Annotation of OpenXM/src/asir-contrib/testing/noro/new_pd.rr, Revision 1.12
1.12 ! noro 1: /* $OpenXM: OpenXM/src/asir-contrib/testing/noro/new_pd.rr,v 1.11 2016/11/13 02:09:36 noro Exp $ */
1.1 noro 2: import("gr")$
3: module noro_pd$
1.8 noro 4: static GBCheck,F4,EProcs,Procs,SatHomo,GBRat,SuccSat,RepColon$
1.1 noro 5:
1.8 noro 6: localf radical_membership_sat$
1.4 noro 7: localf witness$
8: localf get_lc,tomonic,aa,ideal_intersection_m,redbase$
1.8 noro 9: localf para_exec,nd_gr_rat,competitive_exec,call_func,call_func_serial$
1.1 noro 10: localf call_ideal_list_intersection$
1.3 noro 11: localf call_colon,call_prime_dec$
1.7 noro 12: localf prime_dec2, prime_dec_main2$
1.1 noro 13: localf first_second$
14: localf third$
15: localf locsat,iso_comp_para,extract_qj,colon_prime_dec,extract_comp$
16: localf separator$
1.4 noro 17: localf member,mingen,compute_gbsyz,redcoef,recompute_trace,dtop,topnum$
1.1 noro 18: localf prepost$
19: localf monodec0,monodec,prod$
20: localf extract_qd,primary_check$
21: localf second$
1.8 noro 22: localf gbrat,succsat,repcolon,comp_third_tdeg,comp_tord$
1.1 noro 23: localf power$
24:
25: localf syci_dec, syc_dec$
26: localf syca_dec,syc0_dec$
27:
28: localf find_si0,find_si1,find_si2$
29: localf find_ssi0,find_ssi1,find_ssi2$
30:
31: localf init_pprocs, init_eprocs, init_procs, kill_procs$
32:
33: localf sy_dec, pseudo_dec, iso_comp, prima_dec$
34:
35: localf prime_dec, prime_dec_main, lex_predec1, zprimedec, zprimadec$
36: localf complete_qdecomp, partial_qdecomp, partial_qdecomp0, complete_decomp$
37: localf partial_decomp, partial_decomp0, zprimacomp, zprimecomp$
38: localf fast_gb, incremental_gb, elim_gb, ldim, make_mod_subst$
39: localf rsgn, find_npos, gen_minipoly, indepset$
1.8 noro 40: localf maxindep, maxindep2, contraction, contraction_m, ideal_list_intersection, ideal_intersection$
1.1 noro 41: localf radical_membership, modular_radical_membership$
42: localf radical_membership_rep, ideal_product, saturation$
1.11 noro 43: localf sat, satind, sat_ind, sat_ind_var, colon, isat$
1.1 noro 44: localf ideal_colon, ideal_sat, ideal_inclusion, qd_simp_comp, qd_remove_redundant_comp$
1.7 noro 45: localf pd_simp_comp, remove_identical_comp$
1.1 noro 46: localf pd_remove_redundant_comp, ppart, sq, gen_fctr, gen_nf, gen_gb_comp$
47: localf gen_mptop, lcfactor, compute_deg0, compute_deg, member$
48: localf elimination, setintersection, setminus, sep_list$
49: localf first, comp_tdeg, comp_tdeg_first, tdeg, comp_by_ord, comp_by_second$
50: localf gbcheck,f4,sathomo,qd_check,qdb_check$
51:
52: SatHomo=0$
53: GBCheck=1$
54: GBRat=0$
1.8 noro 55: SuccSat=0$
56: RepColon=0$
1.1 noro 57:
58: #define MAX(a,b) ((a)>(b)?(a):(b))
59: #define ACCUM_TIME(C,R) {T1 = time(); C += (T1[0]-T0[0])+(T1[1]-T0[1]); R += (T1[3]-T0[3]); }
60:
61: def gbrat(A)
62: {
1.8 noro 63: GBRat = A;
64: }
65:
66: def succsat(A)
67: {
68: SuccSat = A;
69: }
70:
71: def repcolon(A)
72: {
73: RepColon = A;
1.1 noro 74: }
75:
76: def gbcheck(A)
77: {
78: if ( A ) GBCheck = 1;
79: else GBCheck = -1;
80: }
81:
82: def f4(A)
83: {
84: if ( A ) F4 = 1;
85: else F4 = 0;
86: }
87:
88: def sathomo(A)
89: {
90: if ( A ) SatHomo = 1;
91: else SatHomo = 0;
92: }
93:
94: def init_eprocs()
95: {
96: if ( type(NoX=getopt(nox)) == -1 ) NoX = 0;
97: if ( !EProcs ) {
98: if ( NoX ) {
99: P0 = ox_launch_nox();
100: P1 = ox_launch_nox();
101: } else {
102: P0 = ox_launch();
103: P1 = ox_launch();
104: }
105: EProcs = [P0,P1];
106: }
107: }
108:
109: def init_pprocs(N)
110: {
111: if ( type(NoX=getopt(nox)) == -1 ) NoX = 0;
112: for ( R = [], I = 0; I < N; I++ ) {
113: P = NoX ? ox_launch_nox() : ox_launch();
114: R = cons(P,R);
115: }
116: return reverse(R);
117: }
118:
119: def init_procs()
120: {
121: if ( type(NoX=getopt(nox)) == -1 ) NoX = 0;
122: if ( !Procs ) {
123: if ( NoX ) {
124: P0 = ox_launch_nox();
125: P1 = ox_launch_nox();
126: } else {
127: P0 = ox_launch();
128: P1 = ox_launch();
129: }
130: Procs = [P0,P1];
131: }
132: }
133:
134: def kill_procs()
135: {
136: if ( Procs ) {
137: ox_shutdown(Procs[0]);
138: ox_shutdown(Procs[1]);
139: Procs = 0;
140: }
141: if ( EProcs ) {
142: ox_shutdown(EProcs[0]);
143: ox_shutdown(EProcs[1]);
144: EProcs = 0;
145: }
146: }
147:
148: def qd_check(B,V,QD)
149: {
150: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
151: G = nd_gr(B,V,Mod,0);
152: Iso = ideal_list_intersection(map(first,QD[0]),V,0|mod=Mod);
153: Emb = ideal_list_intersection(map(first,QD[1]),V,0|mod=Mod);
154: GG = ideal_intersection(Iso,Emb,V,0|mod=Mod);
155: return gen_gb_comp(G,GG,Mod);
156: }
157:
158: def primary_check(B,V)
159: {
160: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
161: G = nd_gr(B,V,Mod,0);
162: PL = prime_dec(G,V|indep=1,mod=Mod);
163: if ( length(PL) > 1 ) return 0;
164: P = PL[0][0]; Y = PL[0][1];
165: Z = setminus(V,Y);
166: H = elim_gb(G,Z,Y,Mod,[[0,length(Z)],[0,length(Y)]]);
167: H = contraction(H,Z|mod=Mod);
168: H = nd_gr(H,V,Mod,0);
169: if ( gen_gb_comp(G,H,Mod) ) return nd_gr(P,V,Mod,0);
170: else return 0;
171: }
172:
173: def qdb_check(B,V,QD)
174: {
175: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
176: G = nd_gr(B,V,Mod,0);
177: N = length(QD);
178: for ( I = 0, Q = [1]; I < N; I++ )
179: for ( J = 0, QL = map(first,QD[I]), L = length(QL);
180: J < L; J++ )
1.8 noro 181: Q = ideal_intersection_m(Q,QL[J],V,0|mod=Mod);
182: Q = nd_gr(Q,V,0,0);
1.1 noro 183: if ( !gen_gb_comp(G,Q,Mod) )
184: return 0;
185: for ( I = 0; I < N; I++ ) {
186: T = QD[I];
187: M = length(T);
188: for ( J = 0; J < M; J++ ) {
189: P = primary_check(T[J][0],V|mod=Mod);
190: if ( !P ) return 0;
191: PP = nd_gr(T[J][1],V,Mod,0);
192: if ( !gen_gb_comp(P,PP,Mod) ) return 0;
193: }
194: }
195: return 1;
196: }
197:
198: def extract_qd(QD,V,Ind)
199: {
200: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
201: N = length(Ind);
202: for ( I = 0, Q = [1]; I < N; I++ )
203: for ( J = 0, QL = map(first,QD[Ind[I]]), L = length(QL);
204: J < L; J++ )
205: Q = ideal_intersection(Q,QL[J],V,0|mod=Mod);
206: return Q;
207: }
208:
209: /* SYC primary decomositions */
210:
211: def syc_dec(B,V)
212: {
213: if ( type(SI=getopt(si)) == -1 ) SI = 2;
1.10 ohara 214: SIFList=[noro_pd.find_ssi0, noro_pd.find_ssi1, noro_pd.find_ssi2];
1.1 noro 215: if ( SI<0 || SI>2 ) error("sycb_dec : si should be 0,1,2");
216: SIF = SIFList[SI];
217:
218: if ( type(MaxLevel=getopt(level)) == -1 ) MaxLevel = -1;
219: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
220: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
221: if ( type(Time=getopt(time)) == -1 ) Time = 0;
222: if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
223: if ( type(Colon=getopt(colon)) == -1 ) Colon = 1;
224: Ord = 0;
225: Tall = time();
226: C = Gt = G = fast_gb(B,V,Mod,Ord|trace=1);
227: Q = []; IntQ = [1]; First = 1;
228: Tpd = Tiso = Tsep = 0;
229: RTpd = RTiso = RTsep = 0;
230: for ( Level = 0; MaxLevel < 0 || Level <= MaxLevel; Level++ ) {
231: if ( type(Gt[0])==1 ) break;
232: T3 = T2 = T1 = T0 = time();
233: if ( First ) {
234: PtR = prime_dec(C,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
235: Pt = PtR[0]; IntPt = PtR[1];
236: if ( gen_gb_comp(Gt,IntPt,Mod) ) {
237: /* Gt is radical and Gt = cap Pt */
238: for ( T = Pt, Qt = []; T != []; T = cdr(T) )
239: Qt = cons([car(T)[0],car(T)[0]],Qt);
240: return append(Q,[Qt]);
241: }
242: }
243: T1 = time(); Tpd += (T1[0]-T0[0])+(T1[1]-T0[1]); RTpd += (T1[3]-T0[3]);
244: Qt = iso_comp(Gt,Pt,V,Ord|mod=Mod,first=First,iso=Iso);
245: Q = append(Q,[Qt]);
246: for ( T = Qt; T != []; T = cdr(T) )
247: IntQ = ideal_intersection(IntQ,car(T)[0],V,Ord
248: |mod=Mod,
249: gbblock=[[0,length(IntQ)],[length(IntQ),length(car(T)[0])]]);
250: if ( First ) { IntP = IntPt; First = 0; }
251: if ( gen_gb_comp(IntQ,G,Mod) ) break;
252:
253: M = mingen(IntQ,V);
254: for ( Pt = [], C = [1], T = M; T != []; T = cdr(T) ) {
255: Ci = colon(G,car(T),V|isgb=1);
256: if ( type(Ci[0]) != 1 ) {
257: Pi = prime_dec(Ci,V|indep=1,lexdec=Lexdec,radical=1,mod=Mod);
258: C = ideal_intersection(C,Pi[1],V,Ord);
259: Pt = append(Pt,Pi[0]);
260: }
261: }
262: Pt = pd_simp_comp(Pt,V|first=1,mod=Mod);
263: if ( Colon ) C = ideal_colon(G,IntQ,V|mod=Mod);
264: T2 = time(); Tiso += (T2[0]-T1[0])+(T2[1]-T1[1]); RTiso += (T2[3]-T1[3]);
