { w[i].p = BDY(t); w[i].i = perm[i]; } for ( i = 0; i < len; i++ ) { for ( j = 0; j < i; j++ ) { if ( w[i].p && w[j].p ) { if ( ndl_reducible(HDL(w[i].p),HDL(w[j].p)) ) w[i].p = 0; else if ( ndl_reducible(HDL(w[j].p),HDL(w[i].p)) ) w[j].p = 0; } } } for ( i = j = 0, t0 = 0; i < len; i++ ) { if ( w[i].p ) { NEXTNODE(t0,t); BDY(t) = (pointer)w[i].p; perm[j++] = w[i].i; } } NEXT(t) = 0; x = t0; return x; } /* XXX incomplete */ extern DMMstack dmm_stack; int ndl_module_schreyer_compare(UINT *a,UINT *b); void nd_init_ord(struct order_spec *ord) { nd_module = (ord->id >= 256); if ( nd_module ) { nd_dcomp = -1; nd_module_ordtype = ord->module_ordtype; nd_pot_nelim = ord->pot_nelim; nd_poly_weight_len = ord->nv; nd_poly_weight = ord->top_weight; nd_module_rank = ord->module_rank; nd_module_weight = ord->module_top_weight; } nd_matrix = 0; nd_matrix_len = 0; switch ( ord->id ) { case 0: switch ( ord->ord.simple ) { case 0: nd_dcomp = 1; nd_isrlex = 1; break; case 1: nd_dcomp = 1; nd_isrlex = 0; break; case 2: nd_dcomp = 0; nd_isrlex = 0; ndl_compare_function = ndl_lex_compare; break; case 11: /* XXX */ nd_dcomp = 0; nd_isrlex = 1; ndl_compare_function = ndl_ww_lex_compare; break; default: error("nd_gr : unsupported order"); } break; case 1: /* block order */ /* XXX */ nd_dcomp = -1; nd_isrlex = 0; ndl_compare_function = ndl_block_compare; break; case 2: /* matrix order */ /* XXX */ nd_dcomp = -1; nd_isrlex = 0; nd_matrix_len = ord->ord.matrix.row; nd_matrix = ord->ord.matrix.matrix; ndl_compare_function = ndl_matrix_compare; break; case 3: /* composite order */ nd_dcomp = -1; nd_isrlex = 0; nd_worb_len = ord->ord.composite.length; nd_worb = ord->ord.composite.w_or_b; ndl_compare_function = ndl_composite_compare; break; /* module order */ case 256: switch ( ord->ord.simple ) { case 0: nd_dcomp = 0; nd_isrlex = 1; ndl_compare_function = ndl_module_glex_compare; break; case 1: nd_dcomp = 0; nd_isrlex = 0; ndl_compare_function = ndl_module_glex_compare; break; case 2: nd_dcomp = 0; nd_isrlex = 0; ndl_compare_function = ndl_module_compare; ndl_base_compare_function = ndl_lex_compare; break; default: error("nd_init_ord : unsupported order"); } break; case 257: /* block order */ nd_isrlex = 0; ndl_compare_function = ndl_module_compare; ndl_base_compare_function = ndl_block_compare; break; case 258: /* matrix order */ nd_isrlex = 0; nd_matrix_len = ord->ord.matrix.row; nd_matrix = ord->ord.matrix.matrix; ndl_compare_function = ndl_module_compare; ndl_base_compare_function = ndl_matrix_compare; break; case 259: /* composite order */ nd_isrlex = 0; nd_worb_len = ord->ord.composite.length; nd_worb = ord->ord.composite.w_or_b; ndl_compare_function = ndl_module_compare; ndl_base_compare_function = ndl_composite_compare; break; case 300: /* schreyer order */ if ( ord->base->id != 256 ) error("nd_init_ord : unsupported base order"); ndl_compare_function = ndl_module_schreyer_compare; dmm_stack = ord->dmmstack; switch ( ord->base->ord.simple ) { case 0: nd_isrlex = 1; ndl_base_compare_function = ndl_glex_compare; dl_base_compare_function = cmpdl_revgradlex; break; case 1: nd_isrlex = 0; ndl_base_compare_function = ndl_glex_compare; dl_base_compare_function = cmpdl_gradlex; break; case 2: nd_isrlex = 0; ndl_base_compare_function = ndl_lex_compare; dl_base_compare_function = cmpdl_lex; break; default: error("nd_init_ord : unsupported order"); } break; } nd_ord = ord; } BlockMask nd_create_blockmask(struct order_spec *ord) { int n,i,j,s,l; UINT *t; BlockMask bm; /* we only create mask table for block order */ if ( ord->id != 1 && ord->id != 257 ) return 0; n = ord->ord.block.length; bm = (BlockMask)MALLOC(sizeof(struct oBlockMask)); bm->n = n; bm->order_pair = ord->ord.block.order_pair; bm->mask = (UINT **)MALLOC(n*sizeof(UINT *)); for ( i = 0, s = 0; i < n; i++ ) { bm->mask[i] = t = (UINT *)MALLOC_ATOMIC(nd_wpd*sizeof(UINT)); for ( j = 0; j < nd_wpd; j++ ) t[j] = 0; l = bm->order_pair[i].length; for ( j = 0; j < l; j++, s++ ) PUT_EXP(t,s,nd_mask0); } return bm; } EPOS nd_create_epos(struct order_spec *ord) { int i,j,l,s,ord_l,ord_o; EPOS epos; struct order_pair *op; epos = (EPOS)MALLOC_ATOMIC(nd_nvar*sizeof(struct oEPOS)); switch ( ord->id ) { case 0: case 256: case 300: if ( nd_isrlex ) { for ( i = 0; i < nd_nvar; i++ ) { epos[i].i = nd_exporigin + (nd_nvar-1-i)/nd_epw; epos[i].s = (nd_epw-((nd_nvar-1-i)%nd_epw)-1)*nd_bpe; } } else { for ( i = 0; i < nd_nvar; i++ ) { epos[i].i = nd_exporigin + i/nd_epw; epos[i].s = (nd_epw-(i%nd_epw)-1)*nd_bpe; } } break; case 1: case 257: /* block order */ l = ord->ord.block.length; op = ord->ord.block.order_pair; for ( j = 0, s = 0; j < l; j++ ) { ord_o = op[j].order; ord_l = op[j].length; if ( !ord_o ) for ( i = 0; i < ord_l; i++ ) { epos[s+i].i = nd_exporigin + (s+ord_l-i-1)/nd_epw; epos[s+i].s = (nd_epw-((s+ord_l-i-1)%nd_epw)-1)*nd_bpe; } else for ( i = 0; i < ord_l; i++ ) { epos[s+i].i = nd_exporigin + (s+i)/nd_epw; epos[s+i].s = (nd_epw-((s+i)%nd_epw)-1)*nd_bpe; } s += ord_l; } break; case 2: /* matrix order */ case 3: /* composite order */ default: for ( i = 0; i < nd_nvar; i++ ) { epos[i].i = nd_exporigin + i/nd_epw; epos[i].s = (nd_epw-(i%nd_epw)-1)*nd_bpe; } break; } return epos; } /* external interface */ void nd_nf_p(Obj f,LIST g,LIST v,int m,struct order_spec *ord,Obj *rp) { NODE t,in0,in; ND ndf,nf; NDV ndvf; VL vv,tv; int stat,nvar,max,mrank; union oNDC dn; Q cont; P pp; LIST ppl; if ( !f ) { *rp = 0; return; } pltovl(v,&vv); for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ ); /* max=65536 implies nd_bpe=32 */ max = 65536; nd_module = 0; /* nd_module will be set if ord is a module ordering */ nd_init_ord(ord); nd_setup_parameters(nvar,max); if ( nd_module && OID(f) != O_LIST ) error("nd_nf_p : the first argument must be a list"); if ( nd_module ) mrank = length(BDY((LIST)f)); /* conversion to ndv */ for ( in0 = 0, t = BDY(g); t; t = NEXT(t) ) { NEXTNODE(in0,in); if ( nd_module ) { if ( !BDY(t) || OID(BDY(t)) != O_LIST || length(BDY((LIST)BDY(t))) != mrank ) error("nd_nf_p : inconsistent basis element"); if ( !m ) pltozpl((LIST)BDY(t),&cont,&ppl); else ppl = (LIST)BDY(t); BDY(in) = (pointer)pltondv(CO,vv,ppl); } else { if ( !m ) ptozp((P)BDY(t),1,&cont,&pp); else pp = (P)BDY(t); BDY(in) = (pointer)ptondv(CO,vv,pp); } if ( m ) ndv_mod(m,(NDV)BDY(in)); } if ( in0 ) NEXT(in) = 0; if ( nd_module ) ndvf = pltondv(CO,vv,(LIST)f); else ndvf = ptondv(CO,vv,(P)f); if ( m ) ndv_mod(m,ndvf); ndf = (pointer)ndvtond(m,ndvf); /* dont sort, dont removecont */ ndv_setup(m,0,in0,1,1,0); nd_scale=2; stat = nd_nf(m,0,ndf,nd_ps,1,&nf); if ( !stat ) error("nd_nf_p : exponent too large"); if ( nd_module ) *rp = (Obj)ndvtopl(m,CO,vv,ndtondv(m,nf),mrank); else *rp = (Obj)ndvtop(m,CO,vv,ndtondv(m,nf)); } int nd_to_vect(int mod,UINT *s0,int n,ND d,UINT *r) { NM m; UINT *t,*s; int i; for ( i = 0; i < n; i++ ) r[i] = 0; for ( i = 0, s = s0, m = BDY(d); m; m = NEXT(m) ) { t = DL(m); for ( ; !ndl_equal(t,s); s += nd_wpd, i++ ); r[i] = CM(m); } for ( i = 0; !r[i]; i++ ); return i; } int nd_to_vect_q(UINT *s0,int n,ND d,Z *r) { NM m; UINT *t,*s; int i; for ( i = 0; i < n; i++ ) r[i] = 0; for ( i = 0, s = s0, m = BDY(d); m; m = NEXT(m) ) { t = DL(m); for ( ; !ndl_equal(t,s); s += nd_wpd, i++ ); r[i] = CZ(m); } for ( i = 0; !r[i]; i++ ); return i; } int nd_to_vect_lf(UINT *s0,int n,ND d,mpz_t *r) { NM m; UINT *t,*s; int i; for ( i = 0; i < n; i++ ) { mpz_init(r[i]); mpz_set_ui(r[i],0); } for ( i = 0, s = s0, m = BDY(d); m; m = NEXT(m) ) { t = DL(m); for ( ; !ndl_equal(t,s); s += nd_wpd, i++ ); mpz_set(r[i],BDY(CZ(m))); } for ( i = 0; !mpz_sgn(r[i]); i++ ); return i; } unsigned long *nd_to_vect_2(UINT *s0,int n,int *s0hash,ND p) { NM m; unsigned long *v; int i,j,h,size; UINT *s,*t; size = sizeof(unsigned long)*(n+BLEN-1)/BLEN; v = (unsigned long *)MALLOC_ATOMIC_IGNORE_OFF_PAGE(size); bzero(v,size); for ( i = j = 0, s = s0, m = BDY(p); m; j++, m = NEXT(m) ) { t = DL(m); h = ndl_hash_value(t); for ( ; h != s0hash[i] || !ndl_equal(t,s); s += nd_wpd, i++ ); v[i/BLEN] |= 1L <<(i%BLEN); } return v; } int nd_nm_to_vect_2(UINT *s0,int n,int *s0hash,NDV p,NM m,unsigned long *v) { NMV mr; UINT *d,*t,*s; int i,j,len,h,head; d = DL(m); len = LEN(p); t = (UINT *)MALLOC(nd_wpd*sizeof(UINT)); for ( i = j = 0, s = s0, mr = BDY(p); j < len; j++, NMV_ADV(mr) ) { ndl_add(d,DL(mr),t); h = ndl_hash_value(t); for ( ; h != s0hash[i] || !ndl_equal(t,s); s += nd_wpd, i++ ); if ( j == 0 ) head = i; v[i/BLEN] |= 1L <<(i%BLEN); } return head; } Z *nm_ind_pair_to_vect(int mod,UINT *s0,int n,NM_ind_pair pair) { NM m; NMV mr; UINT *d,*t,*s; NDV p; int i,j,len; Z *r; m = pair->mul; d = DL(m); p = nd_ps[pair->index]; len = LEN(p); r = (Z *)CALLOC(n,sizeof(Q)); t = (UINT *)MALLOC(nd_wpd*sizeof(UINT)); for ( i = j = 0, s = s0, mr = BDY(p); j < len; j++, NMV_ADV(mr) ) { ndl_add(d,DL(mr),t); for ( ; !ndl_equal(t,s); s += nd_wpd, i++ ); r[i] = CZ(mr); } return r; } IndArray nm_ind_pair_to_vect_compress(int trace,UINT *s0,int n,NM_ind_pair pair,int start) { NM m; NMV mr; UINT *d,*t,*s,*u; NDV p; unsigned char *ivc; unsigned short *ivs; UINT *v,*ivi,*s0v; int i,j,len,prev,diff,cdiff,h,st,ed,md,c; IndArray r; m = pair->mul; d = DL(m); if ( trace ) p = nd_demand?nd_ps_trace_sym[pair->index]:nd_ps_trace[pair->index]; else p = nd_demand?nd_ps_sym[pair->index]:nd_ps[pair->index]; len = LEN(p); t = (UINT *)MALLOC(nd_wpd*sizeof(UINT)); v = (unsigned int *)MALLOC(len*sizeof(unsigned int)); for ( prev = start, mr = BDY(p), j = 0; j < len; j++, NMV_ADV(mr) ) { ndl_add(d,DL(mr),t); st = prev; ed = n; while ( ed > st ) { md = (st+ed)/2; u = s0+md*nd_wpd; c = DL_COMPARE(u,t); if ( c == 0 ) break; else if ( c > 0 ) st = md; else ed = md; } prev = v[j] = md; } r = (IndArray)MALLOC(sizeof(struct oIndArray)); r->head = v[0]; diff = 0; for ( i = 1; i < len; i++ ) { cdiff = v[i]-v[i-1]; diff = MAX(cdiff,diff); } if ( diff < 256 ) { r->width = 1; ivc = (unsigned char *)MALLOC_ATOMIC(len*sizeof(unsigned char)); r->index.c = ivc; for ( i = 1, ivc[0] = 0; i < len; i++ ) ivc[i] = v[i]-v[i-1]; } else if ( diff < 65536 ) { r->width = 2; ivs = (unsigned short *)MALLOC_ATOMIC(len*sizeof(unsigned short)); r->index.s = ivs; for ( i = 1, ivs[0] = 0; i < len; i++ ) ivs[i] = v[i]-v[i-1]; } else { r->width = 4; ivi = (unsigned int *)MALLOC_ATOMIC(len*sizeof(unsigned int)); r->index.i = ivi; for ( i = 1, ivi[0] = 0; i < len; i++ ) ivi[i] = v[i]-v[i-1]; } return r; } int compress_array(Z *svect,Z *cvect,int n) { int i,j; for ( i = j = 0; i < n; i++ ) if ( svect[i] ) cvect[j++] = svect[i]; return j; } void expand_array(Z *svect,Z *cvect,int n) { int i,j; for ( i = j = 0; j < n; i++ ) if ( svect[i] ) svect[i] = cvect[j++]; } #if 0 int ndv_reduce_vect_q(Z *svect,int trace,int col,IndArray *imat,NM_ind_pair *rp0,int nred) { int i,j,k,len,pos,prev,nz; Z cs,mcs,c1,c2,cr,gcd,t; IndArray ivect; unsigned char *ivc; unsigned short *ivs; unsigned int *ivi; NDV redv; NMV mr; NODE rp; int maxrs; double hmag; Z *cvect; int l; maxrs = 0; for ( i = 0; i < col && !svect[i]; i++ ); if ( i == col ) return maxrs; hmag = p_mag((P)svect[i])*nd_scale; cvect = (Z *)MALLOC(col*sizeof(Q)); for ( i = 0; i < nred; i++ ) { ivect = imat[i]; k = ivect->head; if ( svect[k] ) { maxrs = MAX(maxrs,rp0[i]->sugar); redv = nd_demand?ndv_load(rp0[i]->index) :(trace?nd_ps_trace[rp0[i]->index]:nd_ps[rp0[i]->index]); len = LEN(redv); mr = BDY(redv); igcd_cofactor(svect[k],CZ(mr),&gcd,&cs,&cr); chsgnz(cs,&mcs); if ( !UNIQ(cr) ) { for ( j = 0; j < col; j++ ) { mulz(svect[j],cr,&c1); svect[j] = c1; } } svect[k] = 