265: Ok = (*SIF)(C,G,IntQ,IntP,V,Ord|mod=Mod);
266: Gt = append(Ok,G);
267: T3 = time(); Tsep += (T3[0]-T2[0])+(T3[1]-T2[1]); RTsep += (T3[3]-T2[3]);
268: }
269: T4 = time(); RTall = (T4[3]-Tall[3]); Tall = (T4[0]-Tall[0])+(T3[1]-Tall[1]);
270: if ( Time ) {
271: print(["cpu","total",Tall,"pd",Tpd,"iso",Tiso,"sep",Tsep]);
272: print(["elapsed","total",RTall,"pd",RTpd,"iso",RTiso,"sep",RTsep]);
273: }
274: return Q;
275: }
276:
277: static Tint2, RTint2$
278:
279: def syci_dec(B,V)
280: {
281: if ( type(SI=getopt(si)) == -1 ) SI = 1;
282: if ( SI<0 || SI>2 ) error("sycb_assdec : si should be 0,1,2");
283: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
284: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
285: if ( type(Time=getopt(time)) == -1 ) Time = 0;
286: if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
287: if ( type(Ass=getopt(ass)) == -1 ) Ass = 0;
288: if ( type(Colon=getopt(colon)) == -1 ) Colon = 0;
289: if ( type(Para=getopt(para)) == -1 ) Para = 0;
1.8 noro 290: if ( type(Trace=getopt(trace)) == -1 ) Trace = 0;
1.1 noro 291: Ord = 0;
292: Tiso = Tint = Tpd = Text = Tint2 = 0;
293: RTiso = RTint = RTpd = RText = RTint2 = 0;
294: T00 = time();
1.8 noro 295: G = fast_gb(B,V,Mod,Ord|trace=Trace);
1.1 noro 296: IntQ = [1]; QL = RL = []; First = 1;
297: for ( Level = 0; ; Level++ ) {
298: T0 = time();
1.8 noro 299: if ( !Level ) {
1.1 noro 300: PtR = prime_dec(G,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
1.8 noro 301: ACCUM_TIME(Tfpd,RTfpd)
1.1 noro 302: Pt = PtR[0]; IntPt = PtR[1]; Rad = IntPt;
1.2 noro 303: if ( gen_gb_comp(G,Rad,Mod) ) {
304: /* Gt is radical and Gt = cap Pt */
305: for ( T = Pt, Qt = []; T != []; T = cdr(T) )
306: Qt = cons([car(T)[0],car(T)[0],car(T)[1]],Qt);
307: return [reverse(Qt)];
308: }
1.1 noro 309: } else
310: Pt = colon_prime_dec(G,IntQ,V|lexdec=Lexdec,mod=Mod,para=Para);
311: ACCUM_TIME(Tpd,RTpd)
312: T0 = time();
313: Rt = iso_comp(G,Pt,V,Ord|mod=Mod,iso=Iso,para=Para,intq=IntQ);
314: ACCUM_TIME(Tiso,RTiso)
1.8 noro 315: if ( !Level ) {
316: if ( Iso == 3 ) {
317: NI = length(Rt);
318: Q = IntQ;
319: T0 = time();
320: if ( Para ) {
321: for ( J = 0, Task = []; J < NI; J++ ) {
322: T = ["noro_pd.extract_qj",Q,V,Rt[J],Rad,Mod,SI,Colon,-1];
323: Task = cons(T,Task);
324: }
325: Task = reverse(Task);
326: print("comps:",2); print(length(Task),2);
327: Rt = para_exec(Para,Task);
328: } else {
329: for ( J = 0, T = []; J < NI; J++ ) {
330: TJ = extract_qj(Q,V,Rt[J],Rad,Mod,SI,Colon,-1);
331: T = cons(TJ,T);
332: }
333: Rt = reverse(T);
334: }
335: ACCUM_TIME(Text,RText)
336: }
337: print("");
338: T0 = time();
339: Int = Rad;
340: for ( T = Rt; T != []; T = cdr(T) )
341: if ( !gb_comp(car(T)[0],car(T)[1]) )
342: Int = ideal_intersection_m(Int,car(T)[0],V,Ord|mod=Mod);
343: IntQ = nd_gr(Int,V,Mod,Ord);
344: ACCUM_TIME(Tint,RTint)
345: RL = append(RL,[Rt]);
346: } else if ( Iso != 3 ) {
1.1 noro 347: T0 = time();
1.8 noro 348: IntQ = ideal_list_intersection(map(first,Rt),V,Ord|mod=Mod,isgb=1);
1.4 noro 349: RL = append(RL,[Rt]);
1.8 noro 350: ACCUM_TIME(Tint,RTint)
1.4 noro 351: } else {
352: NI = length(Rt);
353: Q = IntQ;
1.8 noro 354: if ( Para ) {
355: for ( J = 0, Task = []; J < NI; J++ ) {
356: T = ["noro_pd.extract_qj",Q,V,Rt[J],Rad,Mod,SI,Colon,-1];
357: Task = cons(T,Task);
358: }
359: Task = reverse(Task);
360: print("comps:",2); print(length(Task),2);
361: T0 = time();
362: R = para_exec(Para,Task);
363: ACCUM_TIME(Text,RText)
364: print("");
365: T0 = time();
366: IntQ = ideal_list_intersection(cons(IntQ,map(first,R)),V,Ord|mod=Mod);
367: ACCUM_TIME(Tint,RTint)
368: RL = append(RL,[R]);
369: } else {
370: for ( J = 0, T = []; J < NI; J++ ) {
371: T0 = time();
372: TJ = extract_qj(Q,V,Rt[J],Rad,Mod,SI,Colon,-1);
373: ACCUM_TIME(Text,RText)
374: T = cons(TJ,T);
375: T0 = time();
376: IntQ = ideal_intersection_m(IntQ,TJ[0],V,Ord|mod=Mod);
377: ACCUM_TIME(Tint,RTint)
378: }
379: print("");
380: T0 = time();
381: IntQ = nd_gr(IntQ,V,Mod,Ord);
382: ACCUM_TIME(Tint,RTint)
383: T = reverse(T); RL = append(RL,[T]);
1.4 noro 384: }
385: }
1.1 noro 386: QL = append(QL,[IntQ]);
387: if ( gen_gb_comp(IntQ,G,Mod) ) break;
388: }
389: T0 = time();
1.4 noro 390: if ( Iso != 3 && !Ass )
1.1 noro 391: RL = extract_comp(QL,RL,V,Rad|mod=Mod,para=Para,si=SI,colon=Colon,ass=Ass);
392: ACCUM_TIME(Text,RText)
393: if ( Time ) {
394: T1 = time();
395: Tall = T1[0]-T00[0]+T1[1]-T00[1]; RTall += T1[3]-T00[3];
396: Tass = Tall-Text; RTass = RTall-RText;
1.8 noro 397: print(["total",Tall,"ass",Tass,"pd",Tpd,"(fpd)",Tfpd,"iso",Tiso,"int",Tint,"ext",Text]);
398: print(["elapsed",RTall,"ass",RTass,"pd",RTpd,"(fpd)",RTfpd,"iso",RTiso,"int",RTint,"ext",RText]);
1.1 noro 399: }
400: return RL;
401: }
402:
403: def extract_comp(QL,RL,V,Rad) {
404: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
405: if ( type(Para=getopt(para)) == -1 ) Para = 0;
406: if ( type(Colon=getopt(colon)) == -1 ) Colon = 0;
407: if ( type(SI=getopt(si)) == -1 ) SI = 1;
408: if ( type(Ass=getopt(ass)) == -1 ) Ass = 0;
409:
410: L = length(QL);
411: if ( Para ) {
412: for ( Task = [], I = 1; I < L; I++ ) {
413: QI = QL[I-1]; RI = RL[I]; NI = length(RI);
414: for ( J = 0, TI = []; J < NI; J++ ) {
415: T = ["noro_pd.extract_qj",QI,V,RI[J],Rad,Mod,SI,Colon,I];
416: Task = cons(T,Task);
417: }
418: }
1.8 noro 419: Task = reverse(Task);
1.1 noro 420: print("comps:",2); print(length(Task),2); print("");
421: R = para_exec(Para,Task);
422: S = vector(L);
423: for ( I = 1; I < L; I++ ) S[I] = [];
424: S[0] = RL[0];
425: for ( T = R; T != []; T = cdr(T) ) {
426: U = car(T); Level = U[0]; Body = U[1];
427: S[Level] = cons(Body,S[Level]);
428: }
429: return vtol(S);
430: } else {
431: TL = [RL[0]];
432: for ( I = 1; I < L; I++ ) {
433: print("level:",2); print(I,2);
434: print(" comps:",2); print(length(RL[I]),2); print("");
435: QI = QL[I-1]; RI = RL[I]; NI = length(RI);
436: for ( J = 0, TI = []; J < NI; J++ ) {
437: TIJ = extract_qj(QI,V,RI[J],Rad,Mod,SI,Colon,-1);
438: TI = cons(TIJ,TI);
439: }
440: TI = reverse(TI); TL = cons(TI,TL);
441: }
442: TL = reverse(TL);
443: }
444: return TL;
445: }
446:
447: def colon_prime_dec(G,IntQ,V) {
448: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
449: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
450: if ( type(Para=getopt(para)) == -1 ) Para = 0;
1.3 noro 451: if ( !Para ) {
452: print("colon_pd:",2); print(length(IntQ),2);
453: }
1.1 noro 454: if ( !Mod ) M = mingen(IntQ,V);
455: else M = IntQ;
456: if ( Para ) {
457: L = length(M);
1.3 noro 458: for ( Task = [], J = 0; J < L; J++ )
1.1 noro 459: if ( gen_nf(M[J],G,V,Ord,Mod) ) {
1.3 noro 460: T = ["noro_pd.call_colon",G,M[J],V,Mod,1];
1.1 noro 461: Task = cons(T,Task);
462: }
463: Task = reverse(Task);
464: R = para_exec(Para,Task);
1.3 noro 465: R = pd_simp_comp(R,V|mod=Mod); L = length(R);
466:
467: for ( Task = [], J = 0; J < L; J++ ) {
468: T = ["noro_pd.call_prime_dec",R[J],V,1,Lexdec,Mod];
469: Task = cons(T,Task);
470: }
471: Task = reverse(Task);
472: R = para_exec(Para,Task);
473:
1.1 noro 474: for ( Pt = [], T = R; T != []; T = cdr(T) ) Pt = append(Pt,car(T));
475: } else {
1.3 noro 476: for ( R = [], T = M; T != []; T = cdr(T) ) {
477: Ci = colon(G,car(T),V|isgb=1,mod=Mod);
478: R = cons(Ci,R);
479: }
480: print("->",2); print(length(M),2);
481: R = pd_simp_comp(R,V|mod=Mod);
482: print("->",2); print(length(R));
1.8 noro 483: #if 1
1.3 noro 484: for ( Pt = [], T = R; T != []; T = cdr(T) ) {
485: Pi = prime_dec(car(T),V|indep=1,lexdec=Lexdec,mod=Mod);
1.1 noro 486: Pt = append(Pt,Pi);
487: }
1.8 noro 488: #else
489: J = ideal_list_intersection(R,V,0|mod=Mod);
490: Pt = prime_dec(J,V|indep=1,lexdec=Lexdec,mod=Mod);
491: #endif
1.1 noro 492: }
1.8 noro 493: #if 1
1.1 noro 494: Pt = pd_simp_comp(Pt,V|first=1,mod=Mod);
1.8 noro 495: #endif
1.1 noro 496: return Pt;
497: }
498:
1.3 noro 499: def call_colon(G,F,V,Mod,IsGB)
500: {
501: return colon(G,F,V|isgb=1,mod=Mod);
502: }
503:
504: def call_prime_dec(G,V,Indep,Lexdec,Mod)
1.1 noro 505: {
1.3 noro 506: if ( type(G[0]) != 1 )
507: Pi = prime_dec(G,V|indep=Indep,lexdec=Lexdec,mod=Mod);
1.1 noro 508: else
509: Pi = [];
510: return Pi;
511: }
512:
513: def extract_qj(Q,V,QL,Rad,Mod,SI,Colon,Level)
514: {
1.10 ohara 515: SIFList=[noro_pd.find_ssi0, noro_pd.find_ssi1, noro_pd.find_ssi2];
1.1 noro 516: SIF = SIFList[SI];
517: G = QL[0]; P = QL[1]; PV = QL[2];
1.4 noro 518: if ( Q != [1] ) {
519: C = Colon ? ideal_colon(G,Q,V|mod=Mod) : P;
520: Ok = (*SIF)(C,G,Q,Rad,V,0|mod=Mod);
521: } else
522: Ok = [];
1.1 noro 523: V0 = setminus(V,PV);
524: HJ = elim_gb(append(Ok,G),V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
525: HJ = contraction(HJ,V0|mod=Mod);
526: IJ = nd_gr(HJ,V,Mod,Ord);
527: return Level >= 0 ? [Level,[IJ,P]] : [IJ,P];
528: }
529:
530: def syca_dec(B,V)
531: {
532: T00 = time();
533: if ( type(SI=getopt(si)) == -1 ) SI = 2;
1.10 ohara 534: SIFList=[noro_pd.find_si0, noro_pd.find_si1, noro_pd.find_si2];
535: SIF = SIFList[SI];
1.1 noro 536: if ( !SIF ) error("syca_dec : si should be 0,1,2");
537:
538: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
539: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
540: if ( type(NoSimp=getopt(nosimp)) == -1 ) NoSimp = 0;
541: if ( type(Time=getopt(time)) == -1 ) Time = 0;
542: if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
543: Ord = 0;
544: Gt = G0 = G = fast_gb(B,V,Mod,Ord|trace=1);
545: Q0 = Q = []; IntQ0 = IntQ = [1]; First = 1;
546: C = 0;
547:
548: Tass = Tiso = Tcolon = Tsep = Tirred = 0;
549: Rass = Riso = Rcolon = Rsep = Rirred = 0;
550: while ( 1 ) {
551: if ( type(Gt[0])==1 ) break;
552: T0 = time();
553: PtR = prime_dec(Gt,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
554: T1 = time(); Tass += T1[0]-T0[0]+T1[1]-T0[1]; Rass += T1[3]-T0[3];
555: Pt = PtR[0]; IntPt = PtR[1];
556: if ( gen_gb_comp(Gt,IntPt,Mod) ) {
557: /* Gt is radical and Gt = cap Pt */
558: for ( T = Pt, Qt = []; T != []; T = cdr(T) )
559: Qt = cons([car(T)[0],car(T)[0]],Qt);
560: if ( First )
561: return [Qt,[]];
562: else
563: Q0 = append(Qt,Q0);
564: break;
565: }
566: T0 = time();
567: Qt = iso_comp(Gt,Pt,V,Ord|mod=Mod,isgb=1,iso=Iso);
568: T1 = time(); Tiso += T1[0]-T0[0]+T1[1]-T0[1]; Riso += T1[3]-T0[3];
569: IntQt = ideal_list_intersection(map(first,Qt),V,Ord|mod=Mod);
570: if ( First ) {
571: IntQ0 = IntQ = IntQt; IntP = IntPt; Qi = Qt; First = 0;
572: } else {
573: IntQ1 = ideal_intersection(IntQ,IntQt,V,Ord|mod=Mod);
574: if ( gen_gb_comp(IntQ,IntQ1,Mod) ) {
575: G = Gt; IntP = IntPt; Q = []; IntQ = [1]; C = 0;
576: continue;
577: } else {
578: IntQ = IntQ1;
579: IntQ1 = ideal_intersection(IntQ0,IntQt,V,Ord|mod=Mod);
580: if ( !gen_gb_comp(IntQ0,IntQ1,Mod) ) {
581: Q = append(Qt,Q);
582: for ( T = Qt; T != []; T = cdr(T) )
583: if ( !ideal_inclusion(IntQ0,car(T)[0],V,Ord|mod=Mod) )
584: Q0 = append(Q0,[car(T)]);
585: IntQ0 = IntQ1;
586: }
587: }
588: }
589: if ( gen_gb_comp(IntQt,Gt,Mod) || gen_gb_comp(IntQ,G,Mod) || gen_gb_comp(IntQ0,G0,Mod) ) break;
590: T0 = time();
591: C1 = ideal_colon(G,IntQ,V|mod=Mod);
592: T1 = time(); Tcolon += T1[0]-T0[0]+T1[1]-T0[1]; Rcolon += T1[3]-T0[3];
593: if ( C && gen_gb_comp(C,C1,Mod) ) {
594: G = Gt; IntP = IntPt; Q = []; IntQ = [1]; C = 0;
595: continue;
596: } else C = C1;
597: T0 = time();
598: Ok = (*SIF)(C,G,IntQ,IntP,V,Ord|mod=Mod);
599: G1 = append(Ok,G);
600: Gt1 = incremental_gb(G1,V,Ord|mod=Mod);
601: T1 = time(); Tsep += T1[0]-T0[0]+T1[1]-T0[1]; Rsep += T1[3]-T0[3];
602: Gt = Gt1;
603: }
604: T0 = time();
605: if ( !NoSimp ) Q1 = qd_remove_redundant_comp(G0,Qi,Q0,V,Ord|mod=Mod);
606: else Q1 = Q0;
607: if ( Time ) {
608: T1 = time(); Tirred += T1[0]-T0[0]+T1[1]-T0[1]; Rirred += T1[3]-T0[3];
609: Tall = T1[0]-T00[0]+T1[1]-T00[1]; Rall += T1[3]-T00[3];
610: print(["total",Tall,"ass",Tass,"iso",Tiso, "colon",Tcolon,"sep",Tsep,"irred",Tirred]);
611: print(["Rtotal",Rall,"Rass",Rass,"Riso",Riso, "Rcolon",Rcolon,"Rsep",Rsep,"Rirred",Rirred]);
612: print(["iso",length(Qi),"emb",length(Q0),"->",length(Q1)]);
613: }
614: return [Qi,Q1];
615: }
616:
617: def syc0_dec(B,V)
618: {
619: T00 = time();
620: if ( type(SI=getopt(si)) == -1 ) SI = 1;
1.10 ohara 621: SIFList=[noro_pd.find_si0, noro_pd.find_si1, noro_pd.find_si2, noro_pd.find_ssi0, noro_pd.find_ssi1, noro_pd.find_ssi2];
622: SIF = SIFList[SI];
1.1 noro 623: if ( !SIF ) error("syc0_dec : si should be 0,1,2");
624: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
625: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
626: if ( type(NoSimp=getopt(nosimp)) == -1 ) NoSimp = 0;
627: if ( type(Time=getopt(time)) == -1 ) Time = 0;
628: Ord = 0;
629: G = fast_gb(B,V,Mod,Ord);
630: Q = []; IntQ = [1]; Gt = G; First = 1;
631: Tass = Tiso = Tcolon = Tsep = Tirred = 0;
632: Rass = Riso = Rcolon = Rsep = Rirred = 0;
633: while ( 1 ) {
634: if ( type(Gt[0])==1 ) break;
635: T0 = time();
636: PtR = prime_dec(Gt,V|indep=1,lexdec=Lexdec,mod=Mod,radical=1);
637: T1 = time(); Tass += T1[0]-T0[0]+T1[1]-T0[1]; Rass += T1[3]-T0[3];
638: Pt = PtR[0]; IntPt = PtR[1];
639: if ( gen_gb_comp(Gt,IntPt,Mod) ) {
640: /* Gt is radical and Gt = cap Pt */
641: for ( T = Pt, Qt = []; T != []; T = cdr(T) )
642: Qt = cons([car(T)[0],car(T)[0]],Qt);
643: if ( First )
644: return [Qt,[]];
645: else
646: Q = append(Qt,Q);
647: break;
648: }
649:
650: T0 = time();
651: Qt = iso_comp(Gt,Pt,V,Ord|mod=Mod,isgb=1);
652: T1 = time(); Tiso += T1[0]-T0[0]+T1[1]-T0[1]; Riso += T1[3]-T0[3];
653: IntQt = ideal_list_intersection(map(first,Qt),V,Ord|mod=Mod);
654: if ( First ) {
655: IntQ = IntQt; Qi = Qt; First = 0;
656: } else {
657: IntQ1 = ideal_intersection(IntQ,IntQt,V,Ord|mod=Mod);
658: if ( !gen_gb_comp(IntQ1,IntQ,Mod) )
659: Q = append(Qt,Q);
660: }
661: if ( gen_gb_comp(IntQ,G,Mod) || gen_gb_comp(IntQt,Gt,Mod) )
662: break;
663: T0 = time();
664: C = ideal_colon(Gt,IntQt,V|mod=Mod);
665: T1 = time(); Tcolon += T1[0]-T0[0]+T1[1]-T0[1]; Rcolon += T1[3]-T0[3];
666: T0 = time();
667: Ok = (*SIF)(C,Gt,IntQt,IntPt,V,Ord|mod=Mod);
668: G1 = append(Ok,Gt);
669: Gt = incremental_gb(G1,V,Ord|mod=Mod);
670: T1 = time(); Tsep += T1[0]-T0[0]+T1[1]-T0[1]; Rsep += T1[3]-T0[3];
671: }
672: T0 = time();
673: if ( !NoSimp ) Q1 = qd_remove_redundant_comp(G,Qi,Q,V,Ord|mod=Mod);
674: else Q1 = Q;
675: T1 = time(); Tirred += T1[0]-T0[0]+T1[1]-T0[1]; Rirred += T1[3]-T0[3];
676: Tall = T1[0]-T00[0]+T1[1]-T00[1]; Rall += T1[3]-T00[3];
677: if ( Time ) {
678: print(["total",Tall,"ass",Tass,"iso",Tiso, "colon",Tcolon,"sep",Tsep,"irred",Tirred]);
679: print(["Rtotal",Rall,"Rass",Rass,"Riso",Riso, "Rcolon",Rcolon,"Rsep",Rsep,"Rirred",Rirred]);
680: print(["iso",length(Qi),"emb",length(Q),"->",length(Q1)]);
681: }
682: return [Qi,Q1];
683: }
684:
685: def power(A,I) { return A^I; }
686:
687:
688: /* functions for computating a separing ideal */
689: /* C=G:Q, Rad=rad(Q), return J s.t. Q cap (G+J) = G */
690:
691: def find_si0(C,G,Q,Rad,V,Ord) {
692: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
693: for ( CI = C, I = 1; ; I++ ) {
694: for ( T = CI, S = []; T != []; T = cdr(T) )
695: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
696: if ( S == [] )
697: error("find_si0 : cannot happen");
698: G1 = append(S,G);
699: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
700: /* check whether (Q cap (G+S)) = G */
701: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
702: CI = ideal_product(CI,C,V|mod=Mod);
703: }
704: }
705:
706: def find_si1(C,G,Q,Rad,V,Ord) {
707: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
708: for ( T = C, S = []; T != []; T = cdr(T) )
709: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
710: if ( S == [] )
711: error("find_si1 : cannot happen");
712: G1 = append(S,G);
713: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
714: /* check whether (Q cap (G+S)) = G */
715: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
716:
1.9 ohara 717: C = qsort(C,noro_pd.comp_tdeg);
1.1 noro 718:
719: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
720: Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
721: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
722: Dp = dp_gr_print(); dp_gr_print(0);
723: for ( T = C, S = []; T != []; T = cdr(T) ) {
724: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
725: Ui = U = car(T);
726: for ( I = 1; ; I++ ) {
727: G1 = cons(Ui,G);
728: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
729: if ( gen_gb_comp(Int,G,Mod) ) break;
730: else
731: Ui = gen_nf(Ui*U,G,V,Ord,Mod);
732: }
733: print([length(T),I],2);