0; prev = k; switch ( ivect->width ) { case 1: ivc = ivect->index.c; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivc[j]; prev = pos; muladdtoz(CZ(mr),mcs,&svect[pos]); } break; case 2: ivs = ivect->index.s; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivs[j]; prev = pos; muladdtoz(CZ(mr),mcs,&svect[pos]); } break; case 4: ivi = ivect->index.i; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivi[j]; prev = pos; muladdtoz(CZ(mr),mcs,&svect[pos]); } break; } for ( j = k+1; j < col && !svect[j]; j++ ); if ( j == col ) break; if ( hmag && ((double)p_mag((P)svect[j]) > hmag) ) { nz = compress_array(svect,cvect,col); removecont_array((P *)cvect,nz,1); expand_array(svect,cvect,nz); hmag = ((double)p_mag((P)svect[j]))*nd_scale; } } } nz = compress_array(svect,cvect,col); removecont_array((P *)cvect,nz,1); expand_array(svect,cvect,nz); if ( DP_Print ) { fprintf(asir_out,"-"); fflush(asir_out); } return maxrs; } #else /* direct mpz version */ int ndv_reduce_vect_q(Z *svect0,int trace,int col,IndArray *imat,NM_ind_pair *rp0,int nred) { int i,j,k,len,pos,prev; mpz_t cs,cr,gcd; IndArray ivect; unsigned char *ivc; unsigned short *ivs; unsigned int *ivi; NDV redv; NMV mr; NODE rp; int maxrs; double hmag; int l; static mpz_t *svect; static int svect_len=0; maxrs = 0; for ( i = 0; i < col && !svect0[i]; i++ ); if ( i == col ) return maxrs; hmag = p_mag((P)svect0[i])*nd_scale; if ( col > svect_len ) { svect = (mpz_t *)MALLOC(col*sizeof(mpz_t)); svect_len = col; } for ( i = 0; i < col; i++ ) { mpz_init(svect[i]); if ( svect0[i] ) mpz_set(svect[i],BDY(svect0[i])); else mpz_set_ui(svect[i],0); } mpz_init(gcd); mpz_init(cs); mpz_init(cr); for ( i = 0; i < nred; i++ ) { ivect = imat[i]; k = ivect->head; if ( mpz_sgn(svect[k]) ) { maxrs = MAX(maxrs,rp0[i]->sugar); redv = nd_demand?ndv_load(rp0[i]->index) :(trace?nd_ps_trace[rp0[i]->index]:nd_ps[rp0[i]->index]); len = LEN(redv); mr = BDY(redv); mpz_gcd(gcd,svect[k],BDY(CZ(mr))); mpz_div(cs,svect[k],gcd); mpz_div(cr,BDY(CZ(mr)),gcd); mpz_neg(cs,cs); if ( MUNIMPZ(cr) ) for ( j = 0; j < col; j++ ) mpz_neg(svect[j],svect[j]); else if ( !UNIMPZ(cr) ) for ( j = 0; j < col; j++ ) { if ( mpz_sgn(svect[j]) ) mpz_mul(svect[j],svect[j],cr); } mpz_set_ui(svect[k],0); prev = k; switch ( ivect->width ) { case 1: ivc = ivect->index.c; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivc[j]; prev = pos; mpz_addmul(svect[pos],BDY(CZ(mr)),cs); } break; case 2: ivs = ivect->index.s; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivs[j]; prev = pos; mpz_addmul(svect[pos],BDY(CZ(mr)),cs); } break; case 4: ivi = ivect->index.i; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivi[j]; prev = pos; mpz_addmul(svect[pos],BDY(CZ(mr)),cs); } break; } for ( j = k+1; j < col && !svect[j]; j++ ); if ( j == col ) break; if ( hmag && ((double)mpz_sizeinbase(svect[j],2) > hmag) ) { mpz_removecont_array(svect,col); hmag = ((double)mpz_sizeinbase(svect[j],2))*nd_scale; } } } mpz_removecont_array(svect,col); if ( DP_Print ) { fprintf(asir_out,"-"); fflush(asir_out); } for ( i = 0; i < col; i++ ) if ( mpz_sgn(svect[i]) ) MPZTOZ(svect[i],svect0[i]); else svect0[i] = 0; return maxrs; } #endif int ndv_reduce_vect(int m,UINT *svect,int col,IndArray *imat,NM_ind_pair *rp0,int nred) { int i,j,k,len,pos,prev; UINT c,c1,c2,c3,up,lo,dmy; IndArray ivect; unsigned char *ivc; unsigned short *ivs; unsigned int *ivi; NDV redv; NMV mr; NODE rp; int maxrs; maxrs = 0; for ( i = 0; i < nred; i++ ) { ivect = imat[i]; k = ivect->head; svect[k] %= m; if ( (c = svect[k]) != 0 ) { maxrs = MAX(maxrs,rp0[i]->sugar); c = m-c; redv = nd_ps[rp0[i]->index]; len = LEN(redv); mr = BDY(redv); svect[k] = 0; prev = k; switch ( ivect->width ) { case 1: ivc = ivect->index.c; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivc[j]; c1 = CM(mr); prev = pos; if ( c1 ) { c2 = svect[pos]; DMA(c1,c,c2,up,lo); if ( up ) { DSAB(m,up,lo,dmy,c3); svect[pos] = c3; } else svect[pos] = lo; } } break; case 2: ivs = ivect->index.s; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivs[j]; c1 = CM(mr); prev = pos; if ( c1 ) { c2 = svect[pos]; DMA(c1,c,c2,up,lo); if ( up ) { DSAB(m,up,lo,dmy,c3); svect[pos] = c3; } else svect[pos] = lo; } } break; case 4: ivi = ivect->index.i; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivi[j]; c1 = CM(mr); prev = pos; if ( c1 ) { c2 = svect[pos]; DMA(c1,c,c2,up,lo); if ( up ) { DSAB(m,up,lo,dmy,c3); svect[pos] = c3; } else svect[pos] = lo; } } break; } } } for ( i = 0; i < col; i++ ) if ( svect[i] >= (UINT)m ) svect[i] %= m; return maxrs; } int ndv_reduce_vect_sf(int m,UINT *svect,int col,IndArray *imat,NM_ind_pair *rp0,int nred) { int i,j,k,len,pos,prev; UINT c,c1,c2,c3,up,lo,dmy; IndArray ivect; unsigned char *ivc; unsigned short *ivs; unsigned int *ivi; NDV redv; NMV mr; NODE rp; int maxrs; maxrs = 0; for ( i = 0; i < nred; i++ ) { ivect = imat[i]; k = ivect->head; if ( (c = svect[k]) != 0 ) { maxrs = MAX(maxrs,rp0[i]->sugar); c = _chsgnsf(c); redv = nd_ps[rp0[i]->index]; len = LEN(redv); mr = BDY(redv); svect[k] = 0; prev = k; switch ( ivect->width ) { case 1: ivc = ivect->index.c; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivc[j]; prev = pos; svect[pos] = _addsf(_mulsf(CM(mr),c),svect[pos]); } break; case 2: ivs = ivect->index.s; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivs[j]; prev = pos; svect[pos] = _addsf(_mulsf(CM(mr),c),svect[pos]); } break; case 4: ivi = ivect->index.i; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivi[j]; prev = pos; svect[pos] = _addsf(_mulsf(CM(mr),c),svect[pos]); } break; } } } return maxrs; } ND nd_add_lf(ND p1,ND p2) { int n,c,can; ND r; NM m1,m2,mr0,mr,s; Z t; if ( !p1 ) return p2; else if ( !p2 ) return p1; else { can = 0; for ( n = NV(p1), m1 = BDY(p1), m2 = BDY(p2), mr0 = 0; m1 && m2; ) { c = DL_COMPARE(DL(m1),DL(m2)); switch ( c ) { case 0: addlf(CZ(m1),CZ(m2),&t); s = m1; m1 = NEXT(m1); if ( t ) { can++; NEXTNM2(mr0,mr,s); CZ(mr) = (t); } else { can += 2; FREENM(s); } s = m2; m2 = NEXT(m2); FREENM(s); break; case 1: s = m1; m1 = NEXT(m1); NEXTNM2(mr0,mr,s); break; case -1: s = m2; m2 = NEXT(m2); NEXTNM2(mr0,mr,s); break; } } if ( !mr0 ) if ( m1 ) mr0 = m1; else if ( m2 ) mr0 = m2; else return 0; else if ( m1 ) NEXT(mr) = m1; else if ( m2 ) NEXT(mr) = m2; else NEXT(mr) = 0; BDY(p1) = mr0; SG(p1) = MAX(SG(p1),SG(p2)); LEN(p1) = LEN(p1)+LEN(p2)-can; FREEND(p2); return p1; } } int ndv_reduce_vect_lf(mpz_t *svect,int trace,int col,IndArray *imat,NM_ind_pair *rp0,int nred) { int i,j,k,len,pos,prev; mpz_t c,mc,c1; IndArray ivect; unsigned char *ivc; unsigned short *ivs; unsigned int *ivi; NDV redv; NMV mr; NODE rp; int maxrs; maxrs = 0; lf_lazy = 1; for ( i = 0; i < nred; i++ ) { ivect = imat[i]; k = ivect->head; mpz_mod(svect[k],svect[k],BDY(current_mod_lf)); if ( mpz_sgn(svect[k]) ) { maxrs = MAX(maxrs,rp0[i]->sugar); mpz_neg(svect[k],svect[k]); redv = trace?nd_ps_trace[rp0[i]->index]:nd_ps[rp0[i]->index]; len = LEN(redv); mr = BDY(redv); prev = k; switch ( ivect->width ) { case 1: ivc = ivect->index.c; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivc[j]; prev = pos; mpz_addmul(svect[pos],svect[k],BDY(CZ(mr))); } break; case 2: ivs = ivect->index.s; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivs[j]; prev = pos; mpz_addmul(svect[pos],svect[k],BDY(CZ(mr))); } break; case 4: ivi = ivect->index.i; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivi[j]; prev = pos; mpz_addmul(svect[pos],svect[k],BDY(CZ(mr))); } break; } mpz_set_ui(svect[k],0); } } lf_lazy=0; for ( i = 0; i < col; i++ ) { mpz_mod(svect[i],svect[i],BDY(current_mod_lf)); } return maxrs; } int nd_gauss_elim_lf(mpz_t **mat0,int *sugar,int row,int col,int *colstat) { int i,j,k,l,rank,s; mpz_t a,a1,inv; mpz_t *t,*pivot,*pk; mpz_t **mat; struct oEGT eg0,eg1,eg_forward,eg_mod,eg_back; int size,size1; mpz_init(inv); mpz_init(a); mat = (mpz_t **)mat0; size = 0; for ( rank = 0, j = 0; j < col; j++ ) { for ( i = rank; i < row; i++ ) { mpz_mod(mat[i][j],mat[i][j],BDY(current_mod_lf)); } for ( i = rank; i < row; i++ ) if ( mpz_sgn(mat[i][j]) ) break; if ( i == row ) { colstat[j] = 0; continue; } else colstat[j] = 1; if ( i != rank ) { t = mat[i]; mat[i] = mat[rank]; mat[rank] = t; s = sugar[i]; sugar[i] = sugar[rank]; sugar[rank] = s; } pivot = mat[rank]; s = sugar[rank]; mpz_invert(inv,pivot[j],BDY(current_mod_lf)); for ( k = j, pk = pivot+k; k < col; k++, pk++ ) if ( mpz_sgn(*pk) ) { mpz_mul(a,*pk,inv); mpz_mod(*pk,a,BDY(current_mod_lf)); } for ( i = rank+1; i < row; i++ ) { t = mat[i]; if ( mpz_sgn(t[j]) ) { sugar[i] = MAX(sugar[i],s); mpz_neg(a,t[j]); red_by_vect_lf(t+j,pivot+j,a,col-j); } } rank++; } for ( j = col-1, l = rank-1; j >= 0; j-- ) if ( colstat[j] ) { pivot = mat[l]; s = sugar[l]; for ( k = j; k < col; k++ ) mpz_mod(pivot[k],pivot[k],BDY(current_mod_lf)); for ( i = 0; i < l; i++ ) { t = mat[i]; if ( mpz_sgn(t[j]) ) { sugar[i] = MAX(sugar[i],s); mpz_neg(a,t[j]); red_by_vect_lf(t+j,pivot+j,a,col-j); } } l--; } for ( j = 0, l = 0; l < rank; j++ ) if ( colstat[j] ) { t = mat[l]; for ( k = j; k < col; k++ ) { mpz_mod(t[k],t[k],BDY(current_mod_lf)); } l++; } return rank; } NDV vect_to_ndv(UINT *vect,int spcol,int col,int *rhead,UINT *s0vect) { int j,k,len; UINT *p; UINT c; NDV r; NMV mr0,mr; for ( j = 0, len = 0; j < spcol; j++ ) if ( vect[j] ) len++; if ( !len ) return 0; else { mr0 = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(nmv_adv*len); #if 0 ndv_alloc += nmv_adv*len; #endif mr = mr0; p = s0vect; for ( j = k = 0; j < col; j++, p += nd_wpd ) if ( !rhead[j] ) { if ( (c = vect[k++]) != 0 ) { ndl_copy(p,DL(mr)); CM(mr) = c; NMV_ADV(mr); } } MKNDV(nd_nvar,mr0,len,r); return r; } } NDV vect_to_ndv_2(unsigned long *vect,int col,UINT *s0vect) { int j,k,len; UINT *p; NDV r; NMV mr0,mr; for ( j = 0, len = 0; j < col; j++ ) if ( vect[j/BLEN] & (1L<<(j%BLEN)) ) len++; if ( !len ) return 0; else { mr0 = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(nmv_adv*len); mr = mr0; p = s0vect; for ( j = 0; j < col; j++, p += nd_wpd ) if ( vect[j/BLEN] & (1L<<(j%BLEN)) ) { ndl_copy(p,DL(mr)); CM(mr) = 1; NMV_ADV(mr); } MKNDV(nd_nvar,mr0,len,r); return r; } } /* for preprocessed vector */ NDV vect_to_ndv_q(Z *vect,int spcol,int col,int *rhead,UINT *s0vect) { int j,k,len; UINT *p; Z c; NDV r; NMV mr0,mr; for ( j = 0, len = 0; j < spcol; j++ ) if ( vect[j] ) len++; if ( !len ) return 0; else { mr0 = (NMV)MALLOC(nmv_adv*len); #if 0 ndv_alloc += nmv_adv*len; #endif mr = mr0; p = s0vect; for ( j = k = 0; j < col; j++, p += nd_wpd ) { if ( !rhead[j] ) { if ( (c = vect[k++]) != 0 ) { if ( !INT(c) ) error("vect_to_ndv_q : components must be integers"); ndl_copy(p,DL(mr)); CZ(mr) = c; NMV_ADV(mr); } } } MKNDV(nd_nvar,mr0,len,r); return r; } } NDV vect_to_ndv_lf(mpz_t *vect,int spcol,int col,int *rhead,UINT *s0vect) { int j,k,len; UINT *p; mpz_t c; NDV r; NMV mr0,mr; for ( j = 0, len = 0; j < spcol; j++ ) if ( mpz_sgn(vect[j]) ) len++; if ( !len ) return 0; else { mr0 = (NMV)MALLOC(nmv_adv*len); #if 0 ndv_alloc += nmv_adv*len; #endif mr = mr0; p = s0vect; for ( j = k = 0; j < col; j++, p += nd_wpd ) if ( !rhead[j] ) { c[0] = vect[k++][0]; if ( mpz_sgn(c) ) { ndl_copy(p,DL(mr)); MPZTOZ(c,CZ(mr)); NMV_ADV(mr); } } MKNDV(nd_nvar,mr0,len,r); return r; } } /* for plain vector */ NDV plain_vect_to_ndv_q(Z *vect,int col,UINT *s0vect) { int j,k,len; UINT *p; Z c; NDV r; NMV mr0,mr; for ( j = 0, len = 0; j < col; j++ ) if ( vect[j] ) len++; if ( !len ) return 0; else { mr0 = (NMV)MALLOC(nmv_adv*len); #if 0 ndv_alloc += nmv_adv*len; #endif mr = mr0; p = s0vect; for ( j = k = 0; j < col; j++, p += nd_wpd, k++ ) if ( (c = vect[k]) != 0 ) { if ( !INT(c) ) error("plain_vect_to_ndv_q : components must be integers"); ndl_copy(p,DL(mr)); CZ(mr) = c; NMV_ADV(mr); } MKNDV(nd_nvar,mr0,len,r); return r; } } int nd_sp_f4(int m,int trace,ND_pairs l,PGeoBucket bucket) { ND_pairs t; NODE sp0,sp; int stat; ND spol; for ( t = l; t; t = NEXT(t) ) { stat = nd_sp(m,trace,t,&spol); if ( !stat ) return 0; if ( spol ) { add_pbucket_symbolic(bucket,spol); } } return 1; } int nd_symbolic_preproc(PGeoBucket bucket,int trace,UINT **s0vect,NODE *r) { NODE rp0,rp; NM mul,head,s0,s; int index,col,i,sugar; RHist h; UINT *s0v,*p; NM_ind_pair pair; ND red; NDV *ps; s0 = 0; rp0 = 0; col = 0; if ( nd_demand ) ps = trace?nd_ps_trace_sym:nd_ps_sym; else ps = trace?nd_ps_trace:nd_ps; while ( 1 ) { head = remove_head_pbucket_symbolic(bucket); if ( !head ) break; if ( !s0 ) s0 = head; else NEXT(s) = head; s = head; index = ndl_find_reducer(DL(head)); if ( index >= 0 ) { h = nd_psh[index]; NEWNM(mul); ndl_sub(DL(head),DL(h),DL(mul)); if ( ndl_check_bound2(index,DL(mul)) ) return 0; sugar = TD(DL(mul))+SG(ps[index]); MKNM_ind_pair(pair,mul,index,sugar,0); red = ndv_mul_nm_symbolic(mul,ps[index]); add_pbucket_symbolic(bucket,nd_remove_head(red)); NEXTNODE(rp0,rp); BDY(rp) = (pointer)pair; } col++; } if ( rp0 ) NEXT(rp) = 0; NEXT(s) = 0; s0v = (UINT *)MALLOC_ATOMIC(col*nd_wpd*sizeof(UINT)); for ( i = 0, p = s0v, s = s0; i < col; i++, p += nd_wpd, s = NEXT(s) ) ndl_copy(DL(s),p); *s0vect = s0v; *r = rp0; return col; } void print_ndp(ND_pairs l) { ND_pairs t; for ( t = l; t; t = NEXT(t) ) printf("[%d,%d] ",t->i1,t->i2); printf("\n"); } NODE nd_f4(int m,int checkonly,int **indp) { int i,nh,stat,index,f4red; NODE r,g,tn0,tn,node; ND_pairs d,l,t,ll0,ll,lh; LIST l0,l1; ND spol,red; NDV nf,redv; NM s0,s; NODE rp0,srp0,nflist,nzlist,nzlist_t; int nsp,nred,col,rank,len,k,j,a,i1s,i2s; UINT c; UINT **spmat; UINT *s0vect,*svect,*p,*v; int *colstat; IndArray *imat; int *rhead; int spcol,sprow; int sugar,sugarh; PGeoBucket bucket; struct oEGT eg0,eg1,eg_f4; Z i1,i2,sugarq; init_eg(&f4_symb); init_eg(&f4_conv); init_eg(&f4_conv); init_eg(&f4_elim1); init_eg(&f4_elim2); #if 0 ndv_alloc = 0; #endif Nf4_red=0; g = 0; d = 0; for ( i = 0; i < nd_psn; i++ ) { d = update_pairs(d,g,i,0); g = update_base(g,i); } nzlist = 0; nzlist_t = nd_nzlist; f4red = 1; nd_last_nonzero = 0; while ( d ) { get_eg(&eg0); l = nd_minsugarp(d,&d); sugar = nd_sugarweight?l->sugar2:SG(l); if ( MaxDeg > 0 && sugar > MaxDeg ) break; if ( nzlist_t ) { node = BDY((LIST)BDY(nzlist_t)); sugarh = ZTOS((Q)ARG0(node)); tn = BDY((LIST)ARG1(node)); if ( !tn ) { nzlist_t = NEXT(nzlist_t); continue; } /* tn = [[i1,i2],...] */ lh = nd_ipairtospair(tn); } bucket = create_pbucket(); stat = nd_sp_f4(m,0,l,bucket); if ( !stat ) { for ( t = l; NEXT(t); t = NEXT(t) ); NEXT(t) = d; d = l; d = nd_reconstruct(0,d); continue; } if ( bucket->m < 0 ) continue; col = nd_symbolic_preproc(bucket,0,&s0vect,&rp0); if ( !col ) { for ( t = l; NEXT(t); t = NEXT(t) ); NEXT(t) = d; d = l; d = nd_reconstruct(0,d); continue; } get_eg(&eg1); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg1); add_eg(&f4_symb,&eg0,&eg1); if ( DP_Print ) fprintf(asir_out,"sugar=%d,symb=%.3fsec,", sugar,eg_f4.exectime); nflist = nd_f4_red(m,nd_nzlist?lh:l,0,s0vect,col,rp0,nd_gentrace?&ll:0); if ( checkonly && nflist ) return 0; /* adding new bases */ if ( nflist ) nd_last_nonzero = f4red; for ( r = nflist; r; r = NEXT(r) ) { nf = (NDV)BDY(r); ndv_removecont(m,nf); if ( !m && nd_nalg ) { ND nf1; nf1 = ndvtond(m,nf); nd_monic(0,&nf1); nd_removecont(m,nf1); nf = ndtondv(m,nf1); } nh = ndv_newps(m,nf,0); d = update_pairs(d,g,nh,0); g = update_base(g,nh); } if ( DP_Print ) { fprintf(asir_out,"f4red=%d,gblen=%d\n",f4red,length(g)); fflush(asir_out); } if ( nd_gentrace ) { for ( t = ll, tn0 = 0; t; t = NEXT(t) ) { NEXTNODE(tn0,tn); STOZ(t->i1,i1); STOZ(t->i2,i2); node = mknode(2,i1,i2); MKLIST(l0,node); BDY(tn) = l0; } if ( tn0 ) NEXT(tn) = 0; MKLIST(l0,tn0); STOZ(sugar,sugarq); node = mknode(2,sugarq,l0); MKLIST(l1,node); MKNODE(node,l1,nzlist); nzlist = node; } if ( nd_nzlist ) nzlist_t = NEXT(nzlist_t); f4red++; if ( nd_f4red && f4red > nd_f4red ) break; if ( nd_rank0 && !nflist ) break; } if ( nd_gentrace ) { MKLIST(l0,reverse_node(nzlist)); MKNODE(nd_alltracelist,l0,0); } #if 0 fprintf(asir_out,"ndv_alloc=%d\n",ndv_alloc); #endif if ( DP_Print ) { fprintf(asir_out,"number of red=%d,",Nf4_red); fprintf(asir_out,"symb=%.3fsec,conv=%.3fsec,elim1=%.3fsec,elim2=%.3fsec\n", f4_symb.exectime,f4_conv.exectime,f4_elim1.exectime,f4_elim2.exectime); } conv_ilist(nd_demand,0,g,indp); return g; } NODE nd_f4_trace(int m,int **indp) { int i,nh,stat,index; NODE r,g; ND_pairs d,l,l0,t; ND spol,red; NDV nf,redv,nfqv,nfv; NM s0,s; NODE rp0,srp0,nflist; int nsp,nred,col,rank,len,k,j,a; UINT c; UINT **spmat; UINT *s0vect,*svect,*p,*v; int *colstat; IndArray *imat; int *rhead; int spcol,sprow; int sugar; PGeoBucket bucket; struct oEGT eg0,eg1,eg_f4; g = 0; d = 0; for ( i = 0; i < nd_psn; i++ ) { d = update_pairs(d,g,i,0); g = update_base(g,i); } while ( d ) { get_eg(&eg0); l = nd_minsugarp(d,&d); sugar = SG(l); if ( MaxDeg > 0 && sugar > MaxDeg ) break; bucket = create_pbucket(); stat = nd_sp_f4(m,0,l,bucket); if ( !stat ) { for ( t = l; NEXT(t); t = NEXT(t) ); NEXT(t) = d; d = l; d = nd_reconstruct(1,d); continue; } if ( bucket->m < 0 ) continue; col = nd_symbolic_preproc(bucket,0,&s0vect,&rp0); if ( !col ) { for ( t = l; NEXT(t); t = NEXT(t) ); NEXT(t) = d; d = l; d = nd_reconstruct(1,d); continue; } get_eg(&eg1); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg1); if ( DP_Print ) fprintf(asir_out,"\nsugar=%d,symb=%.3fsec,", sugar,eg_f4.exectime); nflist = nd_f4_red(m,l,0,s0vect,col,rp0,&l0); if ( !l0 ) continue; l = l0; /* over Q */ bucket = create_pbucket(); stat = nd_sp_f4(0,1,l,bucket); if ( !stat ) { for ( t = l; NEXT(t); t = NEXT(t) ); NEXT(t) = d; d = l; d = nd_reconstruct(1,d); continue; } if ( bucket->m < 0 ) continue; col = nd_symbolic_preproc(bucket,1,&s0vect,&rp0); if ( !col ) { for ( t = l; NEXT(t); t = NEXT(t) ); NEXT(t) = d; d = l; d = nd_reconstruct(1,d); continue; } nflist = nd_f4_red(0,l,1,s0vect,col,rp0,0); /* adding new bases */ for ( r = nflist; r; r = NEXT(r) ) { nfqv = (NDV)BDY(r); ndv_removecont(0,nfqv); if ( !remqi((Q)HCZ(nfqv),m) ) return 0; if ( nd_nalg ) { ND nf1; nf1 = ndvtond(m,nfqv); nd_monic(0,&nf1); nd_removecont(0,nf1); nfqv = ndtondv(0,nf1); nd_free(nf1); } nfv = ndv_dup(0,nfqv); ndv_mod(m,nfv); ndv_removecont(m,nfv); nh = ndv_newps(0,nfv,nfqv); d = update_pairs(d,g,nh,0); g = update_base(g,nh); } } #if 0 fprintf(asir_out,"ndv_alloc=%d\n",ndv_alloc); #endif conv_ilist(nd_demand,1,g,indp); return g; } int rref(matrix mat,int *sugar) { int row,col,i,j,k,l,s,wcol,wj; unsigned long bj; unsigned long **a; unsigned long *ai,*ak,*as,*t; int *pivot; row = mat->row; col = mat->col; a = mat->a; wcol = (col+BLEN-1)/BLEN; pivot = (int *)MALLOC_ATOMIC(row*sizeof(int)); i = 0; for ( j = 0; j < col; j++ ) { wj = j/BLEN; bj = 1L<<(j%BLEN); for ( k = i; k < row; k++ ) if ( a[k][wj] & bj ) break; if ( k == row ) continue; pivot[i] = j; if ( k != i ) { t = a[i]; a[i] = a[k]; a[k] = t; s = sugar[i]; sugar[i] = sugar[k]; sugar[k] = s; } ai = a[i]; for ( k = i+1; k < row; k++ ) { ak = a[k]; if ( ak[wj] & bj ) { for ( l = wj; l < wcol; l++ ) ak[l] ^= ai[l]; sugar[k] = MAX(sugar[k],sugar[i]); } } i++; } for ( k = i-1; k >= 0; k-- ) { j = pivot[k]; wj = j/BLEN; bj = 1L<<(j%BLEN); ak = a[k]; for ( s = 0; s < k; s++ ) { as = a[s]; if ( as[wj] & bj ) { for ( l = wj; l < wcol; l++ ) as[l] ^= ak[l]; sugar[s] = MAX(sugar[s],sugar[k]); } } } return i; } void print_matrix(matrix mat) { int row,col,i,j; unsigned long *ai; row = mat->row; col = mat->col; printf("%d x %d\n",row,col); for ( i = 0; i < row; i++ ) { ai = mat->a[i]; for ( j = 0; j < col; j++ ) { if ( ai[j/BLEN] & (1L<<(j%BLEN)) ) putchar('1'); else putchar('0'); } putchar('\n'); } } NDV vect_to_ndv_2(unsigned long *vect,int col,UINT *s0vect); void red_by_vect_2(matrix mat,int *sugar,unsigned long *v,int rhead,int rsugar) { int row,col,wcol,wj,i,j; unsigned long bj; unsigned long *ai; unsigned long **a; int len; int *pos; row = mat->row; col = mat->col; wcol = (col+BLEN-1)/BLEN; pos = (int *)MALLOC(wcol*sizeof(int)); bzero(pos,wcol*sizeof(int)); for ( i = j = 0; i < wcol; i++ ) if ( v[i] ) pos[j++] = i;; len = j; wj = rhead/BLEN; bj = 1L<a; for ( i = 0; i < row; i++ ) { ai = a[i]; if ( ai[wj]&bj ) { for ( j = 0; j < len; j++ ) ai[pos[j]] ^= v[pos[j]]; sugar[i] = MAX(sugar[i],rsugar); } } } NODE nd_f4_red_2(ND_pairs sp0,UINT *s0vect,int col,NODE rp0,ND_pairs *nz) { int nsp,nred,i,i0,k,rank,row; NODE r0,rp; ND_pairs sp; ND spol; NM_ind_pair rt; int *s0hash; UINT *s; int *pivot,*sugar,*head; matrix mat; NM m; NODE r; struct oEGT eg0,eg1,eg2,eg_elim1,eg_elim2; int rhead,rsugar,size; unsigned long *v; get_eg(&eg0); for ( sp = sp0, nsp = 0; sp; sp = NEXT(sp), nsp++ ); nred = length(rp0); mat = alloc_matrix(nsp,col); s0hash = (int *)MALLOC(col*sizeof(int)); for ( i = 0, s = s0vect; i < col; i++, s += nd_wpd ) s0hash[i] = ndl_hash_value(s); sugar = (int *)MALLOC(nsp*sizeof(int)); for ( i = 0, sp = sp0; sp; sp = NEXT(sp) ) { nd_sp(2,0,sp,&spol); if ( spol ) { mat->a[i] = nd_to_vect_2(s0vect,col,s0hash,spol); sugar[i] = SG(spol); i++; } } mat->row = i; if ( DP_Print ) { fprintf(asir_out,"%dx%d,",mat->row,mat->col); fflush(asir_out); } size = ((col+BLEN-1)/BLEN)*sizeof(unsigned long); v = CALLOC((col+BLEN-1)/BLEN,sizeof(unsigned long)); for ( rp = rp0, i = 0; rp; rp = NEXT(rp), i++ ) { rt = (NM_ind_pair)BDY(rp); bzero(v,size); rhead = nd_nm_to_vect_2(s0vect,col,s0hash,nd_ps[rt->index],rt->mul,v); rsugar = SG(nd_ps[rt->index])+TD(DL(rt->mul)); red_by_vect_2(mat,sugar,v,rhead,rsugar); } get_eg(&eg1); init_eg(&eg_elim1); add_eg(&eg_elim1,&eg0,&eg1); rank = rref(mat,sugar); for ( i = 0, r0 = 0; i < rank; i++ ) { NEXTNODE(r0,r); BDY(r) = (pointer)vect_to_ndv_2(mat->a[i],col,s0vect); SG((NDV)BDY(r)) = sugar[i]; } if ( r0 ) NEXT(r) = 0; get_eg(&eg2); init_eg(&eg_elim2); add_eg(&eg_elim2,&eg1,&eg2); if ( DP_Print ) { fprintf(asir_out,"elim1=%.3fsec,elim2=%.3fsec,", eg_elim1.exectime,eg_elim2.exectime); fflush(asir_out); } return r0; } NODE nd_f4_red(int m,ND_pairs sp0,int trace,UINT *s0vect,int col,NODE rp0,ND_pairs *nz) { IndArray *imat; int nsp,nred,i,start; int *rhead; NODE r0,rp; ND_pairs sp; NM_ind_pair *rvect; UINT *s; int *s0hash; struct oEGT eg0,eg1,eg_conv; if ( m == 2 && nd_rref2 ) return nd_f4_red_2(sp0,s0vect,col,rp0,nz); for ( sp = sp0, nsp = 0; sp; sp = NEXT(sp), nsp++ ); nred = length(rp0); imat = (IndArray *)MALLOC(nred*sizeof(IndArray)); rhead = (int *)MALLOC(col*sizeof(int)); for ( i = 0; i < col; i++ ) rhead[i] = 0; /* construction of index arrays */ get_eg(&eg0); if ( DP_Print ) { fprintf(asir_out,"%dx%d,",nsp+nred,col); fflush(asir_out); } rvect = (NM_ind_pair *)MALLOC(nred*sizeof(NM_ind_pair)); for ( start = 0, rp = rp0, i = 0; rp; i++, rp = NEXT(rp) ) { rvect[i] = (NM_ind_pair)BDY(rp); imat[i] = nm_ind_pair_to_vect_compress(trace,s0vect,col,rvect[i],start); rhead[imat[i]->head] = 1; start = imat[i]->head; } get_eg(&eg1); init_eg(&eg_conv); add_eg(&eg_conv,&eg0,&eg1); add_eg(&f4_conv,&eg0,&eg1); if ( DP_Print ) { fprintf(asir_out,"conv=%.3fsec,",eg_conv.exectime); fflush(asir_out); } if ( m > 0 ) #if SIZEOF_LONG==8 r0 = nd_f4_red_mod64_main(m,sp0,nsp,s0vect,col,rvect,rhead,imat,nred,nz); #else r0 = nd_f4_red_main(m,sp0,nsp,s0vect,col,rvect,rhead,imat,nred,nz); #endif