734: Int1 = incremental_gb(append(Int0,[Tmp*Ui]),TV,Ord1
735: |gbblock=[[0,length(Int0)]],mod=Mod);
736: Int = elimination(Int1,V);
737: if ( !gen_gb_comp(Int,G,Mod) ) {
738: break;
739: } else {
740: Int0 = Int1;
741: S = cons(Ui,S);
742: }
743: }
744: print("");
745: dp_gr_print(Dp);
746: return reverse(S);
747: }
748:
749: def find_si2(C,G,Q,Rad,V,Ord) {
750: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
751: for ( T = C, S = []; T != []; T = cdr(T) )
752: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
753: if ( S == [] )
754: error("find_si2 : cannot happen");
755: G1 = append(S,G);
756: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
757: /* check whether (Q cap (G+S)) = G */
758: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
759:
1.9 ohara 760: C = qsort(C,noro_pd.comp_tdeg);
1.1 noro 761:
762: Dp = dp_gr_print(); dp_gr_print(0);
763: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
764: Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
765: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
766: for ( T = C, S = []; T != []; T = cdr(T) ) {
767: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
768: Ui = U = car(T);
769: for ( I = 1; ; I++ ) {
770: Int1 = incremental_gb(append(Int0,[Tmp*Ui]),TV,Ord1
771: |gbblock=[[0,length(Int0)]],mod=Mod);
772: Int = elimination(Int1,V);
773: if ( gen_gb_comp(Int,G,Mod) ) break;
774: else
775: Ui = gen_nf(Ui*U,G,V,Ord,Mod);
776: }
777: print([length(T),I],2);
778: S = cons(Ui,S);
779: }
1.9 ohara 780: S = qsort(S,noro_pd.comp_tdeg);
1.1 noro 781: print("");
782: End = Len = length(S);
783:
784: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
785: Prev = 1;
786: G1 = append(G,[S[0]]);
787: Int0 = incremental_gb(append(vtol(ltov(G1)*Tmp),vtol(ltov(Q)*(1-Tmp))),
788: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
789: if ( End > 1 ) {
790: Cur = 2;
791: while ( Prev < Cur ) {
792: for ( St = [], I = Prev; I < Cur; I++ ) St = cons(Tmp*S[I],St);
793: Int1 = incremental_gb(append(Int0,St),TV,Ord1
794: |gbblock=[[0,length(Int0)]],mod=Mod);
795: Int = elimination(Int1,V);
796: if ( gen_gb_comp(Int,G,Mod) ) {
797: print([Cur],2);
798: Prev = Cur;
799: Cur = Cur+idiv(End-Cur+1,2);
800: Int0 = Int1;
801: } else {
802: End = Cur;
803: Cur = Prev + idiv(Cur-Prev,2);
804: }
805: }
806: for ( St = [], I = 0; I < Prev; I++ ) St = cons(S[I],St);
807: } else
808: St = [S[0]];
809: print("");
810: for ( I = Prev; I < Len; I++ ) {
811: Int1 = incremental_gb(append(Int0,[Tmp*S[I]]),TV,Ord1
812: |gbblock=[[0,length(Int0)]],mod=Mod);
813: Int = elimination(Int1,V);
814: if ( gen_gb_comp(Int,G,Mod) ) {
815: print([I],2);
816: St = cons(S[I],St);
817: Int0 = Int1;
818: }
819: }
820: Ok = reverse(St);
821: print("");
822: print([length(S),length(Ok)]);
823: dp_gr_print(Dp);
824: return Ok;
825: }
826:
827: /* functions for computing a saturated separating ideal */
828:
829: def find_ssi0(C,G,Q,Rad,V,Ord) {
830: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
831: if ( type(Reduce=getopt(red)) == -1 ) Reduce = 0;
832: for ( T = C, S = []; T != []; T = cdr(T) )
833: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
834: if ( S == [] )
835: error("find_ssi0 : cannot happen");
836: G1 = append(S,G);
837: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
838: /* check whether (Q cap (G+S)) = G */
839: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
840:
841: if ( Reduce ) {
842: for ( T = C, U = []; T != []; T = cdr(T) )
843: if ( gen_nf(car(T),Rad,V,Ord,Mod) ) U = cons(car(T),U);
844: U = reverse(U);
845: } else
846: U = C;
847:
848: for ( I = 1; ; I++ ) {
849: print([I],2);
850: S = map(power,U,I);
851: G1 = append(S,G);
852: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
853: /* check whether (Q cap (G+S)) = G */
854: if ( gen_gb_comp(Int,G,Mod) ) { print(""); return reverse(S); }
855: }
856: }
857:
858: def find_ssi1(C,G,Q,Rad,V,Ord) {
859: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
860: if ( type(Reduce=getopt(red)) == -1 ) Reduce = 0;
861: for ( T = C, S = []; T != []; T = cdr(T) )
862: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
863: if ( S == [] )
864: error("find_ssi1 : cannot happen");
865: G1 = append(S,G);
866: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
867: /* check whether (Q cap (G+S)) = G */
868: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
869:
870: dp_ord(Ord); DC = map(dp_ptod,C,V);
1.9 ohara 871: DC = qsort(DC,noro_pd.comp_tord); C = map(dp_dtop,DC,V);
1.1 noro 872: print(length(C),2);
873: if ( Reduce ) {
874: SC = map(sq,C,Mod);
875: SC = reverse(SC); C = reverse(C);
876: for ( T = C, C1 = [], R1 = append(SC,Rad); T != []; T = cdr(T) ) {
877: R0 = car(R1); R1 = cdr(R1);
878: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
879: if ( radical_membership(R0,R1,V|mod=Mod) ) {
880: C1 = cons(car(T),C1);
881: R1 = append(R1,[R0]);
882: }
883: }
884: print("->",0); print(length(C1),2);
885: C = C1;
886: }
887: print(" ",2);
888:
889: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
890: Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
891: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
892: Dp = dp_gr_print(); dp_gr_print(0);
893: for ( J = 0, T = C, S = [], GS = G; T != []; T = cdr(T), J++ ) {
894: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
895: Ui = U = car(T);
896: for ( I = 1; ; I++ ) {
897: Int1 = nd_gr(append(Int0,[Tmp*Ui]),TV,Mod,Ord1
898: |gbblock=[[0,length(Int0)]],newelim=1);
899: if ( Int1 ) {
900: Int = elimination(Int1,V);
901: if ( gen_gb_comp(Int,G,Mod) ) break;
902: }
903: print("x",2);
904: Ui = gen_nf(Ui*U,G,V,Ord,Mod);
905: }
906: print(J,2);
907: Int0 = Int1;
908: S = cons(Ui,S);
909: }
910: print("");
911: dp_gr_print(Dp);
912: return reverse(S);
913: }
914:
915: def find_ssi2(C,G,Q,Rad,V,Ord) {
916: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
917: if ( type(Reduce=getopt(red)) == -1 ) Reduce = 0;
918: for ( T = C, S = []; T != []; T = cdr(T) )
919: if ( gen_nf(car(T),Q,V,Ord,Mod) ) S = cons(car(T),S);
920: if ( S == [] )
921: error("find_ssi2 : cannot happen");
922: G1 = append(S,G);
923: Int = ideal_intersection(G1,Q,V,Ord|mod=Mod);
924: /* check whether (Q cap (G+S)) = G */
925: if ( gen_gb_comp(Int,G,Mod) ) { print([0]); return reverse(S); }
926:
927: #if 0
928: dp_ord(Ord); DC = map(dp_ptod,C,V);
1.9 ohara 929: DC = qsort(DC,noro_pd.comp_tord); C = map(dp_dtop,DC,V);
1.1 noro 930: #else
1.9 ohara 931: C = qsort(C,noro_pd.comp_tdeg);
1.1 noro 932: #endif
933: if ( Reduce ) {
934: for ( T = C, C1 = [], R1 = Rad; T != []; T = cdr(T) ) {
935: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
1.4 noro 936: if ( radical_membership(car(T),R1,V|mod=Mod) ) {
1.1 noro 937: C1 = cons(car(T),C1);
938: R1 = cons(sq(car(T),Mod),R1);
939: }
940: }
941: print(["C",length(C),"->",length(C1)]);
942: C = reverse(C1);
943: }
944: for ( T = C, S = []; T != []; T = cdr(T) ) {
945: if ( !gen_nf(car(T),Rad,V,Ord,Mod) ) continue;
946: Ui = U = car(T);
947: S = cons([Ui,U],S);
948: }
1.9 ohara 949: S = qsort(S,noro_pd.comp_tdeg_first);
1.1 noro 950: print("");
951:
952: Dp = dp_gr_print(); dp_gr_print(0);
953: Tmp = ttttt; TV = cons(Tmp,V); Ord1 = [[0,1],[Ord,length(V)]];
954: Int0 = incremental_gb(append(vtol(ltov(G)*Tmp),vtol(ltov(Q)*(1-Tmp))),
955: TV,Ord1|gbblock=[[0,length(G)]],mod=Mod);
956: OK = [];
957: while ( S != [] ) {
958: Len = length(S); print("remaining gens : ",0); print(Len);
959: S1 = [];
960: for ( Start = Prev = 0; Start < Len; Start = Prev ) {
961: Cur = Start+1;
962: print(Start,2);
963: while ( Prev < Len ) {
964: for ( St = [], I = Prev; I < Cur; I++ ) St = cons(Tmp*S[I][0],St);
965: Int1 = nd_gr(append(Int0,St),TV,Mod,Ord1|gbblock=[[0,length(Int0)]],newelim=1);
966: if ( !Int1 ) {
967: print("x",0); break;
968: }
969: Int = elimination(Int1,V);
970: if ( gen_gb_comp(Int,G,Mod) ) {
971: print([Prev,Cur-1],2);
972: Prev = Cur;
973: Cur += (Prev-Start)+1;
974: if ( Cur > Len ) Cur = Len;
975: Int0 = Int1;
976: } else
977: break;
978: }
979: for ( I = Start; I < Prev; I++ ) OK = cons(S[I][0],OK);
980: if ( Prev == Start ) {
981: Ui = S[I][0]; U = S[I][1];
982: Ui = gen_nf(Ui*U,G,V,Ord,Mod);
983: S1 = cons([Ui,U],S1);
984: Prev++;
985: }
986: }
987: S = reverse(S1);
988: print("");
989: }
990: print("");
991: OK = reverse(OK);