else if ( m == -1 ) r0 = nd_f4_red_sf_main(m,sp0,nsp,s0vect,col,rvect,rhead,imat,nred,nz); else if ( m == -2 ) r0 = nd_f4_red_lf_main(m,sp0,nsp,trace,s0vect,col,rvect,rhead,imat,nred); else r0 = nd_f4_red_q_main(sp0,nsp,trace,s0vect,col,rvect,rhead,imat,nred); return r0; } /* for Fp, 2<=p<2^16 */ NODE nd_f4_red_main(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col, NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred,ND_pairs *nz) { int spcol,sprow,a; int i,j,k,l,rank; NODE r0,r; ND_pairs sp; ND spol; UINT **spmat; UINT *svect,*v; int *colstat; struct oEGT eg0,eg1,eg2,eg_f4,eg_f4_1,eg_f4_2; int maxrs; int *spsugar; ND_pairs *spactive; spcol = col-nred; get_eg(&eg0); /* elimination (1st step) */ spmat = (UINT **)MALLOC(nsp*sizeof(UINT *)); svect = (UINT *)MALLOC(col*sizeof(UINT)); spsugar = (int *)MALLOC(nsp*sizeof(int)); spactive = !nz?0:(ND_pairs *)MALLOC(nsp*sizeof(ND_pairs)); for ( a = sprow = 0, sp = sp0; a < nsp; a++, sp = NEXT(sp) ) { nd_sp(m,0,sp,&spol); if ( !spol ) continue; nd_to_vect(m,s0vect,col,spol,svect); if ( m == -1 ) maxrs = ndv_reduce_vect_sf(m,svect,col,imat,rvect,nred); else maxrs = ndv_reduce_vect(m,svect,col,imat,rvect,nred); for ( i = 0; i < col; i++ ) if ( svect[i] ) break; if ( i < col ) { spmat[sprow] = v = (UINT *)MALLOC_ATOMIC(spcol*sizeof(UINT)); for ( j = k = 0; j < col; j++ ) if ( !rhead[j] ) v[k++] = svect[j]; spsugar[sprow] = MAX(maxrs,SG(spol)); if ( nz ) spactive[sprow] = sp; sprow++; } nd_free(spol); } get_eg(&eg1); init_eg(&eg_f4_1); add_eg(&eg_f4_1,&eg0,&eg1); if ( DP_Print ) { fprintf(asir_out,"elim1=%.3fsec,",eg_f4_1.exectime); fflush(asir_out); } /* free index arrays */ for ( i = 0; i < nred; i++ ) GCFREE(imat[i]->index.c); /* elimination (2nd step) */ colstat = (int *)MALLOC(spcol*sizeof(int)); if ( m == -1 ) rank = nd_gauss_elim_sf(spmat,spsugar,sprow,spcol,m,colstat); else rank = nd_gauss_elim_mod(spmat,spsugar,spactive,sprow,spcol,m,colstat); r0 = 0; for ( i = 0; i < rank; i++ ) { NEXTNODE(r0,r); BDY(r) = (pointer)vect_to_ndv(spmat[i],spcol,col,rhead,s0vect); SG((NDV)BDY(r)) = spsugar[i]; GCFREE(spmat[i]); } if ( r0 ) NEXT(r) = 0; for ( ; i < sprow; i++ ) GCFREE(spmat[i]); get_eg(&eg2); init_eg(&eg_f4_2); add_eg(&eg_f4_2,&eg1,&eg2); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg2); if ( DP_Print ) { fprintf(asir_out,"elim2=%.3fsec,",eg_f4_2.exectime); fprintf(asir_out,"nsp=%d,nred=%d,spmat=(%d,%d),rank=%d ", nsp,nred,sprow,spcol,rank); fprintf(asir_out,"%.3fsec,",eg_f4.exectime); } if ( nz ) { for ( i = 0; i < rank-1; i++ ) NEXT(spactive[i]) = spactive[i+1]; if ( rank > 0 ) { NEXT(spactive[rank-1]) = 0; *nz = spactive[0]; } else *nz = 0; } return r0; } /* for small finite fields */ NODE nd_f4_red_sf_main(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col, NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred,ND_pairs *nz) { int spcol,sprow,a; int i,j,k,l,rank; NODE r0,r; ND_pairs sp; ND spol; UINT **spmat; UINT *svect,*v; int *colstat; struct oEGT eg0,eg1,eg2,eg_f4,eg_f4_1,eg_f4_2; int maxrs; int *spsugar; ND_pairs *spactive; spcol = col-nred; get_eg(&eg0); /* elimination (1st step) */ spmat = (UINT **)MALLOC(nsp*sizeof(UINT *)); svect = (UINT *)MALLOC(col*sizeof(UINT)); spsugar = (int *)MALLOC(nsp*sizeof(int)); spactive = !nz?0:(ND_pairs *)MALLOC(nsp*sizeof(ND_pairs)); for ( a = sprow = 0, sp = sp0; a < nsp; a++, sp = NEXT(sp) ) { nd_sp(m,0,sp,&spol); if ( !spol ) continue; nd_to_vect(m,s0vect,col,spol,svect); maxrs = ndv_reduce_vect_sf(m,svect,col,imat,rvect,nred); for ( i = 0; i < col; i++ ) if ( svect[i] ) break; if ( i < col ) { spmat[sprow] = v = (UINT *)MALLOC_ATOMIC(spcol*sizeof(UINT)); for ( j = k = 0; j < col; j++ ) if ( !rhead[j] ) v[k++] = svect[j]; spsugar[sprow] = MAX(maxrs,SG(spol)); if ( nz ) spactive[sprow] = sp; sprow++; } nd_free(spol); } get_eg(&eg1); init_eg(&eg_f4_1); add_eg(&eg_f4_1,&eg0,&eg1); if ( DP_Print ) { fprintf(asir_out,"elim1=%.3fsec,",eg_f4_1.exectime); fflush(asir_out); } /* free index arrays */ for ( i = 0; i < nred; i++ ) GCFREE(imat[i]->index.c); /* elimination (2nd step) */ colstat = (int *)MALLOC(spcol*sizeof(int)); rank = nd_gauss_elim_sf(spmat,spsugar,sprow,spcol,m,colstat); r0 = 0; for ( i = 0; i < rank; i++ ) { NEXTNODE(r0,r); BDY(r) = (pointer)vect_to_ndv(spmat[i],spcol,col,rhead,s0vect); SG((NDV)BDY(r)) = spsugar[i]; GCFREE(spmat[i]); } if ( r0 ) NEXT(r) = 0; for ( ; i < sprow; i++ ) GCFREE(spmat[i]); get_eg(&eg2); init_eg(&eg_f4_2); add_eg(&eg_f4_2,&eg1,&eg2); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg2); if ( DP_Print ) { fprintf(asir_out,"elim2=%.3fsec,",eg_f4_2.exectime); fprintf(asir_out,"nsp=%d,nred=%d,spmat=(%d,%d),rank=%d ", nsp,nred,sprow,spcol,rank); fprintf(asir_out,"%.3fsec,",eg_f4.exectime); } if ( nz ) { for ( i = 0; i < rank-1; i++ ) NEXT(spactive[i]) = spactive[i+1]; if ( rank > 0 ) { NEXT(spactive[rank-1]) = 0; *nz = spactive[0]; } else *nz = 0; } return r0; } NODE nd_f4_red_lf_main(int m,ND_pairs sp0,int nsp,int trace,UINT *s0vect,int col, NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred) { int spcol,sprow,a; int i,j,k,l,rank; NODE r0,r; ND_pairs sp; ND spol; mpz_t **spmat; mpz_t *svect,*v; int *colstat; struct oEGT eg0,eg1,eg2,eg_f4,eg_f4_1,eg_f4_2; int maxrs; int *spsugar; pointer *w; spcol = col-nred; get_eg(&eg0); /* elimination (1st step) */ spmat = (mpz_t **)MALLOC(nsp*sizeof(mpz_t *)); svect = (mpz_t *)MALLOC(col*sizeof(mpz_t)); spsugar = (int *)MALLOC(nsp*sizeof(int)); for ( a = sprow = 0, sp = sp0; a < nsp; a++, sp = NEXT(sp) ) { nd_sp(m,trace,sp,&spol); if ( !spol ) continue; nd_to_vect_lf(s0vect,col,spol,svect); maxrs = ndv_reduce_vect_lf(svect,trace,col,imat,rvect,nred); for ( i = 0; i < col; i++ ) if ( mpz_sgn(svect[i]) ) break; if ( i < col ) { spmat[sprow] = v = (mpz_t *)MALLOC(spcol*sizeof(mpz_t)); for ( j = k = 0; j < col; j++ ) if ( !rhead[j] ) v[k++][0] = svect[j][0]; spsugar[sprow] = MAX(maxrs,SG(spol)); sprow++; } /* nd_free(spol); */ } get_eg(&eg1); init_eg(&eg_f4_1); add_eg(&eg_f4_1,&eg0,&eg1); if ( DP_Print ) { fprintf(asir_out,"elim1=%.3fsec,",eg_f4_1.exectime); fflush(asir_out); } /* free index arrays */ /* for ( i = 0; i < nred; i++ ) GCFREE(imat[i]->index.c); */ /* elimination (2nd step) */ colstat = (int *)MALLOC(spcol*sizeof(int)); rank = nd_gauss_elim_lf(spmat,spsugar,sprow,spcol,colstat); w = (pointer *)MALLOC(rank*sizeof(pointer)); for ( i = 0; i < rank; i++ ) { #if 0 w[rank-i-1] = (pointer)vect_to_ndv_lf(spmat[i],spcol,col,rhead,s0vect); SG((NDV)w[rank-i-1]) = spsugar[i]; #else w[i] = (pointer)vect_to_ndv_lf(spmat[i],spcol,col,rhead,s0vect); SG((NDV)w[i]) = spsugar[i]; #endif /* GCFREE(spmat[i]); */ } #if 0 qsort(w,rank,sizeof(NDV), (int (*)(const void *,const void *))ndv_compare); #endif r0 = 0; for ( i = 0; i < rank; i++ ) { NEXTNODE(r0,r); BDY(r) = w[i]; } if ( r0 ) NEXT(r) = 0; /* for ( ; i < sprow; i++ ) GCFREE(spmat[i]); */ get_eg(&eg2); init_eg(&eg_f4_2); add_eg(&eg_f4_2,&eg1,&eg2); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg2); if ( DP_Print ) { fprintf(asir_out,"elim2=%.3fsec,",eg_f4_2.exectime); fprintf(asir_out,"nsp=%d,nred=%d,spmat=(%d,%d),rank=%d ", nsp,nred,sprow,spcol,rank); fprintf(asir_out,"%.3fsec,",eg_f4.exectime); } return r0; } NODE nd_f4_red_q_main(ND_pairs sp0,int nsp,int trace,UINT *s0vect,int col, NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred) { int spcol,sprow,a; int i,j,k,l,rank; NODE r0,r; ND_pairs sp; ND spol; Z **spmat; Z *svect,*v; int *colstat; struct oEGT eg0,eg1,eg2,eg_f4,eg_f4_1,eg_f4_2; int maxrs; int *spsugar; pointer *w; spcol = col-nred; get_eg(&eg0); /* elimination (1st step) */ spmat = (Z **)MALLOC(nsp*sizeof(Q *)); svect = (Z *)MALLOC(col*sizeof(Q)); spsugar = (int *)MALLOC(nsp*sizeof(int)); for ( a = sprow = 0, sp = sp0; a < nsp; a++, sp = NEXT(sp) ) { nd_sp(0,trace,sp,&spol); if ( !spol ) continue; nd_to_vect_q(s0vect,col,spol,svect); maxrs = ndv_reduce_vect_q(svect,trace,col,imat,rvect,nred); for ( i = 0; i < col; i++ ) if ( svect[i] ) break; if ( i < col ) { spmat[sprow] = v = (Z *)MALLOC(spcol*sizeof(Q)); for ( j = k = 0; j < col; j++ ) if ( !rhead[j] ) v[k++] = svect[j]; spsugar[sprow] = MAX(maxrs,SG(spol)); sprow++; } /* nd_free(spol); */ } get_eg(&eg1); init_eg(&eg_f4_1); add_eg(&eg_f4_1,&eg0,&eg1); if ( DP_Print ) { fprintf(asir_out,"elim1=%.3fsec,",eg_f4_1.exectime); fflush(asir_out); } /* free index arrays */ /* for ( i = 0; i < nred; i++ ) GCFREE(imat[i]->index.c); */ /* elimination (2nd step) */ colstat = (int *)MALLOC(spcol*sizeof(int)); rank = nd_gauss_elim_q(spmat,spsugar,sprow,spcol,colstat); w = (pointer *)MALLOC(rank*sizeof(pointer)); for ( i = 0; i < rank; i++ ) { #if 0 w[rank-i-1] = (pointer)vect_to_ndv_q(spmat[i],spcol,col,rhead,s0vect); SG((NDV)w[rank-i-1]) = spsugar[i]; #else w[i] = (pointer)vect_to_ndv_q(spmat[i],spcol,col,rhead,s0vect); SG((NDV)w[i]) = spsugar[i]; #endif /* GCFREE(spmat[i]); */ } #if 0 qsort(w,rank,sizeof(NDV), (int (*)(const void *,const void *))ndv_compare); #endif r0 = 0; for ( i = 0; i < rank; i++ ) { NEXTNODE(r0,r); BDY(r) = w[i]; } if ( r0 ) NEXT(r) = 0; /* for ( ; i < sprow; i++ ) GCFREE(spmat[i]); */ get_eg(&eg2); init_eg(&eg_f4_2); add_eg(&eg_f4_2,&eg1,&eg2); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg2); if ( DP_Print ) { fprintf(asir_out,"elim2=%.3fsec,",eg_f4_2.exectime); fprintf(asir_out,"nsp=%d,nred=%d,spmat=(%d,%d),rank=%d ", nsp,nred,sprow,spcol,rank); fprintf(asir_out,"%.3fsec,",eg_f4.exectime); } return r0; } FILE *nd_write,*nd_read; void nd_send_int(int a) { write_int(nd_write,(unsigned int *)&a); } void nd_send_intarray(int *p,int len) { write_intarray(nd_write,(unsigned int *)p,len); } int nd_recv_int() { int a; read_int(nd_read,(unsigned int *)&a); return a; } void nd_recv_intarray(int *p,int len) { read_intarray(nd_read,(unsigned int *)p,len); } void nd_send_ndv(NDV p) { int len,i; NMV m; if ( !p ) nd_send_int(0); else { len = LEN(p); nd_send_int(len); m = BDY(p); for ( i = 0; i < len; i++, NMV_ADV(m) ) { nd_send_int(CM(m)); nd_send_intarray((int *)DL(m),nd_wpd); } } } void nd_send_nd(ND p) { int len,i; NM m; if ( !p ) nd_send_int(0); else { len = LEN(p); nd_send_int(len); m = BDY(p); for ( i = 0; i < len; i++, m = NEXT(m) ) { nd_send_int(CM(m)); nd_send_intarray((int *)DL(m),nd_wpd); } } } NDV nd_recv_ndv() { int len,i; NMV m,m0; NDV r; len = nd_recv_int(); if ( !len ) return 0; else { m0 = m = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(nmv_adv*len); #if 0 ndv_alloc += len*nmv_adv; #endif for ( i = 0; i < len; i++, NMV_ADV(m) ) { CM(m) = nd_recv_int(); nd_recv_intarray((int *)DL(m),nd_wpd); } MKNDV(nd_nvar,m0,len,r); return r; } } int nd_gauss_elim_q(Z **mat0,int *sugar,int row,int col,int *colstat) { int i,j,t,c,rank,inv; int *ci,*ri; Z dn; MAT m,nm; NEWMAT(m); m->row = row; m->col = col; m->body = (pointer **)mat0; rank = generic_gauss_elim(m,&nm,&dn,&ri,&ci); for ( i = 0; i < row; i++ ) for ( j = 0; j < col; j++ ) mat0[i][j] = 0; c = col-rank; for ( i = 0; i < rank; i++ ) { mat0[i][ri[i]] = dn; for ( j = 0; j < c; j++ ) mat0[i][ci[j]] = (Z)BDY(nm)[i][j]; } return rank; } int nd_gauss_elim_mod(UINT **mat0,int *sugar,ND_pairs *spactive,int row,int col,int md,int *colstat) { int i,j,k,l,inv,a,rank,s; unsigned int *t,*pivot,*pk; unsigned int **mat; ND_pairs pair; mat = (unsigned int **)mat0; for ( rank = 0, j = 0; j < col; j++ ) { for ( i = rank; i < row; i++ ) mat[i][j] %= md; for ( i = rank; i < row; i++ ) if ( mat[i][j] ) break; if ( i == row ) { colstat[j] = 0; continue; } else colstat[j] = 1; if ( i != rank ) { t = mat[i]; mat[i] = mat[rank]; mat[rank] = t; s = sugar[i]; sugar[i] = sugar[rank]; sugar[rank] = s; if ( spactive ) { pair = spactive[i]; spactive[i] = spactive[rank]; spactive[rank] = pair; } } pivot = mat[rank]; s = sugar[rank]; inv = invm(pivot[j],md); for ( k = j, pk = pivot+k; k < col; k++, pk++ ) if ( *pk ) { if ( *pk >= (unsigned int)md ) *pk %= md; DMAR(*pk,inv,0,md,*pk) } for ( i = rank+1; i < row; i++ ) { t = mat[i]; if ( (a = t[j]) != 0 ) { sugar[i] = MAX(sugar[i],s); red_by_vect(md,t+j,pivot+j,md-a,col-j); } } rank++; } for ( j = col-1, l = rank-1; j >= 0; j-- ) if ( colstat[j] ) { pivot = mat[l]; s = sugar[l]; for ( i = 0; i < l; i++ ) { t = mat[i]; t[j] %= md; if ( (a = t[j]) != 0 ) { sugar[i] = MAX(sugar[i],s); red_by_vect(md,t+j,pivot+j,md-a,col-j); } } l--; } for ( j = 0, l = 0; l < rank; j++ ) if ( colstat[j] ) { t = mat[l]; for ( k = j; k < col; k++ ) if ( t[k] >= (unsigned int)md ) t[k] %= md; l++; } return rank; } int nd_gauss_elim_sf(UINT **mat0,int *sugar,int row,int col,int md,int *colstat) { int i,j,k,l,inv,a,rank,s; unsigned int *t,*pivot,*pk; unsigned int **mat; mat = (unsigned int **)mat0; for ( rank = 0, j = 0; j < col; j++ ) { for ( i = rank; i < row; i++ ) if ( mat[i][j] ) break; if ( i == row ) { colstat[j] = 0; continue; } else colstat[j] = 1; if ( i != rank ) { t = mat[i]; mat[i] = mat[rank]; mat[rank] = t; s = sugar[i]; sugar[i] = sugar[rank]; sugar[rank] = s; } pivot = mat[rank]; s = sugar[rank]; inv = _invsf(pivot[j]); for ( k = j, pk = pivot+k; k < col; k++, pk++ ) if ( *pk ) *pk = _mulsf(*pk,inv); for ( i = rank+1; i < row; i++ ) { t = mat[i]; if ( (a = t[j]) != 0 ) { sugar[i] = MAX(sugar[i],s); red_by_vect_sf(md,t+j,pivot+j,_chsgnsf(a),col-j); } } rank++; } for ( j = col-1, l = rank-1; j >= 0; j-- ) if ( colstat[j] ) { pivot = mat[l]; s = sugar[l]; for ( i = 0; i < l; i++ ) { t = mat[i]; if ( (a = t[j]) != 0 ) { sugar[i] = MAX(sugar[i],s); red_by_vect_sf(md,t+j,pivot+j,_chsgnsf(a),col-j); } } l--; } return rank; } int ndv_ishomo(NDV p) { NMV m; int len,h; if ( !p ) return 1; len = LEN(p); m = BDY(p); h = TD(DL(m)); NMV_ADV(m); for ( len--; len; len--, NMV_ADV(m) ) if ( TD(DL(m)) != h ) { return 0; } return 1; } void ndv_save(NDV p,int index) { FILE *s; char name[BUFSIZ]; short id; int nv,sugar,len,n,i,td,e,j; NMV m; unsigned int *dl; int mpos; sprintf(name,"%s/%d",Demand,index); s = fopen(name,"w"); savevl(s,0); if ( !p ) { saveobj(s,0); return; } id = O_DP; nv = NV(p); sugar = SG(p); len = LEN(p); write_short(s,(unsigned short *)&id); write_int(s,(unsigned int *)&nv); write_int(s,(unsigned int *)&sugar); write_int(s,(unsigned int *)&len); for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) { saveobj(s,(Obj)CZ(m)); dl = DL(m); td = TD(dl); write_int(s,(unsigned int *)&td); for ( j = 0; j < nv; j++ ) { e = GET_EXP(dl,j); write_int(s,(unsigned int *)&e); } if ( nd_module ) { mpos = MPOS(dl); write_int(s,(unsigned int *)&mpos); } } fclose(s); } void nd_save_mod(ND p,int index) { FILE *s; char name[BUFSIZ]; int nv,sugar,len,c; NM m; sprintf(name,"%s/%d",Demand,index); s = fopen(name,"w"); if ( !p ) { len = 0; write_int(s,(unsigned int *)&len); fclose(s); return; } nv = NV(p); sugar = SG(p); len = LEN(p); write_int(s,(unsigned int *)&nv); write_int(s,(unsigned int *)&sugar); write_int(s,(unsigned int *)&len); for ( m = BDY(p); m; m = NEXT(m) ) { c = CM(m); write_int(s,(unsigned int *)&c); write_intarray(s,(unsigned int *)DL(m),nd_wpd); } fclose(s); } NDV ndv_load(int index) { FILE *s; char name[BUFSIZ]; short id; int nv,sugar,len,n,i,td,e,j; NDV d; NMV m0,m; unsigned int *dl; Obj obj; int mpos; sprintf(name,"%s/%d",Demand,index); s = fopen(name,"r"); if ( !s ) return 0; skipvl(s); read_short(s,(unsigned short *)&id); if ( !id ) return 0; read_int(s,(unsigned int *)&nv); read_int(s,(unsigned int *)&sugar); read_int(s,(unsigned int *)&len); m0 = m = MALLOC(len*nmv_adv); for ( i = 0; i < len; i++, NMV_ADV(m) ) { loadobj(s,&obj); CZ(m) = (Z)obj; dl = DL(m); ndl_zero(dl); read_int(s,(unsigned int *)&td); TD(dl) = td; for ( j = 0; j < nv; j++ ) { read_int(s,(unsigned int *)&e); PUT_EXP(dl,j,e); } if ( nd_module ) { read_int(s,(unsigned int *)&mpos); MPOS(dl) = mpos; } if ( nd_blockmask ) ndl_weight_mask(dl); } fclose(s); MKNDV(nv,m0,len,d); SG(d) = sugar; return d; } ND nd_load_mod(int index) { FILE *s; char name[BUFSIZ]; int nv,sugar,len,i,c; ND d; NM m0,m; sprintf(name,"%s/%d",Demand,index); s = fopen(name,"r"); /* if the file does not exist, it means p[index]=0 */ if ( !s ) return 0; read_int(s,(unsigned int *)&nv); if ( !nv ) { fclose(s); return 0; } read_int(s,(unsigned int *)&sugar); read_int(s,(unsigned int *)&len); for ( m0 = 0, i = 0; i < len; i++ ) { NEXTNM(m0,m); read_int(s,(unsigned int *)&c); CM(m) = c; read_intarray(s,(unsigned int *)DL(m),nd_wpd); } NEXT(m) = 0; MKND(nv,m0,len,d); SG(d) = sugar; fclose(s); return d; } void nd_det(int mod,MAT f,P *rp) { VL fv,tv; int n,i,j,max,e,nvar,sgn,k0,l0,len0,len,k,l,a; pointer **m; P **w; P mp,r; NDV **dm; NDV *t,*mi,*mj; NDV d,s,mij,mjj; ND u; NMV nmv; UINT *bound; PGeoBucket bucket; struct order_spec *ord; Z dq,dt,ds; Z mone; Z gn,qn,dn0,nm,dn; create_order_spec(0,0,&ord); nd_init_ord(ord); get_vars((Obj)f,&fv); if ( f->row != f->col ) error("nd_det : non-square matrix"); n = f->row; m = f->body; for ( nvar = 0, tv = fv; tv; tv = NEXT(tv), nvar++ ); if ( !nvar ) { if ( !mod ) detp(CO,(P **)m,n,rp); else { w = (P **)almat_pointer(n,n); for ( i = 0; i < n; i++ ) for ( j = 0; j < n; j++ ) ptomp(mod,(P)m[i][j],&w[i][j]); detmp(CO,mod,w,n,&mp); mptop(mp,rp); } return; } if ( !mod ) { w = (P **)almat_pointer(n,n); dq = ONE; for ( i = 0; i < n; i++ ) { dn0 = ONE; for ( j = 0; j < n; j++ ) { if ( !m[i][j] ) continue; lgp(m[i][j],&nm,&dn); gcdz(dn0,dn,&gn); divsz(dn0,gn,&qn); mulz(qn,dn,&dn0); } if ( !UNIZ(dn0) ) { ds = dn0; for ( j = 0; j < n; j++ ) mulp(CO,(P)m[i][j],(P)ds,&w[i][j]); mulz(dq,ds,&dt); dq = dt; } else for ( j = 0; j < n; j++ ) w[i][j] = (P)m[i][j]; } m = (pointer **)w; } for ( i = 0, max = 1; i < n; i++ ) for ( j = 0; j < n; j++ ) for ( tv = fv; tv; tv = NEXT(tv) ) { e = getdeg(tv->v,(P)m[i][j]); max = MAX(e,max); } nd_setup_parameters(nvar,max); dm = (NDV **)almat_pointer(n,n); for ( i = 0, max = 1; i < n; i++ ) for ( j = 0; j < n; j++ ) { dm[i][j] = ptondv(CO,fv,m[i][j]); if ( mod ) ndv_mod(mod,dm[i][j]); if ( dm[i][j] && !LEN(dm[i][j]) ) dm[i][j] = 0; } d = ptondv(CO,fv,(P)ONE); if ( mod ) ndv_mod(mod,d); chsgnz(ONE,&mone); for ( j = 0, sgn = 1; j < n; j++ ) { if ( DP_Print ) { fprintf(asir_out,"."); } for ( i = j; i < n && !dm[i][j]; i++ ); if ( i == n ) { *rp = 0; return; } k0 = i; l0 = j; len0 = LEN(dm[k0][l0]); for ( k = j; k < n; k++ ) for ( l = j; l < n; l++ ) if ( dm[k][l] && LEN(dm[k][l]) < len0 ) { k0 = k; l0 = l; len0 = LEN(dm[k][l]); } if ( k0 != j ) { t = dm[j]; dm[j] = dm[k0]; dm[k0] = t; sgn = -sgn; } if ( l0 != j ) { for ( k = j; k < n; k++ ) { s = dm[k][j]; dm[k][j] = dm[k][l0]; dm[k][l0] = s; } sgn = -sgn; } bound = nd_det_compute_bound(dm,n,j); for ( k = 0; k < nd_nvar; k++ ) if ( bound[k]*2 > nd_mask0 ) break; if ( k < nd_nvar ) nd_det_reconstruct(dm,n,j,d); for ( i = j+1, mj = dm[j], mjj = mj[j]; i < n; i++ ) { /* if ( DP_Print ) fprintf(asir_out," i=%d\n ",i); */ mi = dm[i]; mij = mi[j]; if ( mod ) ndv_mul_c(mod,mij,mod-1); else ndv_mul_c_q(mij,mone); for ( k = j+1; k < n; k++ ) { /* if ( DP_Print ) fprintf(asir_out,"k=%d ",k); */ bucket = create_pbucket(); if ( mi[k] ) { nmv = BDY(mjj); len = LEN(mjj); for ( a = 0; a < len; a++, NMV_ADV(nmv) ) { u = ndv_mul_nmv_trunc(mod,nmv,mi[k],DL(BDY(d))); add_pbucket(mod,bucket,u); } } if ( mj[k] && mij ) { nmv = BDY(mij); len = LEN(mij); for ( a = 0; a < len; a++, NMV_ADV(nmv) ) { u = ndv_mul_nmv_trunc(mod,nmv,mj[k],DL(BDY(d))); add_pbucket(mod,bucket,u); } } u = nd_quo(mod,bucket,d); mi[k] = ndtondv(mod,u); } /* if ( DP_Print ) fprintf(asir_out,"\n",k); */ } d = mjj; } if ( DP_Print ) { fprintf(asir_out,"\n"); } if ( sgn < 0 ) { if ( mod ) ndv_mul_c(mod,d,mod-1); else ndv_mul_c_q(d,mone); } r = ndvtop(mod,CO,fv,d); if ( !mod && !UNIQ(dq) ) divsp(CO,r,(P)dq,rp); else *rp = r; } ND ndv_mul_nmv_trunc(int mod,NMV m0,NDV p,UINT *d) { NM mr,mr0; NM tnm; NMV m; UINT *d0,*dt,*dm; int c,n,td,i,c1,c2,len; Z q; ND r; if ( !p ) return 0; else { n = NV(p); m = BDY(p); len = LEN(p); d0 = DL(m0); td = TD(d); mr0 = 0; NEWNM(tnm); if ( mod ) { c = CM(m0); for ( i = 0; i < len; i++, NMV_ADV(m) ) { ndl_add(DL(m),d0,DL(tnm)); if ( ndl_reducible(DL(tnm),d) ) { NEXTNM(mr0,mr); c1 = CM(m); DMAR(c1,c,0,mod,c2); CM(mr) = c2; ndl_copy(DL(tnm),DL(mr)); } } } else { q = CZ(m0); for ( i = 0; i < len; i++, NMV_ADV(m) ) { ndl_add(DL(m),d0,DL(tnm)); if ( ndl_reducible(DL(tnm),d) ) { NEXTNM(mr0,mr); mulz(CZ(m),q,&CZ(mr)); ndl_copy(DL(tnm),DL(mr)); } } } if ( !mr0 ) return 0; else { NEXT(mr) = 0; for ( len = 0, mr = mr0; mr; mr = NEXT(mr), len++ ); MKND(NV(p),mr0,len,r); SG(r) = SG(p) + TD(d0); return r; } } } void nd_det_reconstruct(NDV **dm,int n,int j,NDV d) { int i,obpe,oadv,h,k,l; static NM prev_nm_free_list; EPOS oepos; obpe = nd_bpe; oadv = nmv_adv; oepos = nd_epos; if ( obpe < 2 ) nd_bpe = 2; else if ( obpe < 3 ) nd_bpe = 3; else if ( obpe < 4 ) nd_bpe = 4; else if ( obpe < 5 ) nd_bpe = 5; else if ( obpe < 6 ) nd_bpe = 6; else if ( obpe < 8 ) nd_bpe = 8; else if ( obpe < 10 ) nd_bpe = 10; else if ( obpe < 16 ) nd_bpe = 16; else if ( obpe < 32 ) nd_bpe = 32; else error("nd_det_reconstruct : exponent too large"); nd_setup_parameters(nd_nvar,0); prev_nm_free_list = _nm_free_list; _nm_free_list = 0; for ( k = j; k < n; k++ ) for (l = j; l < n; l++ ) ndv_realloc(dm[k][l],obpe,oadv,oepos); ndv_realloc(d,obpe,oadv,oepos); prev_nm_free_list = 0; #if 0 GC_gcollect(); #endif } /* returns a UINT array containing degree bounds */ UINT *nd_det_compute_bound(NDV **dm,int n,int j) { UINT *d0,*d1,*d,*t,*r; int k,l,i; d0 = (UINT *)MALLOC(nd_nvar*sizeof(UINT)); for ( k = 0; k < nd_nvar; k++ ) d0[k] = 0; for ( k = j; k < n; k++ ) for ( l = j; l < n; l++ ) if ( dm[k][l] ) { d = ndv_compute_bound(dm[k][l]); for ( i = 0; i < nd_nvar; i++ ) d0[i] = MAX(d0[i],d[i]); } return d0; } DL nd_separate_d(UINT *d,UINT *trans) { int n,td,i,e,j; DL a; ndl_zero(trans); td = 0; for ( i = 0; i < nd_ntrans; i++ ) { e = GET_EXP(d,i); PUT_EXP(trans,i,e); td += MUL_WEIGHT(e,i); } if ( nd_ntrans+nd_nalg < nd_nvar ) { /* homogenized */ i = nd_nvar-1; e = GET_EXP(d,i); PUT_EXP(trans,i,e); td += MUL_WEIGHT(e,i); } TD(trans) = td; if ( nd_blockmask) ndl_weight_mask(trans); NEWDL(a,nd_nalg); td = 0; for ( i = 0; i < nd_nalg; i++ ) { j = nd_ntrans+i; e = GET_EXP(d,j); a->d[i] = e; td += e; } a->td = td; return a; } int nd_monic(int mod,ND *p) { UINT *trans,*t; DL alg; MP mp0,mp; NM m,m0,m1,ma0,ma,mb,mr0,mr; ND r; DL dl; DP nm; NDV ndv; DAlg inv,cd; ND s,c; Z l,mul; Z ln; int n,ntrans,i,e,td,is_lc,len; NumberField nf; struct oEGT eg0,eg1; if ( !