992: dp_gr_print(Dp);
993: return OK;
994: }
995:
996: /* SY primary decompsition */
997:
998: def sy_dec(B,V)
999: {
1000: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1001: if ( type(Lexdec=getopt(lexdec)) == -1 ) Lexdec = 0;
1002: Ord = 0;
1003: G = fast_gb(B,V,Mod,Ord);
1004: Q = [];
1005: IntQ = [1];
1006: Gt = G;
1007: First = 1;
1008: while ( 1 ) {
1009: if ( type(Gt[0]) == 1 ) break;
1010: Pt = prime_dec(Gt,V|indep=1,lexdec=Lexdec,mod=Mod);
1011: L = pseudo_dec(Gt,Pt,V,Ord|mod=Mod);
1012: Qt = L[0]; Rt = L[1]; St = L[2];
1013: IntQt = ideal_list_intersection(map(first,Qt),V,Ord|mod=Mod);
1014: if ( First ) {
1015: IntQ = IntQt;
1016: Qi = Qt;
1017: First = 0;
1018: } else {
1019: IntQ = ideal_intersection(IntQ,IntQt,V,Ord|mod=Mod);
1020: Q = append(Qt,Q);
1021: }
1022: if ( gen_gb_comp(IntQ,G,Mod) ) break;
1023: for ( T = Rt; T != []; T = cdr(T) ) {
1024: if ( type(car(T)[0]) == 1 ) continue;
1025: U = sy_dec(car(T),V|lexdec=Lexdec,mod=Mod);
1026: IntQ = ideal_list_intersection(cons(IntQ,map(first,U)),
1027: V,Ord|mod=Mod);
1028: Q = append(U,Q);
1029: if ( gen_gb_comp(IntQ,G,Mod) ) break;
1030: }
1031: Gt = fast_gb(append(Gt,St),V,Mod,Ord);
1032: }
1033: Q = qd_remove_redundant_comp(G,Qi,Q,V,Ord|mod=Mod);
1034: return append(Qi,Q);
1035: }
1036:
1037: def pseudo_dec(G,L,V,Ord)
1038: {
1039: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1040: N = length(L);
1041: S = vector(N);
1042: Q = vector(N);
1043: R = vector(N);
1044: L0 = map(first,L);
1045: for ( I = 0; I < N; I++ ) {
1046: LI = setminus(L0,[L0[I]]);
1047: PI = ideal_list_intersection(LI,V,Ord|mod=Mod);
1.9 ohara 1048: PI = qsort(PI,noro_pd.comp_tdeg);
1.1 noro 1049: for ( T = PI; T != []; T = cdr(T) )
1050: if ( gen_nf(car(T),L0[I],V,Ord,Mod) ) break;
1051: if ( T == [] ) error("separator : cannot happen");
1.11 noro 1052: SI = sat_ind(G,car(T),V|mod=Mod);
1.1 noro 1053: QI = SI[0];
1054: S[I] = car(T)^SI[1];
1055: PV = L[I][1];
1056: V0 = setminus(V,PV);
1057: #if 0
1058: GI = fast_gb(QI,append(V0,PV),Mod,
1059: [[Ord,length(V0)],[Ord,length(PV)]]);
1060: #else
1061: GI = fast_gb(QI,append(V0,PV),Mod,
1062: [[2,length(V0)],[Ord,length(PV)]]);
1063: #endif
1064: LCFI = lcfactor(GI,V0,Ord,Mod);
1065: for ( F = 1, T = LCFI, Gt = QI; T != []; T = cdr(T) ) {
1.11 noro 1066: St = sat_ind(Gt,T[0],V|mod=Mod);
1.1 noro 1067: Gt = St[0]; F *= T[0]^St[1];
1068: }
1069: Q[I] = [Gt,L0[I]];
1070: R[I] = fast_gb(cons(F,QI),V,Mod,Ord);
1071: }
1072: return [vtol(Q),vtol(R),vtol(S)];
1073: }
1074:
1075: def iso_comp(G,L,V,Ord)
1076: {
1077: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1078: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
1079: if ( type(Iso=getopt(iso)) == -1 ) Iso = 0;
1080: if ( type(Para=getopt(para)) == -1 ) Para = 0;
1081: if ( type(Q=getopt(intq)) == -1 ) Q = 0;
1.4 noro 1082: if ( type(S=getopt(sep)) == -1 ) S = 0;
1.1 noro 1083:
1.4 noro 1084: if ( !S ) S = separator(L,V|mod=Mod);
1.1 noro 1085: N = length(L);
1086: print("comps : ",2); print(N); print("",2);
1087: if ( Para ) {
1088: Task = [];
1089: for ( I = 0; I < N; I++ ) {
1090: T = ["noro_pd.locsat",G,V,L[I],S[I],Mod,IsGB,Iso,Q];
1091: Task = cons(T,Task);
1092: }
1093: Task = reverse(Task);
1094: R = para_exec(Para,Task);
1095: return R;
1096: } else {
1097: for ( I = 0, R = []; I < N; I++ ) {
1098: QI = locsat(G,V,L[I],S[I],Mod,IsGB,Iso,Q);
1099: if ( type(QI[0][0])==1 )
1100: error("iso_comp : cannot happen");
1101: print(".",2);
1102: R = cons(QI,R);
1103: }
1104: print("");
1105: return reverse(R);
1106: }
1107: }
1108:
1109: def locsat(G,V,L,S,Mod,IsGB,Iso,Q)
1110: {
1111: P = L[0]; PV = L[1]; V0 = setminus(V,PV);
1112: if ( Iso==1 ) {
1113: QI = sat(G,S,V|isgb=IsGB,mod=Mod);
1114: GI = elim_gb(QI,V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
1.8 noro 1115: GI = nd_gr(contraction(GI,V0|mod=Mod,allv=V),V,Mod,0);
1.1 noro 1116: } else if ( Iso==0 ) {
1117: HI = elim_gb(G,V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
1.8 noro 1118: GI = nd_gr(contraction(HI,V0|mod=Mod,allv=V),V,Mod,0);
1.1 noro 1119: GI = sat(GI,S,V|isgb=IsGB,mod=Mod);
1120: } else if ( Iso==2 ) {
1121: HI = elim_gb(G,V0,PV,Mod,[[0,length(V0)],[0,length(PV)]]);
1122: TV = ttttt;
1123: if ( Mod )
1124: GI = nd_gr(cons(TV*S-1,HI),cons(TV,V0),Mod,[[0,1],[0,length(V0)]]);
1125: else
1126: GI = nd_gr_trace(append(HI,[TV*S-1]),cons(TV,V0),
1127: 1,1,[[0,1],[0,length(V0)]]|gbblock=[[0,length(HI)]]);
1128: GI = elimination(GI,V);
1.8 noro 1129: GI = nd_gr(contraction(GI,V0|mod=Mod,allv=V),V,Mod,0);
1.4 noro 1130: } else if ( Iso==3 ) {
1131: GI = sat(G,S,V|isgb=IsGB,mod=Mod);
1.1 noro 1132: }
1133: if ( Q )
1134: GI = ideal_intersection(Q,GI,V,0|mod=Mod);
1135: return [GI,P,PV];
1136: }
1137:
1138: /* GTZ primary decompsition */
1139:
1140: def prima_dec(B,V)
1141: {
1142: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1143: if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
1144: G0 = fast_gb(B,V,Mod,0);
1145: G = fast_gb(G0,V,Mod,Ord);
1146: IntP = [1];
1147: QD = [];
1148: while ( 1 ) {
1149: if ( type(G[0])==1 || ideal_inclusion(IntP,G0,V,0|mod=Mod) )
1150: break;
1151: W = maxindep(G,V,Ord); NP = length(W);
1152: V0 = setminus(V,W); N = length(V0);
1153: V1 = append(V0,W);
1154: G1 = fast_gb(G,V1,Mod,[[Ord,N],[Ord,NP]]);
1155: LCF = lcfactor(G1,V0,Ord,Mod);
1156: L = zprimacomp(G,V0|mod=Mod);
1157: F = 1;
1158: for ( T = LCF, G2 = G; T != []; T = cdr(T) ) {
1.11 noro 1159: S = sat_ind(G2,T[0],V1|mod=Mod);
1.1 noro 1160: G2 = S[0]; F *= T[0]^S[1];
1161: }
1162: for ( T = L, QL = []; T != []; T = cdr(T) )
1163: QL = cons(car(T)[0],QL);
1164: Int = ideal_list_intersection(QL,V,0|mod=Mod);
1165: IntP = ideal_intersection(IntP,Int,V,0|mod=Mod);
1166: QD = append(QD,L);
1167: F = gen_nf(F,G,V,0,Mod);
1168: G = fast_gb(cons(F,G),V,Mod,Ord);
1169: }
1170: QD = qd_remove_redundant_comp(G0,[],QD,V,0);
1171: return QD;
1172: }
1173:
1174: /* SL prime decomposition */
1175:
1176: def prime_dec(B,V)
1177: {
1178: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1179: if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
1.7 noro 1180: if ( type(LexDec=getopt(lexdec)) == -1 ) LexDec = 0;
1.1 noro 1181: if ( type(Rad=getopt(radical)) == -1 ) Rad = 0;
1182: B = map(sq,B,Mod);
1183: if ( LexDec )
1184: PD = lex_predec1(B,V|mod=Mod);
1185: else
1186: PD = [B];
1187: if ( length(PD) > 1 ) {
1188: G = ideal_list_intersection(PD,V,0|mod=Mod);
1189: PD = pd_remove_redundant_comp(G,PD,V,0|mod=Mod);
1190: }
1.8 noro 1191: R = []; RL = [];
1192: for ( T = PD; T != []; T = cdr(T) ) {
1193: PDT = prime_dec_main(car(T),V|indep=Indep,mod=Mod);
1194: R = append(R,PDT[0]);
1195: GT = nd_gr(PDT[1],V,Mod,0);
1196: RL = append(RL,[GT]);
1197: }
1198: if ( LexDec ) R = pd_simp_comp(R,V|first=Indep,mod=Mod);
1199: if ( Rad ) {
1200: G = ideal_list_intersection(RL,V,0|mod=Mod);
1201: return [R,G];
1202: } else return R;
1.7 noro 1203: }
1204:
1205: def prime_dec2(B,V)
1206: {
1207: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1208: if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
1209: if ( type(LexDec=getopt(lexdec)) == -1 ) LexDec = 0;
1210: if ( type(Rad=getopt(radical)) == -1 ) Rad = 0;
1211: if ( type(Para=getopt(para)) == -1 || type(Para) != 4 ) Para = [];
1212: B = map(sq,B,Mod);
1213: if ( LexDec )
1214: PD = lex_predec1(B,V|mod=Mod);
1215: else
1216: PD = [B];
1217: if ( length(PD) > 1 ) {
1218: G = ideal_list_intersection(PD,V,0|mod=Mod);
1219: PD = pd_remove_redundant_comp(G,PD,V,0|mod=Mod);
1220: }
1221: R = [];
1222: for ( T = PD; T != []; T = cdr(T) )
1223: R = append(prime_dec_main2(car(T),V|indep=Indep,mod=Mod,para=Para),R);
1224: if ( Indep ) {
1225: G = ideal_list_intersection(map(first,R),V,0|mod=Mod);
1226: R = pd_simp_comp(R,V|first=1,mod=Mod);
1227: } else {
1228: G = ideal_list_intersection(R,V,0|mod=Mod);
1229: R = pd_simp_comp(R,V|mod=Mod);
1.1 noro 1230: }
1231: return Rad ? [R,G] : R;
1232: }
1233:
1.8 noro 1234: /* returns [PD,rad(I)] */
1235:
1.1 noro 1236: def prime_dec_main(B,V)
1237: {
1.8 noro 1238: Tpint = RTpint = 0;
1.1 noro 1239: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1240: if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
1241: G = fast_gb(B,V,Mod,0);
1242: IntP = [1];
1243: PD = [];
1.4 noro 1244: DG = ltov(map(dp_ptod,G,V));
1245: for ( Ind = [], I = length(G)-1; I >= 0; I-- ) Ind = cons(I,Ind);
1246: if ( Mod ) DG = map(dp_mod,DG,Mod,[]);
1.1 noro 1247: while ( 1 ) {
1.8 noro 1248: print([length(PD)],2);
1.1 noro 1249: /* rad(G) subset IntP */
1250: /* check if IntP subset rad(G) */
1.4 noro 1251: /* print([length(PD),length(IntP)],2); */
1.7 noro 1252: for ( T = IntP; T != []; T = cdr(T) )
1.8 noro 1253: if ( (G0 = radical_membership_sat(car(T),G,V|mod=Mod,isgb=1,dg=[DG,Ind])) ) {
1.1 noro 1254: F = car(T);
1255: break;
1256: }
1.8 noro 1257: if ( T == [] ) {
1258: print(["pint",Tpint,"rpint",RTpint]);
1259: return [PD,IntP];
1260: }
1.1 noro 1261: PD0 = zprimecomp(G0,V,Indep|mod=Mod);
1.7 noro 1262: Int = ideal_list_intersection(Indep?map(first,PD0):PD0,V,0|mod=Mod);
1263: PD = append(PD,PD0);
1.8 noro 1264: #if 1
1265: T0=time();
1.4 noro 1266: IntP = ideal_intersection_m(IntP,Int,V,0|mod=Mod);
1.8 noro 1267: dp_ord(0); DC = map(dp_ptod,IntP,V);
1.9 ohara 1268: DC = qsort(DC,noro_pd.comp_tord); IntP = map(dp_dtop,DC,V);
1.8 noro 1269: ACCUM_TIME(Tpint,RTpint)
1.4 noro 1270: #else
1.7 noro 1271: IntP = ideal_intersection(IntP,Int,V,0|mod=Mod,gbblock=[[0,length(IntP)]]);
1.4 noro 1272: #endif
1.1 noro 1273: }
1274: }
1275:
1.8 noro 1276: localf callsat,callzcomp;
1277:
1278: def callsat(F,G,V,Mod,DG)
1279: {
1280: return radical_membership(F,G,V|mod=Mod,isgb=1,dg=DG,sat=1);
1281: }
1282:
1283: def callzcomp(F,V,Indep,Mod)
1284: {
1285: PD0 = zprimecomp(F,V,Indep|mod=Mod);
1286: Int = ideal_list_intersection(Indep?map(first,PD0):PD0,V,0|mod=Mod);
1287: return [PD0,Int];
1288: }
1289:
1.7 noro 1290: def prime_dec_main2(B,V)
1291: {
1292: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1293: if ( type(Indep=getopt(indep)) == -1 ) Indep = 0;
1294: if ( type(Para=getopt(para)) == -1 || type(Para) != 4 ) Para = [];
1295: NPara = length(Para);
1296:
1297: G = fast_gb(B,V,Mod,0);
1298: IntP = [1];
1299: PD = [];
1300: DG = ltov(map(dp_ptod,G,V));
1301: for ( Ind = [], I = length(G)-1; I >= 0; I-- ) Ind = cons(I,Ind);
1302: if ( Mod ) DG = map(dp_mod,DG,Mod,[]);
1.8 noro 1303: if ( NPara )
1304: while ( 1 ) {
1305: IntPM = mingen(IntP,V);
1306: for ( T = IntPM, CallSat = []; T != []; T = cdr(T) )
1307: CallSat = cons(["noro_pd.callsat",car(T),G,V,Mod,[DG,Ind]],CallSat);
1308: CallSat = reverse(CallSat);
1309: /* SatL = [[..],0,[...],...] */
1310: SatL = para_exec(Para,CallSat);
1311: for ( T = SatL, Sat = []; T != []; T = cdr(T) ) if ( car(T) ) Sat = cons(car(T),Sat);
1312: if ( Sat == [] ) return PD;
1313: print(length(Sat),2); print("->",2);
1314: Sat = remove_identical_comp(Sat|mod=Mod);
1315: print(length(Sat));
1316: for ( T = Sat, CallComp = []; T != []; T = cdr(T) )
1317: CallComp = cons(["noro_pd.callzcomp",car(T),V,Indep,Mod],CallComp);
1318: CallComp = reverse(CallComp);
1319: /* PDL = [[PD0,Int],...] */
1320: PDL = para_exec(Para,CallComp);
1321: for ( T = PDL; T != []; T = cdr(T) ) PD = append(PD,car(T)[0]);
1322: Int = ideal_list_intersection(map(second,PDL),V,0|mod=Mod);
1.7 noro 1323: IntP = ideal_intersection(IntP,Int,V,0|mod=Mod,gbblock=[[0,length(IntP)]]);
1324: }
1.8 noro 1325: else
1326: while ( 1 ) {
1327: /* rad(G) subset IntP */
1328: /* check if IntP subset rad(G) */
1329: /* print([length(PD),length(IntP)],2); */
1330: Sat = [];
1331: IntPM = mingen(IntP,V);
1332: for ( T = IntPM; T != [] && length(Sat) < 16; T = cdr(T) )
1333: if ( G0 = radical_membership(car(T),G,V|mod=Mod,isgb=1,dg=[DG,Ind],sat=1) )
1334: Sat = cons(G0,Sat);
1335: if ( Sat == [] ) return PD;
1336: print(length(Sat),2); print("->",2);
1337: Sat = remove_identical_comp(Sat|mod=Mod);
1338: print(length(Sat));
1339: for ( T = Sat; T != []; T = cdr(T) ) {
1340: PD0 = zprimecomp(car(T),V,Indep|mod=Mod); PD = append(PD,PD0);
1341: Int = ideal_list_intersection(Indep?map(first,PD0):PD0,V,0|mod=Mod);
1342: IntP = ideal_intersection(IntP,Int,V,0|mod=Mod,gbblock=[[0,length(IntP)]]);
1343: }
1344: }
1.7 noro 1345: }
1346:
1.1 noro 1347: /* pre-decomposition */
1348:
1349: def lex_predec1(B,V)
1350: {
1351: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1352: G = fast_gb(B,V,Mod,2);
1353: for ( T = G; T != []; T = cdr(T) ) {
1354: F = gen_fctr(car(T),Mod);
1355: if ( length(F) > 2 || length(F) == 2 && F[1][1] > 1 ) {
1356: for ( R = [], S = cdr(F); S != []; S = cdr(S) ) {
1357: Ft = car(S)[0];
1358: Gt = map(ptozp,map(gen_nf,G,[Ft],V,0,Mod));
1359: R1 = fast_gb(cons(Ft,Gt),V,Mod,0);
1360: R = cons(R1,R);
1361: }
1362: return R;
1363: }
1364: }
1365: return [G];
1366: }
1367:
1368: /* zero-dimensional prime/primary decomosition */
1369:
1370: def zprimedec(B,V,Mod)
1371: {
1372: L = partial_decomp(B,V,Mod);
1373: P = L[0]; NP = L[1];
1374: R = [];
1375: for ( ; P != []; P = cdr(P) ) R = cons(car(car(P)),R);
1376: for ( T = NP; T != []; T = cdr(T) ) {
1377: R1 = complete_decomp(car(T),V,Mod);
1378: R = append(R1,R);
1379: }
1380: return R;
1381: }
1382:
1383: def zprimadec(B,V,Mod)
1384: {
1385: L = partial_qdecomp(B,V,Mod);
1386: Q = L[0]; NQ = L[1];
1387: R = [];
1388: for ( ; Q != []; Q = cdr(Q) ) {
1389: T = car(Q); R = cons([T[0],T[1]],R);
1390: }
1391: for ( T = NQ; T != []; T = cdr(T) ) {
1392: R1 = complete_qdecomp(car(T),V,Mod);
1393: R = append(R1,R);
1394: }
1395: return R;
1396: }
1397:
1398: def complete_qdecomp(GD,V,Mod)
1399: {
1400: GQ = GD[0]; GP = GD[1]; D = GD[2];
1401: W = vars(GP);
1402: PV = setminus(W,V);
1403: N = length(V); PN = length(PV);
1404: U = find_npos([GP,D],V,PV,Mod);
1405: NV = ttttt;
1406: M = gen_minipoly(cons(NV-U,GQ),cons(NV,V),PV,0,NV,Mod);
1407: M = ppart(M,NV,Mod);
1.6 noro 1408: MF = Mod ? modfctr(M,Mod) : fctr(M);
1.1 noro 1409: R = [];
1410: for ( T = cdr(MF); T != []; T = cdr(T) ) {
1411: S = car(T);
1412: Mt = subst(S[0],NV,U);
1413: GP1 = fast_gb(cons(Mt,GP),W,Mod,0);
1414: GQ1 = fast_gb(cons(Mt^S[1],GQ),W,Mod,0);
1415: if ( PV != [] ) {
1416: GP1 = elim_gb(GP1,V,PV,Mod,[[0,N],[0,PN]]);
1417: GQ1 = elim_gb(GQ1,V,PV,Mod,[[0,N],[0,PN]]);
1418: }
1419: R = cons([GQ1,GP1],R);
1420: }
1421: return R;
1422: }
1423:
1424: def partial_qdecomp(B,V,Mod)
1425: {
1426: Elim = (Elim=getopt(elim))&&type(Elim)!=-1 ? 1 : 0;
1427: N = length(V);
1428: W = vars(B);
1429: PV = setminus(W,V);
1430: NP = length(PV);
1431: W = append(V,PV);
1432: if ( Elim && PV != [] ) Ord = [[0,N],[0,NP]];
1433: else Ord = 0;
1434: if ( Mod )
1435: B = nd_f4(B,W,Mod,Ord);
1436: else
1437: B = nd_gr_trace(B,W,1,GBCheck,Ord);
1438: Q = []; NQ = [[B,B,vector(N+1)]];
1439: for ( I = length(V)-1; I >= 0; I-- ) {
1440: NQ1 = [];
1441: for ( T = NQ; T != []; T = cdr(T) ) {
1442: L = partial_qdecomp0(car(T),V,PV,Ord,I,Mod);
1443: Q = append(L[0],Q);
1444: NQ1 = append(L[1],NQ1);
1445: }
1446: NQ = NQ1;
1447: }
1448: return [Q,NQ];
1449: }
1450:
1451: def partial_qdecomp0(GD,V,PV,Ord,I,Mod)
1452: {
1453: GQ = GD[0]; GP = GD[1]; D = GD[2];
1454: N = length(V); PN = length(PV);
1455: W = append(V,PV);
1456: VI = V[I];
1457: M = gen_minipoly(GQ,V,PV,Ord,VI,Mod);
1458: M = ppart(M,VI,Mod);
1459: if ( Mod )
1460: MF = modfctr(M,Mod);
1461: else
1462: MF = fctr(M);
1463: Q = []; NQ = [];
1464: if ( length(MF) == 2 && MF[1][1] == 1 ) {
1465: D1 = D*1; D1[I] = M;
1466: GQelim = elim_gb(GQ,V,PV,Mod,Ord);
1467: GPelim = elim_gb(GP,V,PV,Mod,Ord);
1468: LD = ldim(GQelim,V);
1469: if ( deg(M,VI) == LD )
1470: Q = cons([GQelim,GPelim,D1],Q);
1471: else
1472: NQ = cons([GQelim,GPelim,D1],NQ);
1473: return [Q,NQ];
1474: }
1475: for ( T = cdr(MF); T != []; T = cdr(T) ) {
1476: S = car(T); Mt = S[0]; D1 = D*1; D1[I] = Mt;
1477:
1478: GQ1 = fast_gb(cons(Mt^S[1],GQ),W,Mod,Ord);
1479: GQelim = elim_gb(GQ1,V,PV,Mod,Ord);
1480: GP1 = fast_gb(cons(Mt,GP),W,Mod,Ord);
1481: GPelim = elim_gb(GP1,V,PV,Mod,Ord);
1482:
1483: D1[N] = LD = ldim(GPelim,V);
1484:
1485: for ( J = 0; J < N; J++ )
1486: if ( D1[J] && deg(D1[J],V[J]) == LD ) break;
1487: if ( J < N )
1488: Q = cons([GQelim,GPelim,D1],Q);
1489: else
1490: NQ = cons([GQelim,GPelim,D1],NQ);
1491: }
1492: return [Q,NQ];
1493: }
1494:
1495: def complete_decomp(GD,V,Mod)
1496: {
1497: G = GD[0]; D = GD[1];
1498: W = vars(G);
1499: PV = setminus(W,V);
1500: N = length(V); PN = length(PV);
1501: U = find_npos(GD,V,PV,Mod);
1502: NV = ttttt;
1503: M = gen_minipoly(cons(NV-U,G),cons(NV,V),PV,0,NV,Mod);