(nf = get_numberfield()) ) error("nd_monic : current_numberfield is not set"); /* Q coef -> DAlg coef */ NEWNM(ma0); ma = ma0; m = BDY(*p); is_lc = 1; while ( 1 ) { NEWMP(mp0); mp = mp0; mp->c = (Obj)CZ(m); mp->dl = nd_separate_d(DL(m),DL(ma)); NEWNM(mb); for ( m = NEXT(m); m; m = NEXT(m) ) { alg = nd_separate_d(DL(m),DL(mb)); if ( !ndl_equal(DL(ma),DL(mb)) ) break; NEXTMP(mp0,mp); mp->c = (Obj)CZ(m); mp->dl = alg; } NEXT(mp) = 0; MKDP(nd_nalg,mp0,nm); MKDAlg(nm,ONE,cd); if ( is_lc == 1 ) { /* if the lc is a rational number, we have nothing to do */ if ( !mp0->dl->td ) return 1; get_eg(&eg0); invdalg(cd,&inv); get_eg(&eg1); add_eg(&eg_invdalg,&eg0,&eg1); /* check the validity of inv */ if ( mod && !remqi((Q)inv->dn,mod) ) return 0; CA(ma) = nf->one; is_lc = 0; ln = ONE; } else { muldalg(cd,inv,&CA(ma)); lcmz(ln,CA(ma)->dn,&ln); } if ( m ) { NEXT(ma) = mb; ma = mb; } else { NEXT(ma) = 0; break; } } /* l = lcm(denoms) */ l = ln; for ( mr0 = 0, m = ma0; m; m = NEXT(m) ) { divsz(l,CA(m)->dn,&mul); for ( mp = BDY(CA(m)->nm); mp; mp = NEXT(mp) ) { NEXTNM(mr0,mr); mulz((Z)mp->c,mul,&CZ(mr)); dl = mp->dl; td = TD(DL(m)); ndl_copy(DL(m),DL(mr)); for ( i = 0; i < nd_nalg; i++ ) { e = dl->d[i]; PUT_EXP(DL(mr),i+nd_ntrans,e); td += MUL_WEIGHT(e,i+nd_ntrans); } if ( nd_module ) MPOS(DL(mr)) = MPOS(DL(m)); TD(DL(mr)) = td; if ( nd_blockmask) ndl_weight_mask(DL(mr)); } } NEXT(mr) = 0; for ( len = 0, mr = mr0; mr; mr = NEXT(mr), len++ ); MKND(NV(*p),mr0,len,r); /* XXX */ SG(r) = SG(*p); nd_free(*p); *p = r; return 1; } NODE reverse_node(NODE n) { NODE t,t1; for ( t = 0; n; n = NEXT(n) ) { MKNODE(t1,BDY(n),t); t = t1; } return t; } P ndc_div(int mod,union oNDC a,union oNDC b) { union oNDC c; int inv,t; if ( mod == -1 ) c.m = _mulsf(a.m,_invsf(b.m)); else if ( mod == -2 ) divlf(a.z,b.z,&c.z); else if ( mod ) { inv = invm(b.m,mod); DMAR(a.m,inv,0,mod,t); c.m = t; } else if ( nd_vc ) divsp(nd_vc,a.p,b.p,&c.p); else divsz(a.z,b.z,&c.z); return ndctop(mod,c); } P ndctop(int mod,union oNDC c) { Z q; int e; GFS gfs; if ( mod == -1 ) { e = IFTOF(c.m); MKGFS(e,gfs); return (P)gfs; } else if ( mod == -2 ) { q = c.z; return (P)q; } else if ( mod > 0 ) { STOZ(c.m,q); return (P)q; } else return (P)c.p; } /* [0,0,0,cont] = p -> p/cont */ void finalize_tracelist(int i,P cont) { LIST l; NODE node; Z iq; if ( !UNIQ(cont) ) { node = mknode(4,NULLP,NULLP,NULLP,cont); MKLIST(l,node); MKNODE(node,l,nd_tracelist); nd_tracelist = node; } STOZ(i,iq); nd_tracelist = reverse_node(nd_tracelist); MKLIST(l,nd_tracelist); node = mknode(2,iq,l); MKLIST(l,node); MKNODE(node,l,nd_alltracelist); MKLIST(l,node); nd_alltracelist = node; nd_tracelist = 0; } void conv_ilist(int demand,int trace,NODE g,int **indp) { int n,i,j; int *ind; NODE t; n = length(g); ind = (int *)MALLOC(n*sizeof(int)); for ( i = 0, t = g; i < n; i++, t = NEXT(t) ) { j = (long)BDY(t); ind[i] = j; BDY(t) = (pointer)(demand?ndv_load(j):(trace?nd_ps_trace[j]:nd_ps[j])); } if ( indp ) *indp = ind; } NODE conv_ilist_s(int demand,int trace,int **indp) { int n,i,j; int *ind; NODE g0,g; n = nd_psn; ind = (int *)MALLOC(n*sizeof(int)); g0 = 0; for ( i = 0; i < n; i++ ) { ind[i] = i; NEXTNODE(g0,g); BDY(g) = (pointer)(demand?ndv_load(i):(trace?nd_ps_trace[i]:nd_ps[i])); } if ( g0 ) NEXT(g) = 0; if ( indp ) *indp = ind; return g0; } void parse_nd_option(NODE opt) { NODE t,p,u; int i,s,n; char *key; Obj value; nd_gentrace = 0; nd_gensyz = 0; nd_nora = 0; nd_gbblock = 0; nd_newelim = 0; nd_intersect = 0; nd_nzlist = 0; nd_splist = 0; nd_check_splist = 0; nd_sugarweight = 0; nd_f4red =0; nd_rank0 = 0; for ( t = opt; t; t = NEXT(t) ) { p = BDY((LIST)BDY(t)); key = BDY((STRING)BDY(p)); value = (Obj)BDY(NEXT(p)); if ( !strcmp(key,"gentrace") ) nd_gentrace = value?1:0; else if ( !strcmp(key,"gensyz") ) nd_gensyz = value?1:0; else if ( !strcmp(key,"nora") ) nd_nora = value?1:0; else if ( !strcmp(key,"gbblock") ) { if ( value && OID(value) == O_LIST ) { u = BDY((LIST)value); nd_gbblock = MALLOC((2*length(u)+1)*sizeof(int)); for ( i = 0; u; u = NEXT(u) ) { p = BDY((LIST)BDY(u)); s = nd_gbblock[i++] = ZTOS((Q)BDY(p)); nd_gbblock[i++] = s+ZTOS((Q)BDY(NEXT(p)))-1; } nd_gbblock[i] = -1; } else nd_gbblock = 0; } else if ( !strcmp(key,"newelim") ) nd_newelim = value?1:0; else if ( !strcmp(key,"intersect") ) nd_intersect = value?1:0; else if ( !strcmp(key,"syzgen") ) nd_intersect = ZTOS((Q)value); else if ( !strcmp(key,"lf") ) nd_lf = value?1:0; else if ( !strcmp(key,"trace") ) { if ( value ) { u = BDY((LIST)value); nd_nzlist = BDY((LIST)ARG2(u)); nd_bpe = ZTOS((Q)ARG3(u)); } } else if ( !strcmp(key,"f4red") ) { nd_f4red = ZTOS((Q)value); } else if ( !strcmp(key,"rank0") ) { nd_rank0 = value?1:0; } else if ( !strcmp(key,"splist") ) { nd_splist = value?1:0; } else if ( !strcmp(key,"check_splist") ) { nd_check_splist = BDY((LIST)value); } else if ( !strcmp(key,"sugarweight") ) { u = BDY((LIST)value); n = length(u); nd_sugarweight = MALLOC(n*sizeof(int)); for ( i = 0; i < n; i++, u = NEXT(u) ) nd_sugarweight[i] = ZTOS((Q)BDY(u)); } } } ND mdptond(DP d); ND nd_mul_nm(int mod,NM m0,ND p); ND nd_mul_nm_lf(NM m0,ND p); ND *btog(NODE ti,ND **p,int nb,int mod); ND btog_one(NODE ti,ND *p,int nb,int mod); MAT nd_btog(LIST f,LIST v,int m,struct order_spec *ord,LIST tlist,MAT *rp); VECT nd_btog_one(LIST f,LIST v,int m,struct order_spec *ord,LIST tlist,int pos,MAT *rp); /* d:monomial */ ND mdptond(DP d) { NM m; ND r; if ( OID(d) == 1 ) r = ptond(CO,CO,(P)d); else { NEWNM(m); dltondl(NV(d),BDY(d)->dl,DL(m)); CZ(m) = (Z)BDY(d)->c; NEXT(m) = 0; MKND(NV(d),m,1,r); } return r; } ND nd_mul_nm(int mod,NM m0,ND p) { UINT *d0; int c0,c1,c; NM tm,mr,mr0; ND r; if ( !p ) return 0; d0 = DL(m0); c0 = CM(m0); mr0 = 0; for ( tm = BDY(p); tm; tm = NEXT(tm) ) { NEXTNM(mr0,mr); c = CM(tm); DMAR(c0,c,0,mod,c1); CM(mr) = c1; ndl_add(d0,DL(tm),DL(mr)); } NEXT(mr) = 0; MKND(NV(p),mr0,LEN(p),r); return r; } ND nd_mul_nm_lf(NM m0,ND p) { UINT *d0; Z c0,c1,c; NM tm,mr,mr0; ND r; if ( !p ) return 0; d0 = DL(m0); c0 = CZ(m0); mr0 = 0; for ( tm = BDY(p); tm; tm = NEXT(tm) ) { NEXTNM(mr0,mr); c = CZ(tm); mullf(c0,CZ(tm),&c1); CZ(mr) = c1; ndl_add(d0,DL(tm),DL(mr)); } NEXT(mr) = 0; MKND(NV(p),mr0,LEN(p),r); return r; } ND *btog(NODE ti,ND **p,int nb,int mod) { PGeoBucket *r; int i,ci; NODE t,s; ND m,tp; ND *pi,*rd; P c; r = (PGeoBucket *)MALLOC(nb*sizeof(PGeoBucket)); for ( i = 0; i < nb; i++ ) r[i] = create_pbucket(); for ( t = ti; t; t = NEXT(t) ) { s = BDY((LIST)BDY(t)); if ( ARG0(s) ) { m = mdptond((DP)ARG2(s)); ptomp(mod,(P)HCZ(m),&c); if ( (ci = ((MQ)c)->cont) != 0 ) { HCM(m) = ci; pi = p[ZTOS((Q)ARG1(s))]; for ( i = 0; i < nb; i++ ) { tp = nd_mul_nm(mod,BDY(m),pi[i]); add_pbucket(mod,r[i],tp); } } ci = 1; } else { ptomp(mod,(P)ARG3(s),&c); ci = ((MQ)c)->cont; ci = invm(ci,mod); } } rd = (ND *)MALLOC(nb*sizeof(ND)); for ( i = 0; i < nb; i++ ) rd[i] = normalize_pbucket(mod,r[i]); if ( ci != 1 ) for ( i = 0; i < nb; i++ ) nd_mul_c(mod,rd[i],ci); return rd; } /* YYY */ ND *btog_lf(NODE ti,ND **p,int nb) { PGeoBucket *r; int i; NODE t,s; ND m,tp; ND *pi,*rd; LM lm; Z lf,c; r = (PGeoBucket *)MALLOC(nb*sizeof(PGeoBucket)); for ( i = 0; i < nb; i++ ) r[i] = create_pbucket(); for ( t = ti; t; t = NEXT(t) ) { s = BDY((LIST)BDY(t)); if ( ARG0(s) ) { m = mdptond((DP)ARG2(s)); simp_ff((Obj)HCZ(m),(Obj *)&lm); if ( lm ) { lmtolf(lm,&lf); HCZ(m) = lf; pi = p[ZTOS((Q)ARG1(s))]; for ( i = 0; i < nb; i++ ) { tp = nd_mul_nm_lf(BDY(m),pi[i]); add_pbucket(-2,r[i],tp); } } c = ONE; } else { simp_ff((Obj)ARG3(s),(Obj *)&lm); lmtolf(lm,&lf); invz(lf,current_mod_lf,&c); } } rd = (ND *)MALLOC(nb*sizeof(ND)); for ( i = 0; i < nb; i++ ) rd[i] = normalize_pbucket(-2,r[i]); for ( i = 0; i < nb; i++ ) nd_mul_c_lf(rd[i],c); return rd; } ND btog_one(NODE ti,ND *p,int nb,int mod) { PGeoBucket r; int i,ci,j; NODE t,s; ND m,tp; ND pi,rd; P c; r = create_pbucket(); for ( t = ti; t; t = NEXT(t) ) { s = BDY((LIST)BDY(t)); if ( ARG0(s) ) { m = mdptond((DP)ARG2(s)); ptomp(mod,(P)HCZ(m),&c); if ( (ci = ((MQ)c)->cont) != 0 ) { HCM(m) = ci; pi = p[j=ZTOS((Q)ARG1(s))]; if ( !pi ) { pi = nd_load_mod(j); tp = nd_mul_nm(mod,BDY(m),pi); nd_free(pi); add_pbucket(mod,r,tp); } else { tp = nd_mul_nm(mod,BDY(m),pi); add_pbucket(mod,r,tp); } } ci = 1; } else { ptomp(mod,(P)ARG3(s),&c); ci = ((MQ)c)->cont; ci = invm(ci,mod); } } rd = normalize_pbucket(mod,r); free_pbucket(r); if ( ci != 1 ) nd_mul_c(mod,rd,ci); return rd; } MAT nd_btog_lf(LIST f,LIST v,struct order_spec *ord,LIST tlist,MAT *rp); MAT nd_btog(LIST f,LIST v,int mod,struct order_spec *ord,LIST tlist,MAT *rp) { int i,j,n,m,nb,pi0,pi1,nvar; VL fv,tv,vv; NODE permtrace,perm,trace,intred,ind,t,pi,ti; ND **p; ND *c; ND u; P inv; MAT mat; if ( mod == -2 ) return nd_btog_lf(f,v,ord,tlist,rp); parse_nd_option(current_option); get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc); for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ ); switch ( ord->id ) { case 1: if ( ord->nv != nvar ) error("nd_check : invalid order specification"); break; default: break; } nd_init_ord(ord); #if 0 nd_bpe = ZTOS((Q)ARG7(BDY(tlist))); #else nd_bpe = 32; #endif nd_setup_parameters(nvar,0); permtrace = BDY((LIST)ARG2(BDY(tlist))); intred = BDY((LIST)ARG3(BDY(tlist))); ind = BDY((LIST)ARG4(BDY(tlist))); perm = BDY((LIST)BDY(permtrace)); trace =NEXT(permtrace); for ( i = length(perm)-1, t = trace; t; t = NEXT(t) ) { j = ZTOS((Q)BDY(BDY((LIST)BDY(t)))); if ( j > i ) i = j; } n = i+1; nb = length(BDY(f)); p = (ND **)MALLOC(n*sizeof(ND *)); for ( t = perm, i = 0; t; t = NEXT(t), i++ ) { pi = BDY((LIST)BDY(t)); pi0 = ZTOS((Q)ARG0(pi)); pi1 = ZTOS((Q)ARG1(pi)); p[pi0] = c = (ND *)MALLOC(nb*sizeof(ND)); ptomp(mod,(P)ARG2(pi),&inv); ((MQ)inv)->cont = invm(((MQ)inv)->cont,mod); u = ptond(CO,vv,(P)ONE); HCM(u) = ((MQ)inv)->cont; c[pi1] = u; } for ( t = trace,i=0; t; t = NEXT(t), i++ ) { printf("%d ",i); fflush(stdout); ti = BDY((LIST)BDY(t)); p[j=ZTOS((Q)ARG0(ti))] = btog(BDY((LIST)ARG1(ti)),p,nb,mod); } for ( t = intred, i=0; t; t = NEXT(t), i++ ) { printf("%d ",i); fflush(stdout); ti = BDY((LIST)BDY(t)); p[j=ZTOS((Q)ARG0(ti))] = btog(BDY((LIST)ARG1(ti)),p,nb,mod); } m = length(ind); MKMAT(mat,nb,m); for ( j = 0, t = ind; j < m; j++, t = NEXT(t) ) for ( i = 0, c = p[ZTOS((Q)BDY(t))]; i < nb; i++ ) BDY(mat)[i][j] = ndtodp(mod,c[i]); return mat; } MAT nd_btog_lf(LIST f,LIST v,struct order_spec *ord,LIST tlist,MAT *rp) { int i,j,n,m,nb,pi0,pi1,nvar; VL fv,tv,vv; NODE permtrace,perm,trace,intred,ind,t,pi,ti; ND **p; ND *c; ND u; MAT mat; LM lm; Z lf,inv; parse_nd_option(current_option); get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc); for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ ); switch ( ord->id ) { case 1: if ( ord->nv != nvar ) error("nd_check : invalid order specification"); break; default: break; } nd_init_ord(ord); #if 0 nd_bpe = ZTOS((Q)ARG7(BDY(tlist))); #else nd_bpe = 32; #endif nd_setup_parameters(nvar,0); permtrace = BDY((LIST)ARG2(BDY(tlist))); intred = BDY((LIST)ARG3(BDY(tlist))); ind = BDY((LIST)ARG4(BDY(tlist))); perm = BDY((LIST)BDY(permtrace)); trace =NEXT(permtrace); for ( i = length(perm)-1, t = trace; t; t = NEXT(t) ) { j = ZTOS((Q)BDY(BDY((LIST)BDY(t)))); if ( j > i ) i = j; } n = i+1; nb = length(BDY(f)); p = (ND **)MALLOC(n*sizeof(ND *)); for ( t = perm, i = 0; t; t = NEXT(t), i++ ) { pi = BDY((LIST)BDY(t)); pi0 = ZTOS((Q)ARG0(pi)); pi1 = ZTOS((Q)ARG1(pi)); p[pi0] = c = (ND *)MALLOC(nb*sizeof(ND)); simp_ff((Obj)ARG2(pi),(Obj *)&lm); lmtolf(lm,&lf); invz(lf,current_mod_lf,&inv); u = ptond(CO,vv,(P)ONE); HCZ(u) = inv; c[pi1] = u; } for ( t = trace,i=0; t; t = NEXT(t), i++ ) { printf("%d ",i); fflush(stdout); ti = BDY((LIST)BDY(t)); p[j=ZTOS((Q)ARG0(ti))] = btog_lf(BDY((LIST)ARG1(ti)),p,nb); } for ( t = intred, i=0; t; t = NEXT(t), i++ ) { printf("%d ",i); fflush(stdout); ti = BDY((LIST)BDY(t)); p[j=ZTOS((Q)ARG0(ti))] = btog_lf(BDY((LIST)ARG1(ti)),p,nb); } m = length(ind); MKMAT(mat,nb,m); for ( j = 0, t = ind; j < m; j++, t = NEXT(t) ) for ( i = 0, c = p[ZTOS((Q)BDY(t))]; i < nb; i++ ) BDY(mat)[i][j] = ndtodp(-2,c[i]); return mat; } VECT nd_btog_one(LIST f,LIST v,int mod,struct order_spec *ord, LIST tlist,int pos,MAT *rp) { int i,j,n,m,nb,pi0,pi1,nvar; VL fv,tv,vv; NODE