1504: M = ppart(M,NV,Mod);
1.6 noro 1505: MF = Mod ? modfctr(M,Mod) : fctr(M);
1.1 noro 1506: if ( length(MF) == 2 ) return [G];
1507: R = [];
1508: for ( T = cdr(MF); T != []; T = cdr(T) ) {
1509: Mt = subst(car(car(T)),NV,U);
1510: G1 = fast_gb(cons(Mt,G),W,Mod,0);
1511: if ( PV != [] ) G1 = elim_gb(G1,V,PV,Mod,[[0,N],[0,PN]]);
1512: R = cons(G1,R);
1513: }
1514: return R;
1515: }
1516:
1517: def partial_decomp(B,V,Mod)
1518: {
1519: Elim = (Elim=getopt(elim))&&type(Elim)!=-1 ? 1 : 0;
1520: N = length(V);
1521: W = vars(B);
1522: PV = setminus(W,V);
1523: NP = length(PV);
1524: W = append(V,PV);
1525: if ( Elim && PV != [] ) Ord = [[0,N],[0,NP]];
1526: else Ord = 0;
1527: if ( Mod )
1528: B = nd_f4(B,W,Mod,Ord);
1529: else
1530: B = nd_gr_trace(B,W,1,GBCheck,Ord);
1531: P = []; NP = [[B,vector(N+1)]];
1532: for ( I = length(V)-1; I >= 0; I-- ) {
1533: NP1 = [];
1534: for ( T = NP; T != []; T = cdr(T) ) {
1535: L = partial_decomp0(car(T),V,PV,Ord,I,Mod);
1536: P = append(L[0],P);
1537: NP1 = append(L[1],NP1);
1538: }
1539: NP = NP1;
1540: }
1541: return [P,NP];
1542: }
1543:
1544: def partial_decomp0(GD,V,PV,Ord,I,Mod)
1545: {
1546: G = GD[0]; D = GD[1];
1547: N = length(V); PN = length(PV);
1548: W = append(V,PV);
1549: VI = V[I];
1550: M = gen_minipoly(G,V,PV,Ord,VI,Mod);
1551: M = ppart(M,VI,Mod);
1552: if ( Mod )
1553: MF = modfctr(M,Mod);
1554: else
1555: MF = fctr(M);
1556: if ( length(MF) == 2 && MF[1][1] == 1 ) {
1557: D1 = D*1;
1558: D1[I] = M;
1559: Gelim = elim_gb(G,V,PV,Mod,Ord);
1560: D1[N] = LD = ldim(Gelim,V);
1561: GD1 = [Gelim,D1];
1562: for ( J = 0; J < N; J++ )
1563: if ( D1[J] && deg(D1[J],V[J]) == LD )
1564: return [[GD1],[]];
1565: return [[],[GD1]];
1566: }
1567: P = []; NP = [];
1568: GI = elim_gb(G,V,PV,Mod,Ord);
1569: for ( T = cdr(MF); T != []; T = cdr(T) ) {
1570: Mt = car(car(T));
1571: D1 = D*1;
1572: D1[I] = Mt;
1573: GIt = map(gen_nf,GI,[Mt],V,Ord,Mod);
1574: G1 = cons(Mt,GIt);
1575: Gelim = elim_gb(G1,V,PV,Mod,Ord);
1576: D1[N] = LD = ldim(Gelim,V);
1577: for ( J = 0; J < N; J++ )
1578: if ( D1[J] && deg(D1[J],V[J]) == LD ) break;
1579: if ( J < N )
1580: P = cons([Gelim,D1],P);
1581: else
1582: NP = cons([Gelim,D1],NP);
1583: }
1584: return [P,NP];
1585: }
1586:
1587: /* prime/primary components over rational function field */
1588:
1589: def zprimacomp(G,V) {
1590: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1591: L = zprimadec(G,V,0|mod=Mod);
1592: R = [];
1593: dp_ord(0);
1594: for ( T = L; T != []; T = cdr(T) ) {
1595: S = car(T);
1596: UQ = contraction(S[0],V|mod=Mod);
1597: UP = contraction(S[1],V|mod=Mod);
1598: R = cons([UQ,UP],R);
1599: }
1600: return R;
1601: }
1602:
1603: def zprimecomp(G,V,Indep) {
1604: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1605: W = maxindep(G,V,0|mod=Mod);
1606: V0 = setminus(V,W);
1607: V1 = append(V0,W);
1608: #if 0
1609: O1 = [[0,length(V0)],[0,length(W)]];
1610: G1 = fast_gb(G,V1,Mod,O1);
1611: dp_ord(0);
1612: #else
1613: G1 = G;
1614: #endif
1615: PD = zprimedec(G1,V0,Mod);
1616: dp_ord(0);
1617: R = [];
1618: for ( T = PD; T != []; T = cdr(T) ) {
1619: U = contraction(car(T),V0|mod=Mod);
1620: U = nd_gr(U,V,Mod,0);
1.7 noro 1621: R = cons(Indep?[U,W]:U,R);
1.1 noro 1622: }
1.7 noro 1623: return R;
1.1 noro 1624: }
1625:
1626: def fast_gb(B,V,Mod,Ord)
1627: {
1628: if ( type(Block=getopt(gbblock)) == -1 ) Block = 0;
1629: if ( type(NoRA=getopt(nora)) == -1 ) NoRA = 0;
1630: if ( type(Trace=getopt(trace)) == -1 ) Trace = 0;
1631: if ( Mod )
1632: G = nd_f4(B,V,Mod,Ord|nora=NoRA);
1633: else if ( F4 )
1634: G = map(ptozp,f4_chrem(B,V,Ord));
1635: else if ( Trace ) {
1636: if ( Block )
1637: G = nd_gr_trace(B,V,1,1,Ord|nora=NoRA,gbblock=Block);
1638: else
1639: G = nd_gr_trace(B,V,1,1,Ord|nora=NoRA);
1640: } else {
1641: if ( Block )
1642: G = nd_gr(B,V,0,Ord|nora=NoRA,gbblock=Block);
1643: else
1644: G = nd_gr(B,V,0,Ord|nora=NoRA);
1645: }
1646: return G;
1647: }
1648:
1649: def incremental_gb(A,V,Ord)
1650: {
1651: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1652: if ( type(Block=getopt(gbblock)) == -1 ) Block = 0;
1653: if ( Mod ) {
1654: if ( Block )
1655: G = nd_gr(A,V,Mod,Ord|gbblock=Block);
1656: else
1657: G = nd_gr(A,V,Mod,Ord);
1658: } else if ( Procs ) {
1659: Arg0 = ["nd_gr",A,V,0,Ord];
1660: Arg1 = ["nd_gr_trace",A,V,1,GBCheck,Ord];
1661: G = competitive_exec(Procs,Arg0,Arg1);
1662: } else if ( Block )
1663: G = nd_gr(A,V,0,Ord|gbblock=Block);
1664: else
1665: G = nd_gr(A,V,0,Ord);
1666: return G;
1667: }
1668:
1669: def elim_gb(G,V,PV,Mod,Ord)
1670: {
1671: N = length(V); PN = length(PV);
1672: O1 = [[0,N],[0,PN]];
1673: if ( Ord == O1 )
1674: Ord = Ord[0][0];
1675: if ( Mod ) /* XXX */ {
1676: for ( T = G, H = []; T != []; T = cdr(T) )
1677: if ( car(T) ) H = cons(car(T),H);
1678: G = reverse(H);
1679: G = dp_gr_mod_main(G,V,0,Mod,Ord);
1680: } else if ( EProcs ) {
1681: #if 1
1682: Arg0 = ["dp_gr_main",G,V,0,0,Ord];
1683: #else
1684: Arg0 = ["nd_gr",G,V,0,Ord];
1685: #endif
1686: Arg1 = ["noro_pd.nd_gr_rat",G,V,PV,O1,Ord];
1687: G = competitive_exec(EProcs,Arg0,Arg1);
1688: } else if ( GBRat ) {
1689: G1 = nd_gr(G,append(V,PV),0,O1);
1.8 noro 1690: if ( GBRat == 1 )
1691: G1 = nd_gr_postproc(G1,V,0,Ord,0|nora=1);
1.1 noro 1692: return G1;
1693: } else
1694: #if 1
1.2 noro 1695: #if 0
1.1 noro 1696: G = dp_gr_main(G,V,0,0,Ord);
1697: #else
1698: G = nd_gr_trace(G,V,1,1,Ord);
1699: #endif
1700: #else
1701: G = nd_gr(G,V,0,Ord);
1702: #endif
1703: return G;
1704: }
1705:
1706: def ldim(G,V)
1707: {
1708: O0 = dp_ord(); dp_ord(0);
1709: D = length(dp_mbase(map(dp_ptod,G,V)));
1710: dp_ord(O0);
1711: return D;
1712: }
1713:
1714: /* over Q only */
1715:
1716: def make_mod_subst(GD,V,PV,HC)
1717: {
1718: N = length(V);
1719: PN = length(PV);
1720: G = GD[0]; D = GD[1];
1721: for ( I = 0; ; I = (I+1)%100 ) {
1722: Mod = lprime(I);
1723: S = [];
1724: for ( J = PN-1; J >= 0; J-- )
1725: S = append([PV[J],random()%Mod],S);
1726: for ( T = HC; T != []; T = cdr(T) )
1727: if ( !(subst(car(T),S)%Mod) ) break;
1728: if ( T != [] ) continue;
1729: for ( J = 0; J < N; J++ ) {
1730: M = subst(D[J],S);
1731: F = modsqfr(M,Mod);
1732: if ( length(F) != 2 || F[1][1] != 1 ) break;
1733: }
1734: if ( J < N ) continue;
1735: G0 = map(subst,G,S);
1736: return [G0,Mod];
1737: }
1738: }
1739:
1740: def rsgn()
1741: {
1742: return random()%2 ? 1 : -1;
1743: }
1744:
1745: def find_npos(GD,V,PV,Mod)
1746: {
1747: N = length(V); PN = length(PV);
1748: G = GD[0]; D = GD[1]; LD = D[N];
1.5 noro 1749: DH = map(dp_dtop,map(dp_ht,map(dp_ptod,D,V)),V);
1.1 noro 1750: Ord0 = dp_ord(); dp_ord(0);
1751: HC = map(dp_hc,map(dp_ptod,G,V));
1752: dp_ord(Ord0);
1753: if ( !Mod ) {
1754: W = append(V,PV);
1755: G1 = nd_gr_trace(G,W,1,GBCheck,[[0,N],[0,PN]]);
1756: L = make_mod_subst([G1,D],V,PV,HC);
1757: return find_npos([L[0],D],V,[],L[1]);
1758: }
1759: N = length(V);
1760: NV = ttttt;
1761: for ( B = 2; ; B++ ) {
1762: for ( J = N-2; J >= 0; J-- ) {
1.5 noro 1763: for ( U = 0, K = J; K < N; K++ ) {
1764: if ( DH[K] == V[K] ) continue;
1.1 noro 1765: U += rsgn()*((random()%B+1))*V[K];
1.5 noro 1766: }
1.6 noro 1767: #if 0
1.1 noro 1768: M = minipolym(G,V,0,U,NV,Mod);
1.6 noro 1769: #else
1770: M = gen_minipoly(cons(NV-U,G),cons(NV,V),PV,0,NV,Mod);
1771: #endif
1.1 noro 1772: if ( deg(M,NV) == LD ) return U;
1773: }
1774: }
1775: }
1776:
1777: def gen_minipoly(G,V,PV,Ord,VI,Mod)
1778: {
1.6 noro 1779: O0 = dp_ord();
1.1 noro 1780: if ( PV == [] ) {
1781: NV = sssss;
1782: if ( Mod )
1783: M = minipolym(G,V,Ord,VI,NV,Mod);
1784: else
1785: M = minipoly(G,V,Ord,VI,NV);
1.6 noro 1786: dp_ord(O0);
1.1 noro 1787: return subst(M,NV,VI);
1788: }
1789: W = setminus(V,[VI]);
1790: PV1 = cons(VI,PV);
1791: #if 0
1792: while ( 1 ) {
1793: V1 = append(W,PV1);
1794: if ( Mod )
1795: G = nd_gr(G,V1,Mod,[[0,1],[0,length(V1)-1]]|nora=1);
1796: else
1797: G = nd_gr_trace(G,V1,1,GBCheck,[[0,1],[0,length(V1)-1]]|nora=1);
1798: if ( W == [] ) break;
1799: else {
1800: W = cdr(W);
1801: G = elimination(G,cdr(V1));
1802: }
1803: }
1.8 noro 1804: #elif 1
1.1 noro 1805: if ( Mod ) {
1806: V1 = append(W,PV1);
1807: G = nd_gr(G,V1,Mod,[[0,length(W)],[0,length(PV1)]]);
1808: G = elimination(G,PV1);
1809: } else {
1810: PV2 = setminus(PV1,[PV1[length(PV1)-1]]);