permtrace,perm,trace,intred,ind,t,pi,ti; ND *p; ND *c; ND u; P inv; VECT vect; if ( mod == -2 ) error("nd_btog_one : not implemented yet for a large finite field"); parse_nd_option(current_option); get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc); for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ ); switch ( ord->id ) { case 1: if ( ord->nv != nvar ) error("nd_check : invalid order specification"); break; default: break; } nd_init_ord(ord); #if 0 nd_bpe = ZTOS((Q)ARG7(BDY(tlist))); #else nd_bpe = 32; #endif nd_setup_parameters(nvar,0); permtrace = BDY((LIST)ARG2(BDY(tlist))); intred = BDY((LIST)ARG3(BDY(tlist))); ind = BDY((LIST)ARG4(BDY(tlist))); perm = BDY((LIST)BDY(permtrace)); trace =NEXT(permtrace); for ( i = length(perm)-1, t = trace; t; t = NEXT(t) ) { j = ZTOS((Q)BDY(BDY((LIST)BDY(t)))); if ( j > i ) i = j; } n = i+1; nb = length(BDY(f)); p = (ND *)MALLOC(n*sizeof(ND *)); for ( t = perm, i = 0; t; t = NEXT(t), i++ ) { pi = BDY((LIST)BDY(t)); pi0 = ZTOS((Q)ARG0(pi)); pi1 = ZTOS((Q)ARG1(pi)); if ( pi1 == pos ) { ptomp(mod,(P)ARG2(pi),&inv); ((MQ)inv)->cont = invm(((MQ)inv)->cont,mod); u = ptond(CO,vv,(P)ONE); HCM(u) = ((MQ)inv)->cont; p[pi0] = u; } } for ( t = trace,i=0; t; t = NEXT(t), i++ ) { printf("%d ",i); fflush(stdout); ti = BDY((LIST)BDY(t)); p[j=ZTOS((Q)ARG0(ti))] = btog_one(BDY((LIST)ARG1(ti)),p,nb,mod); if ( Demand ) { nd_save_mod(p[j],j); nd_free(p[j]); p[j] = 0; } } for ( t = intred, i=0; t; t = NEXT(t), i++ ) { printf("%d ",i); fflush(stdout); ti = BDY((LIST)BDY(t)); p[j=ZTOS((Q)ARG0(ti))] = btog_one(BDY((LIST)ARG1(ti)),p,nb,mod); if ( Demand ) { nd_save_mod(p[j],j); nd_free(p[j]); p[j] = 0; } } m = length(ind); MKVECT(vect,m); for ( j = 0, t = ind; j < m; j++, t = NEXT(t) ) { u = p[ZTOS((Q)BDY(t))]; if ( !u ) { u = nd_load_mod(ZTOS((Q)BDY(t))); BDY(vect)[j] = ndtodp(mod,u); nd_free(u); } else BDY(vect)[j] = ndtodp(mod,u); } return vect; } void ndv_print_lf(NDV p) { NMV m; int i,len; if ( !p ) printf("0\n"); else { len = LEN(p); for ( m = BDY(p), i = 0; i < len; i++, NMV_ADV(m) ) { printf("+"); mpz_out_str(asir_out,10,BDY(CZ(m))); printf("*"); ndl_print(DL(m)); } printf("\n"); } } void nd_f4_lf_trace(LIST f,LIST v,int trace,int homo,struct order_spec *ord,LIST *rp) { VL tv,fv,vv,vc,av; NODE fd,fd0,in0,in,r,r0,t,s,cand,alist; int m,nocheck,nvar,mindex,e,max; NDV c; NMV a; P p,zp; Q dmy; EPOS oepos; int obpe,oadv,wmax,i,len,cbpe,ishomo,nalg,mrank,trank,ompos; Alg alpha,dp; P poly; LIST f1,f2,zpl; Obj obj; NumberField nf; struct order_spec *ord1; struct oEGT eg_check,eg0,eg1; NODE tr,tl1,tl2,tl3,tl4; LIST l1,l2,l3,l4,l5; int *perm; int j,ret; NODE retn; Q jq,bpe; nd_module = 0; parse_nd_option(current_option); get_vars((Obj)f,&fv); pltovl(v,&vv); vlminus(fv,vv,&nd_vc); if ( nd_vc ) error("nd_f4_lf_trace : computation over a rational function field is not implemented"); for ( nvar = 0, tv = vv; tv; tv = NEXT(tv), nvar++ ); switch ( ord->id ) { case 1: if ( ord->nv != nvar ) error("nd_f4_lf_trace : invalid order specification"); break; default: break; } nd_ntrans = nvar; nd_nalg = 0; nocheck = 0; mindex = 0; /* do not use on-demand load/save */ nd_demand = 0; m = trace > 1 ? trace : get_lprime(mindex); nd_init_ord(ord); mrank = 0; for ( t = BDY(f), max = 1; t; t = NEXT(t) ) for ( tv = vv; tv; tv = NEXT(tv) ) { if ( nd_module ) { s = BDY((LIST)BDY(t)); trank = length(s); mrank = MAX(mrank,trank); for ( ; s; s = NEXT(s) ) { e = getdeg(tv->v,(P)BDY(s)); max = MAX(e,max); } } else { e = getdeg(tv->v,(P)BDY(t)); max = MAX(e,max); } } nd_setup_parameters(nvar,max); obpe = nd_bpe; oadv = nmv_adv; oepos = nd_epos; ompos = nd_mpos; ishomo = 1; /* XXX */ for ( in0 = 0, fd0 = 0, t = BDY(f); t; t = NEXT(t) ) { if ( nd_module ) { c = (pointer)pltondv(CO,vv,(LIST)BDY(t)); } else { c = (pointer)ptondv(CO,vv,(P)BDY(t)); } if ( ishomo ) ishomo = ishomo && ndv_ishomo(c); if ( c ) { NEXTNODE(fd0,fd); BDY(fd) = (pointer)ndv_dup(0,c); ndv_mod(-2,c); NEXTNODE(in0,in); BDY(in) = (pointer)c; } } if ( in0 ) NEXT(in) = 0; if ( fd0 ) NEXT(fd) = 0; if ( !ishomo && homo ) { for ( t = in0, wmax = max; t; t = NEXT(t) ) { c = (NDV)BDY(t); len = LEN(c); for ( a = BDY(c), i = 0; i < len; i++, NMV_ADV(a) ) wmax = MAX(TD(DL(a)),wmax); } homogenize_order(ord,nvar,&ord1); nd_init_ord(ord1); nd_setup_parameters(nvar+1,wmax); for ( t = fd0; t; t = NEXT(t) ) ndv_homogenize((NDV)BDY(t),obpe,oadv,oepos,ompos); } if ( MaxDeg > 0 ) nocheck = 1; ret = ndv_setup(-2,m,fd0,nd_gbblock?1:0,0,0); if ( ret ) cand = nd_f4_lf_trace_main(m,&perm); if ( !ret || !cand ) { *rp = 0; return; } if ( !ishomo && homo ) { /* dehomogenization */ for ( t = cand; t; t = NEXT(t) ) ndv_dehomogenize((NDV)BDY(t),ord); nd_init_ord(ord); nd_setup_parameters(nvar,0); } cand = ndv_reducebase(cand,perm); cand = ndv_reduceall(-2,cand); cbpe = nd_bpe; get_eg(&eg0); if ( (ret = ndv_check_membership(-2,in0,obpe,oadv,oepos,cand)) != 0 ) { /* gbcheck : cand is a GB of Id(cand) ? */ retn = nd_f4(-2,0,0); } if ( !retn ) { /* failure */ *rp = 0; return; } get_eg(&eg1); init_eg(&eg_check); add_eg(&eg_check,&eg0,&eg1); if ( DP_Print ) fprintf(asir_out,"check=%.3fsec\n",eg_check.exectime); /* dp->p */ nd_bpe = cbpe; nd_setup_parameters(nd_nvar,0); for ( r = cand; r; r = NEXT(r) ) { if ( nd_module ) BDY(r) = ndvtopl(-2,CO,vv,BDY(r),mrank); else BDY(r) = (pointer)ndvtop(-2,CO,vv,BDY(r)); } MKLIST(*rp,cand); } NODE nd_f4_lf_trace_main(int m,int **indp) { int i,nh,stat,index; NODE r,rm,g; ND_pairs d,l,l0,t; ND spol,red; NDV nf,redv,nfqv,nfv; NM s0,s; NODE rp0,srp0,nflist,nflist_lf; int nsp,nred,col,rank,len,k,j,a; UINT c; UINT **spmat; UINT *s0vect,*svect,*p,*v; int *colstat; IndArray *imat; int *rhead; int spcol,sprow; int sugar; PGeoBucket bucket; struct oEGT eg0,eg1,eg_f4; g = 0; d = 0; for ( i = 0; i < nd_psn; i++ ) { d = update_pairs(d,g,i,0); g = update_base(g,i); } while ( d ) { get_eg(&eg0); l = nd_minsugarp(d,&d); sugar = SG(l); if ( MaxDeg > 0 && sugar > MaxDeg ) break; bucket = create_pbucket(); stat = nd_sp_f4(m,0,l,bucket); if ( !stat ) { for ( t = l; NEXT(t); t = NEXT(t) ); NEXT(t) = d; d = l; d = nd_reconstruct(1,d); continue; } if ( bucket->m < 0 ) continue; col = nd_symbolic_preproc(bucket,0,&s0vect,&rp0); if ( !col ) { for ( t = l; NEXT(t); t = NEXT(t) ); NEXT(t) = d; d = l; d = nd_reconstruct(1,d); continue; } get_eg(&eg1); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg1); if ( DP_Print ) fprintf(asir_out,"\nsugar=%d,symb=%.3fsec,",sugar,eg_f4.exectime); nflist = nd_f4_red(m,l,0,s0vect,col,rp0,&l0); if ( !l0 ) continue; l = l0; /* over LF */ bucket = create_pbucket(); stat = nd_sp_f4(-2,1,l,bucket); if ( !stat ) { for ( t = l; NEXT(t); t = NEXT(t) ); NEXT(t) = d; d = l; d = nd_reconstruct(1,d); continue; } if ( bucket->m < 0 ) continue; col = nd_symbolic_preproc(bucket,1,&s0vect,&rp0); if ( !col ) { for ( t = l; NEXT(t); t = NEXT(t) ); NEXT(t) = d; d = l; d = nd_reconstruct(1,d); continue; } nflist_lf = nd_f4_red(-2,l,1,s0vect,col,rp0,0); /* adding new bases */ for ( rm = nflist, r = nflist_lf; r && rm; rm = NEXT(rm), r = NEXT(r) ) { nfv = (NDV)BDY(rm); nfqv = (NDV)BDY(r); if ( DL_COMPARE(HDL(nfv),HDL(nfqv)) ) return 0; ndv_removecont(m,nfv); ndv_removecont(-2,nfqv); nh = ndv_newps(-2,nfv,nfqv); d = update_pairs(d,g,nh,0); g = update_base(g,nh); } if ( r || rm ) return 0; } conv_ilist(nd_demand,1,g,indp); return g; } #if SIZEOF_LONG==8 NDV vect64_to_ndv(mp_limb_t *vect,int spcol,int col,int *rhead,UINT *s0vect) { int j,k,len; UINT *p; UINT c; NDV r; NMV mr0,mr; for ( j = 0, len = 0; j < spcol; j++ ) if ( vect[j] ) len++; if ( !len ) return 0; else { mr0 = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(nmv_adv*len); #if 0 ndv_alloc += nmv_adv*len; #endif mr = mr0; p = s0vect; for ( j = k = 0; j < col; j++, p += nd_wpd ) if ( !rhead[j] ) { if ( (c = (UINT)vect[k++]) != 0 ) { ndl_copy(p,DL(mr)); CM(mr) = c; NMV_ADV(mr); } } MKNDV(nd_nvar,mr0,len,r); return r; } } NDV vect64_to_ndv_s(mp_limb_t *vect,int col,UINT *s0vect) { int j,k,len; UINT *p; UINT c; NDV r; NMV mr0,mr; for ( j = 0, len = 0; j < col; j++ ) if ( vect[j] ) len++; if ( !len ) return 0; else { mr0 = (NMV)MALLOC_ATOMIC_IGNORE_OFF_PAGE(nmv_adv*len); mr = mr0; p = s0vect; for ( j = k = 0; j < col; j++, p += nd_wpd ) if ( (c = (UINT)vect[k++]) != 0 ) { ndl_copy(p,DL(mr)); CM(mr) = c; NMV_ADV(mr); } MKNDV(nd_nvar,mr0,len,r); return r; } } int nd_to_vect64(int mod,UINT *s0,int n,ND d,mp_limb_t *r) { NM m; UINT *t,*s,*u; int i,st,ed,md,prev,c; for ( i = 0; i < n; i++ ) r[i] = 0; prev = 0; for ( i = 0, m = BDY(d); m; m = NEXT(m) ) { t = DL(m); st = prev; ed = n; while ( ed > st ) { md = (st+ed)/2; u = s0+md*nd_wpd; c = DL_COMPARE(u,t); if ( c == 0 ) break; else if ( c > 0 ) st = md; else ed = md; } r[md] = (mp_limb_t)CM(m); prev = md; } for ( i = 0; !r[i]; i++ ); return i; } #define MOD128(a,c,m) ((a)=(((c)!=0||((a)>=(m)))?(((((U128)(c))<<64)+(a))%(m)):(a))) int ndv_reduce_vect64(int m,mp_limb_t *svect,mp_limb_t *cvect,int col,IndArray *imat,NM_ind_pair *rp0,int nred,SIG sig) { int i,j,k,len,pos,prev; mp_limb_t a,c,c1,c2; IndArray ivect; unsigned char *ivc; unsigned short *ivs; unsigned int *ivi; NDV redv; NMV mr; NODE rp; int maxrs; for ( i = 0; i < col; i++ ) cvect[i] = 0; maxrs = 0; for ( i = 0; i < nred; i++ ) { ivect = imat[i]; k = ivect->head; a = svect[k]; c = cvect[k]; MOD128(a,c,m); svect[k] = a; cvect[k] = 0; if ( (c = svect[k]) != 0 && (sig == 0 || comp_sig(sig,rp0[i]->sig) > 0 ) ) { Nf4_red++; maxrs = MAX(maxrs,rp0[i]->sugar); c = m-c; redv = nd_ps[rp0[i]->index]; len = LEN(redv); mr = BDY(redv); svect[k] = 0; prev = k; switch ( ivect->width ) { case 1: ivc = ivect->index.c; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivc[j]; c1 = CM(mr); prev = pos; c2 = svect[pos]+c1*c; if ( c2 < svect[pos] ) cvect[pos]++; svect[pos] = c2; } break; case 2: ivs = ivect->index.s; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivs[j]; c1 = CM(mr); prev = pos; c2 = svect[pos]+c1*c; if ( c2 < svect[pos] ) cvect[pos]++; svect[pos] = c2; } break; case 4: ivi = ivect->index.i; for ( j = 1, NMV_ADV(mr); j < len; j++, NMV_ADV(mr) ) { pos = prev+ivi[j]; c1 = CM(mr); prev = pos; c2 = svect[pos]+c1*c; if ( c2 < svect[pos] ) cvect[pos]++; svect[pos] = c2; } break; } } } for ( i = 0; i < col; i++ ) { a = svect[i]; c = cvect[i]; MOD128(a,c,m); svect[i] = a; } return maxrs; } /* for Fp, 2^15=index.c); /* elimination (2nd step) */ colstat = (int *)MALLOC(spcol*sizeof(int)); rank = nd_gauss_elim_mod64(spmat,spsugar,spactive,sprow,spcol,m,colstat); r0 = 0; for ( i = 0; i < rank; i++ ) { NEXTNODE(r0,r); BDY(r) = (pointer)vect64_to_ndv(spmat[i],spcol,col,rhead,s0vect); SG((NDV)BDY(r)) = spsugar[i]; GCFREE(spmat[i]); } if ( r0 ) NEXT(r) = 0; for ( ; i < sprow; i++ ) GCFREE(spmat[i]); get_eg(&eg2); init_eg(&eg_f4_2); add_eg(&eg_f4_2,&eg1,&eg2); add_eg(&f4_elim2,&eg1,&eg2); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg2); if ( DP_Print ) { fprintf(asir_out,"elim2=%.3fsec,",eg_f4_2.exectime); fprintf(asir_out,"nsp=%d,nred=%d,spmat=(%d,%d),rank=%d ", nsp,nred,sprow,spcol,rank); fprintf(asir_out,"%.3fsec,",eg_f4.exectime); } if ( nz ) { for ( i = 0; i < rank-1; i++ ) NEXT(spactive[i]) = spactive[i+1]; if ( rank > 0 ) { NEXT(spactive[rank-1]) = 0; *nz = spactive[0]; } else *nz = 0; } return r0; } int nd_gauss_elim_mod64(mp_limb_t **mat,int *sugar,ND_pairs *spactive,int row,int col,int md,int *colstat) { int i,j,k,l,rank,s; mp_limb_t inv; mp_limb_t a; UINT c; mp_limb_t *t,*pivot,*pk; UINT *ck; UINT **cmat; UINT *ct; ND_pairs pair; cmat = (UINT **)MALLOC(row*sizeof(UINT *)); for ( i = 0; i < row; i++ ) { cmat[i] = MALLOC_ATOMIC(col*sizeof(UINT)); bzero(cmat[i],col*sizeof(UINT)); } for ( rank = 0, j = 0; j < col; j++ ) { for ( i = rank; i < row; i++ ) { a = mat[i][j]; c = cmat[i][j]; MOD128(a,c,md); mat[i][j] = a; cmat[i][j] = 0; } for ( i = rank; i < row; i++ ) if ( mat[i][j] ) break; if ( i == row ) { colstat[j] = 0; continue; } else colstat[j] = 1; if ( i != rank ) { t = mat[i]; mat[i] = mat[rank]; mat[rank] = t; ct = cmat[i]; cmat[i] = cmat[rank]; cmat[rank] = ct; s = sugar[i]; sugar[i] = sugar[rank]; sugar[rank] = s; if ( spactive ) { pair = spactive[i]; spactive[i] = spactive[rank]; spactive[rank] = pair; } } /* column j is normalized */ s = sugar[rank]; inv = invm((UINT)mat[rank][j],md); /* normalize pivot row */ for ( k = j, pk = mat[rank]+j, ck = cmat[rank]+j; k < col; k++, pk++, ck++ ) { a = *pk; c = *ck; MOD128(a,c,md); *pk = (a*inv)%md; *ck = 0; } for ( i = rank+1; i < row; i++ ) { if ( (a = mat[i][j]) != 0 ) { sugar[i] = MAX(sugar[i],s); red_by_vect64(md,mat[i]+j,cmat[i]+j,mat[rank]+j,(int)(md-a),col-j); Nf4_red++; } } rank++; } for ( j = col-1, l = rank-1; j >= 0; j-- ) if ( colstat[j] ) { for ( k = j, pk = mat[l]+j, ck = cmat[l]+j; k < col; k++, pk++, ck++ ) { a = *pk; c = *ck; MOD128(a,c,md); *pk = a; *ck = 0; } s = sugar[l]; for ( i = 0; i < l; i++ ) { a = mat[i][j]; c = cmat[i][j]; MOD128(a,c,md); mat[i][j] = a; cmat[i][j] = 0; if ( a ) { sugar[i] = MAX(sugar[i],s); red_by_vect64(md,mat[i]+j,cmat[i]+j,mat[l]+j,(int)(md-a),col-j); Nf4_red++; } } l--; } for ( i = 0; i < row; i++ ) GCFREE(cmat[i]); GCFREE(cmat); return rank; } #endif int nd_gauss_elim_mod64_s(mp_limb_t **mat,int *sugar,ND_pairs *spactive,int row,int col,int md,int *colstat,SIG *sig) { int i,j,k,l,rank,s,imin; mp_limb_t inv; mp_limb_t a; UINT c; mp_limb_t *t,*pivot,*pk; UINT *ck; UINT **cmat; UINT *ct; ND_pairs pair; SIG sg; int *used; used = (int *)MALLOC(row*sizeof(int)); cmat = (UINT **)MALLOC(row*sizeof(UINT *)); for ( i = 0; i < row; i++ ) { cmat[i] = MALLOC_ATOMIC(col*sizeof(UINT)); bzero(cmat[i],col*sizeof(UINT)); } for ( j = 0; j < col; j++ ) { for ( i = 0; i < row; i++ ) { a = mat[i][j]; c = cmat[i][j]; MOD128(a,c,md); mat[i][j] = a; cmat[i][j] = 0; } for ( i = 0; i < row; i++ ) if ( !used[i] && mat[i][j] ) break; if ( i == row ) { colstat[j] = 0; continue; } else { colstat[j] = 1; used[i] = 1; } /* column j is normalized */ s = sugar[i]; inv = invm((UINT)mat[i][j],md); /* normalize pivot row */ for ( k = j, pk = mat[i]+j, ck = cmat[i]+j; k < col; k++, pk++, ck++ ) { a = *pk; c = *ck; MOD128(a,c,md); *pk = (a*inv)%md; *ck = 0; } for ( k = i+1; k < row; k++ ) { if ( (a = mat[k][j]) != 0 ) { sugar[k] = MAX(sugar[k],s); red_by_vect64(md,mat[k]+j,cmat[k]+j,mat[i]+j,(int)(md-a),col-j); Nf4_red++; } } } rank = 0; for ( i = 0; i < row; i++ ) { for ( j = 0; j < col; j++ ) if ( mat[i][j] ) break; if ( j == col ) sugar[i] = -1; else rank++; } for ( i = 0; i < row; i++ ) GCFREE(cmat[i]); GCFREE(cmat); return rank; } NODE nd_f4_red_mod64_main_s(int m,ND_pairs sp0,int nsp,UINT *s0vect,int col, NM_ind_pair *rvect,int *rhead,IndArray *imat,int nred,NODE *syzlistp) { int spcol,sprow,a; int i,j,k,l,rank; NODE r0,r; ND_pairs sp; ND spol; mp_limb_t **spmat; mp_limb_t *svect,*cvect; mp_limb_t *v; int *colstat; struct oEGT eg0,eg1,eg2,eg_f4,eg_f4_1,eg_f4_2; int maxrs; int *spsugar; ND_pairs *spactive; SIG *spsig; get_eg(&eg0); /* elimination (1st step) */ spmat = (mp_limb_t **)MALLOC(nsp*sizeof(mp_limb_t *)); cvect = (mp_limb_t *)MALLOC(col*sizeof(mp_limb_t)); spsugar = (int *)MALLOC(nsp*sizeof(int)); spsig = (SIG *)MALLOC(nsp*sizeof(SIG)); for ( a = sprow = 0, sp = sp0; a < nsp; a++, sp = NEXT(sp) ) { nd_sp(m,0,sp,&spol); if ( !spol ) { syzlistp[sp->sig->pos] = insert_sig(syzlistp[sp->sig->pos],sp->sig); continue; } svect = (mp_limb_t *)MALLOC(col*sizeof(mp_limb_t)); nd_to_vect64(m,s0vect,col,spol,svect); maxrs = ndv_reduce_vect64(m,svect,cvect,col,imat,rvect,nred,spol->sig); for ( i = 0; i < col; i++ ) if ( svect[i] ) break; if ( i < col ) { spmat[sprow] = svect; spsugar[sprow] = MAX(maxrs,SG(spol)); spsig[sprow] = sp->sig; sprow++; } else { syzlistp[sp->sig->pos] = insert_sig(syzlistp[sp->sig->pos],sp->sig); } nd_free(spol); } get_eg(&eg1); init_eg(&eg_f4_1); add_eg(&eg_f4_1,&eg0,&eg1); add_eg(&f4_elim1,&eg0,&eg1); if ( DP_Print ) { fprintf(asir_out,"elim1=%.3fsec,",eg_f4_1.exectime); fflush(asir_out); } /* free index arrays */ for ( i = 0; i < nred; i++ ) GCFREE(imat[i]->index.c); /* elimination (2nd step) */ colstat = (int *)MALLOC(col*sizeof(int)); rank = nd_gauss_elim_mod64_s(spmat,spsugar,0,sprow,col,m,colstat,spsig); r0 = 0; for ( i = 0; i < sprow; i++ ) { if ( spsugar[i] >= 0 ) { NEXTNODE(r0,r); BDY(r) = vect64_to_ndv_s(spmat[i],col,s0vect); SG((NDV)BDY(r)) = spsugar[i]; ((NDV)BDY(r))->sig = spsig[i]; } else syzlistp[spsig[i]->pos] = insert_sig(syzlistp[spsig[i]->pos],spsig[i]); GCFREE(spmat[i]); } if ( r0 ) NEXT(r) = 0; get_eg(&eg2); init_eg(&eg_f4_2); add_eg(&eg_f4_2,&eg1,&eg2); add_eg(&f4_elim2,&eg1,&eg2); init_eg(&eg_f4); add_eg(&eg_f4,&eg0,&eg2); if ( DP_Print ) { fprintf(asir_out,"elim2=%.3fsec,",eg_f4_2.exectime); fprintf(asir_out,"nsp=%d,nred=%d,spmat=(%d,%d),rank=%d ", nsp,nred,sprow,col,rank); fprintf(asir_out,"%.3fsec,",eg_f4.exectime); } return r0; } NODE nd_f4_red_s(int m,ND_pairs sp0,int trace,UINT *s0vect,int col,NODE rp0,NODE *syzlistp) { IndArray *imat; int nsp,nred,i,start; int *rhead; NODE r0,rp; ND_pairs sp; NM_ind_pair *rvect; UINT *s; int *s0hash; struct oEGT eg0,eg1,eg_conv; for ( sp = sp0, nsp = 0; sp; sp = NEXT(sp), nsp++ ); nred = length(rp0); imat = (IndArray *)MALLOC(nred*sizeof(IndArray)); rhead = (int *)MALLOC(col*sizeof(int)); for ( i = 0; i < col; i++ ) rhead[i] = 0; /* construction of index arrays */ get_eg(&eg0); if ( DP_Print ) { fprintf(asir_out,"%dx%d,",nsp+nred,col); fflush(asir_out); } rvect = (NM_ind_pair *)MALLOC(nred*sizeof(NM_ind_pair)); for ( start = 0, rp = rp0, i = 0; rp; i++, rp = NEXT(rp) ) { rvect[i] = (NM_ind_pair)BDY(rp); imat[i] = nm_ind_pair_to_vect_compress(trace,s0vect,col,rvect[i],start); rhead[imat[i]->head] = 1; start = imat[i]->head; } get_eg(&eg1); init_eg(&eg_conv); add_eg(&eg_conv,&eg0,&eg1); add_eg(&f4_conv,&eg0,&eg1); if ( DP_Print ) { fprintf(asir_out,"conv=%.3fsec,",eg_conv.exectime); fflush(asir_out); } if ( m > 0 ) r0 = nd_f4_red_mod64_main_s(m,sp0,nsp,s0vect,col,rvect,rhead,imat,nred,syzlistp); else // r0 = nd_f4_red_q_main_s(sp0,nsp,trace,s0vect,col,rvect,rhead,imat,nred); error("nd_f4_red_q_main_s : not implemented yet"); return r0; } INLINE int ndl_find_reducer_minsig(UINT *dg) { RHist r; int i,singular,ret,d,k,imin; SIG t; static int wpd,nvar; static SIG quo,quomin; static UINT *tmp; if ( !quo || nvar != nd_nvar ) { NEWSIG(quo); NEWSIG(quomin); } if ( wpd != nd_wpd ) { wpd = nd_wpd; tmp = (UINT *)MALLOC(wpd*sizeof(UINT)); } #if 0 d = ndl_hash_value(dg); for ( r = nd_red[d], k = 0; r; r = NEXT(r), k++ ) { if ( ndl_equal(dg,DL(r)) ) { return r->index; } } #endif imin = -1; for ( i = 0; i < nd_psn; i++ ) { r = nd_psh[i]; if ( ndl_reducible(dg,DL(r)) ) { ndl_sub(dg,DL(r),tmp); _ndltodl(tmp,DL(quo)); _addtodl(nd_nvar,DL(nd_psh[i]->sig),DL(quo)); quo->pos = nd_psh[i]->sig->pos; if ( imin < 0 || comp_sig(quomin,quo) > 0 ) { t = quo; quo = quomin; quomin = t; imin = i; } } } if ( imin == -1 ) return nd_psn; else { #if 0 nd_append_red(dg,i); #endif return imin; } } int nd_symbolic_preproc_s(PGeoBucket bucket,int trace,UINT **s0vect,NODE *r) { NODE rp0,rp; NM mul,head,s0,s; int index,col,i,sugar; RHist h; UINT *s0v,*p; NM_ind_pair pair; ND red; NDV *ps; SIG sig; s0 = 0; rp0 = 0; col = 0; if ( nd_demand ) ps = trace?nd_ps_trace_sym:nd_ps_sym; else ps = trace?nd_ps_trace:nd_ps; while ( 1 ) { head = remove_head_pbucket_symbolic(bucket); if ( !head ) break; if ( !s0 ) s0 = head; else NEXT(s) = head; s = head; index = ndl_find_reducer_minsig(DL(head)); if ( index >= 0 && index < nd_psn ) { h = nd_psh[index]; NEWNM(mul); ndl_sub(DL(head),DL(h),DL(mul)); if ( ndl_check_bound2(index,DL(mul)) ) return 0; sugar = TD(DL(mul))+SG(ps[index]); NEWSIG(sig); _ndltodl(DL(mul),DL(sig)); _addtodl(nd_nvar,DL(nd_psh[index]->sig),DL(sig)); sig->pos = nd_psh[index]->sig->pos; MKNM_ind_pair(pair,mul,index,sugar,sig); red = ndv_mul_nm_symbolic(mul,ps[index]); add_pbucket_symbolic(bucket,nd_remove_head(red)); NEXTNODE(rp0,rp); BDY(rp) = (pointer)pair; } col++; } if ( rp0 ) NEXT(rp) = 0; NEXT(s) = 0; s0v = (UINT *)MALLOC_ATOMIC(col*nd_wpd*sizeof(UINT)); for ( i = 0, p = s0v, s = s0; i < col; i++, p += nd_wpd, s = NEXT(s) ) ndl_copy(DL(s),p); *s0vect = s0v; *r = rp0; return col; } NODE nd_sba_f4(int m,int **indp) { int i,nh,stat,index,f4red,f4step; int col,rank,len,k,j,a,sugar,nbase,psugar,ms; NODE r,g,rp0,nflist; ND_pairs d,l,t; ND h,nf; NDV nfv; union oNDC hc; UINT *s0vect; UINT c; PGeoBucket bucket; NODE *syzlist; SIG sig; struct oEGT eg0,eg1,eg_f4; struct oEGT eg2,eg_update,eg_remove,eg_large,eg_nf,eg_nfzero; Nf4_red=0; d = 0; syzlist = (NODE *)MALLOC(nd_psn*sizeof(NODE)); for ( i = 0; i < nd_psn; i++ ) { d = update_pairs_s(d,i,syzlist); } nd_nbase = nd_psn; f4red = 1; psugar = 0; f4step = 0; while ( d ) { for ( t = d, ms = SG(d); t; t = NEXT(t) ) if ( SG(t) < ms ) ms = SG(t); if ( ms == psugar && f4step >= 2 ) { again: l = d; d = d->next; if ( small_lcm(l) ) { if ( DP_Print ) fprintf(asir_out,"M"); continue; } sig = l->sig; stat = nd_sp(m,0,l,&h); if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(0,d); goto again; } get_eg(&eg1); #if USE_GEOBUCKET stat = m?nd_nf_pbucket_s(m,h,nd_ps,!Top,&nf):nd_nf_s(m,0,h,nd_ps,!Top,&nf); #else stat = nd_nf_s(m,0,h,nd_ps,!Top,&nf); #endif get_eg(&eg2); if ( !stat ) { NEXT(l) = d; d = l; d = nd_reconstruct(0,d); goto again; } else if ( stat == -1 ) { if ( DP_Print ) { printf("S"); fflush(stdout); } FREENDP(l); } else if ( nf ) { if ( DP_Print ) { printf("+"); fflush(stdout); } add_eg(&eg_nf,&eg1,&eg2); hc = HCU(nf); nd_removecont(m,nf); nfv = ndtondv(m,nf); nd_free(nf); nh = ndv_newps(m,nfv,0); d = update_pairs_s(d,nh,syzlist); nd_sba_pos[sig->pos] = append_one(nd_sba_pos[sig->pos],nh); FREENDP(l); } else { add_eg(&eg_nfzero,&eg1,&eg2); // syzygy get_eg(&eg1); d = remove_spair_s(d,sig); get_eg(&eg2); add_eg(&eg_remove,&eg1,&eg2); syzlist[sig->pos] = insert_sig(syzlist[sig->pos],sig); if ( DP_Print ) { printf("."); fflush(stdout); } FREENDP(l); } } else { if ( ms != psugar ) f4step = 1; else f4step++; again2: psugar = ms; l = nd_minsugarp_s(d,&d); sugar = nd_sugarweight?d->sugar2:SG(d); bucket = create_pbucket(); stat = nd_sp_f4(m,0,l,bucket); if ( !stat ) { for ( t = l; NEXT(t); t = NEXT(t) ); NEXT(t) = d; d = l; d = nd_reconstruct(0,d); goto again2; } if ( bucket->m < 0 ) continue; col = nd_symbolic_preproc_s(bucket,0,&s0vect,&rp0); if ( !col ) { for ( t = l; NEXT(t); t = NEXT(t) ) ; NEXT(t) = d; d = l; d = nd_reconstruct(0,d); goto again2; } if ( DP_Print ) fprintf(asir_out,"\nsugar=%d,",psugar); nflist = nd_f4_red_s(m,l,0,s0vect,col,rp0,syzlist); /* adding new bases */ for ( r = nflist; r; r = NEXT(r) ) { nfv = (NDV)BDY(r); ndv_removecont(m,nfv); nh = ndv_newps(m,nfv,0); d = update_pairs_s(d,nh,syzlist); nd_sba_pos[nfv->sig->pos] = append_one(nd_sba_pos[nfv->sig->pos],nh); } for ( i = 0; i < nd_nbase; i++ ) for ( r = syzlist[i]; r; r = NEXT(r) ) d = remove_spair_s(d,(SIG)BDY(r)); d = remove_large_lcm(d); if ( DP_Print ) { fprintf(asir_out,"f4red=%d,gblen=%d",f4red,nd_psn); fflush(asir_out); } f4red++; } } if ( DP_Print ) { fprintf(asir_out,"\nnumber of red=%d,",Nf4_red); } g = conv_ilist_s(nd_demand,0,indp); return g; }