1811: V2 = append(W,PV2);
1812: G = nd_gr_trace(G,V2,1,GBCheck,[[0,length(W)],[0,length(PV2)]]|nora=1);
1813: G = elimination(G,PV1);
1814: }
1815: #else
1816: V1 = append(W,PV1);
1817: if ( Mod )
1818: G = nd_gr(G,V1,Mod,[[0,length(W)],[0,length(PV1)]]|nora=1);
1819: else
1820: G = nd_gr_trace(G,V1,1,GBCheck,[[0,length(W)],[0,length(PV1)]]|nora=1);
1821: G = elimination(G,PV1);
1822: #endif
1823: if ( Mod )
1824: G = nd_gr(G,PV1,Mod,[[0,1],[0,length(PV)]]|nora=1);
1825: else
1826: G = nd_gr_trace(G,PV1,1,GBCheck,[[0,1],[0,length(PV)]]|nora=1);
1827: for ( M = car(G), T = cdr(G); T != []; T = cdr(T) )
1828: if ( deg(car(T),VI) < deg(M,VI) ) M = car(T);
1.6 noro 1829: dp_ord(O0);
1.1 noro 1830: return M;
1831: }
1832:
1833: def indepset(V,H)
1834: {
1835: if ( H == [] ) return V;
1836: N = -1;
1837: for ( T = V; T != []; T = cdr(T) ) {
1838: VI = car(T);
1839: HI = [];
1840: for ( S = H; S != []; S = cdr(S) )
1841: if ( !tdiv(car(S),VI) ) HI = cons(car(S),HI);
1842: RI = indepset(setminus(V,[VI]),HI);
1843: if ( length(RI) > N ) {
1844: R = RI; N = length(RI);
1845: }
1846: }
1847: return R;
1848: }
1849:
1850: def maxindep(B,V,O)
1851: {
1852: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1853: G = fast_gb(B,V,Mod,O);
1854: Old = dp_ord();
1855: dp_ord(O);
1856: H = map(dp_dtop,map(dp_ht,map(dp_ptod,G,V)),V);
1857: H = map(sq,H,0);
1858: H = nd_gr(H,V,0,0);
1859: H = monodec0(H,V);
1860: N = length(V);
1861: Dep = [];
1862: for ( T = H, Len = N+1; T != []; T = cdr(T) ) {
1863: M = length(car(T));
1864: if ( M < Len ) {
1865: Dep = [car(T)];
1866: Len = M;
1867: } else if ( M == Len )
1868: Dep = cons(car(T),Dep);
1869: }
1870: R = setminus(V,Dep[0]);
1871: dp_ord(Old);
1872: return R;
1873: }
1874:
1.7 noro 1875: def maxindep2(B,V,O)
1876: {
1877: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1878: G = fast_gb(B,V,Mod,O);
1879: Old = dp_ord();
1880: dp_ord(O);
1881: H = map(dp_dtop,map(dp_ht,map(dp_ptod,G,V)),V);
1882: H = map(sq,H,0);
1883: H = nd_gr(H,V,0,0);
1884: H = monodec0(H,V);
1885: N = length(V);
1886: Dep = [];
1887: for ( T = H, Len = N+1; T != []; T = cdr(T) ) {
1888: M = length(car(T));
1889: if ( M < Len ) {
1890: Dep = [car(T)];
1891: Len = M;
1892: } else if ( M == Len )
1893: Dep = cons(car(T),Dep);
1894: }
1895: R = [];
1896: for ( T = Dep; T != []; T = cdr(T) )
1897: R = cons(setminus(V,car(T)),R);
1898: dp_ord(Old);
1899: return reverse(R);
1900: }
1901:
1902:
1.1 noro 1903: /* ideal operations */
1904: def contraction(G,V)
1905: {
1.8 noro 1906: if ( type(AllV=getopt(allv)) == -1 ) AllV = 0;
1.1 noro 1907: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1.8 noro 1908:
1909: if ( RepColon ) return contraction_m(G,V|allv=AllV,mod=Mod);
1910:
1.1 noro 1911: C = [];
1912: for ( T = G; T != []; T = cdr(T) ) {
1913: C1 = dp_hc(dp_ptod(car(T),V));
1914: S = gen_fctr(C1,Mod);
1915: for ( S = cdr(S); S != []; S = cdr(S) )
1916: if ( !member(S[0][0],C) ) C = cons(S[0][0],C);
1917: }
1918: W = vars(G);
1919: PV = setminus(W,V);
1.8 noro 1920: if ( AllV ) W = AllV;
1921: else W = append(V,PV);
1.1 noro 1922: NV = ttttt;
1.8 noro 1923: if ( SuccSat ) {
1924: W1 = cons(NV,W);
1925: O1 = [[0,1],[0,length(W)]];
1926: Block = [];
1927: for ( T = C; T != []; T = cdr(T) ) {
1928: G1 = nd_gr(append(G,[NV*car(T)-1]),W1,Mod,O1|gbblock=Block);
1929: G = elimination(G1,W);
1930: Block = [[0,length(G)]];
1931: }
1932: } else {
1933: for ( T = C, S = 1; T != []; T = cdr(T) )
1934: S *= car(T);
1935: G = saturation([G,NV],S,W|mod=Mod);
1936: }
1.1 noro 1937: return G;
1938: }
1939:
1.8 noro 1940: def contraction_m(G,V)
1941: {
1942: if ( type(AllV=getopt(allv)) == -1 ) AllV = 0;
1943: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1944: C = [];
1945: for ( T = G; T != []; T = cdr(T) ) {
1946: C1 = dp_hc(dp_ptod(car(T),V));
1947: S = gen_fctr(C1,Mod);
1948: for ( S = cdr(S); S != []; S = cdr(S) )
1949: if ( !member(S[0][0],C) ) C = cons(S[0][0],C);
1950: }
1951: W = vars(G);
1952: PV = setminus(W,V);
1953: if ( AllV ) W = AllV;
1954: else W = append(V,PV);
1955: H = H0 = G;
1956: while ( 1 ) {
1957: for ( T = C; T != []; T = cdr(T) )
1958: H = map(sdiv,ideal_intersection_m([car(T)],H,W,0),car(T));
1959: H = nd_gr(H,W,0,0);
1960: if ( gb_comp(H0,H) ) break;
1961: else H0 = H;
1962: }
1963: return H;
1964: }
1965:
1.1 noro 1966: def ideal_list_intersection(L,V,Ord)
1967: {
1968: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1.4 noro 1969: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
1.1 noro 1970: N = length(L);
1971: if ( N == 0 ) return [1];
1.4 noro 1972: if ( N == 1 )
1973: return IsGB ? L[0] : fast_gb(L[0],V,Mod,Ord);
1.8 noro 1974: else {
1.4 noro 1975: for ( I = 0, T = [1]; I < N; I++ )
1976: T = ideal_intersection_m(T,L[I],V,Ord|mod=Mod);
1977: T = nd_gr(T,V,Mod,Ord);
1978: return T;
1.1 noro 1979: }
1980: }
1981:
1.4 noro 1982: def call_ideal_list_intersection(L,V,Mod,Ord,IsGB)
1.1 noro 1983: {
1.4 noro 1984: return ideal_list_intersection(L,V,Ord|mod=Mod,isgb=IsGB);
1.1 noro 1985: }
1986:
1987: def ideal_intersection(A,B,V,Ord)
1988: {
1989: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1990: if ( type(Block=getopt(gbblock)) == -1 ) Block = 0;
1991: T = ttttt;
1992: if ( Mod ) {
1993: if ( Block )
1994: G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
1995: cons(T,V),Mod,[[0,1],[Ord,length(V)]]|gbblock=Block,nora=0);
1996: else
1997: G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
1998: cons(T,V),Mod,[[0,1],[Ord,length(V)]]|nora=0);
1999: } else
2000: if ( Procs ) {
2001: Arg0 = ["nd_gr",
2002: append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
2003: cons(T,V),0,[[0,1],[Ord,length(V)]]];
2004: Arg1 = ["nd_gr_trace",
2005: append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
2006: cons(T,V),1,GBCheck,[[0,1],[Ord,length(V)]]];
2007: G = competitive_exec(Procs,Arg0,Arg1);
2008: } else {
2009: if ( Block )
2010: G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
2011: cons(T,V),0,[[0,1],[Ord,length(V)]]|gbblock=Block,nora=0);
2012: else
2013: G = nd_gr(append(vtol(ltov(A)*T),vtol(ltov(B)*(1-T))),
2014: cons(T,V),0,[[0,1],[Ord,length(V)]]|nora=0);
2015: }
2016: G0 = elimination(G,V);
2017: if ( 0 && !Procs )
2018: G0 = nd_gr_postproc(G0,V,Mod,Ord,0);
2019: return G0;
2020: }
2021:
1.4 noro 2022:
2023: def aa(A) { return [A,A]; }
2024:
2025: def ideal_intersection_m(A,B,V,Ord)
2026: {
2027: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2028:
2029: dp_ord(Ord);
2030: DA = map(dp_ptod,A,V); DB = ltov(map(dp_ptod,B,V));
2031: if ( Mod ) {
2032: DA = map(dp_mod,DA,Mod,[]); DB = map(dp_mod,DB,Mod,[]);
2033: setmod(Mod);
2034: }
2035: N = length(B);
2036: for ( Ind = [], I = N-1; I >= 0; I-- ) Ind = cons(I,Ind);
2037: for ( T = DA, C = []; T != []; T = cdr(T) ) {
2038: L = Mod?dp_true_nf_mod(Ind,car(T),DB,1,Mod):dp_true_nf(Ind,car(T),DB,1);
2039: R = dp_dtop(L[0],V); Q = dp_dtop(car(T)*L[1]-L[0],V);
2040: C = cons([R,-Q],C);
2041: }
2042: G = nd_gr(append(C,map(aa,B)),V,Mod,[1,Ord]|intersect=1);
2043: G = map(second,G);
2044: return G;
2045: }
2046:
1.1 noro 2047: /* returns GB if F notin rad(G) */
2048:
2049: def radical_membership(F,G,V) {
2050: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2051: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
1.4 noro 2052: if ( type(L=getopt(dg)) == -1 ) L = 0;
1.7 noro 2053: if ( type(Sat=getopt(sat)) == -1 ) Sat = 0;
1.4 noro 2054: dp_ord(0);
2055: if ( L ) { DG = L[0]; Ind = L[1]; }
2056: else {
2057: DG = ltov(map(dp_ptod,G,V));
2058: if ( Mod ) DG = map(dp_mod,DG,Mod,[]);
2059: for ( Ind = [], I = length(G)-1; I >= 0; I-- ) Ind = cons(I,Ind);
2060: }
2061: DF = dp_ptod(F,V); DFI = dp_ptod(1,V);
2062: if ( Mod ) {
2063: DF = dp_mod(DF,Mod,[]); DFI = dp_mod(DFI,Mod,[]);
2064: setmod(Mod);
2065: }
2066: for ( I = 0; I < 3; I++ ) {
2067: DFI = Mod?dp_nf_mod(Ind,DF*DFI,DG,0,Mod):dp_nf(Ind,DF*DFI,DG,0);
2068: if ( !DFI ) return 0;
2069: }
1.1 noro 2070: NV = ttttt;
2071: if ( IsGB )
2072: T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,0
2073: |gbblock=[[0,length(G)]]);
2074: else
2075: T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,0);
1.7 noro 2076: if ( type(car(T)) == 1 ) return 0;
2077: else if ( Sat ) {
2078: G1 = fast_gb(T,cons(NV,V),Mod,[[0,1],[0,length(V)]]);
2079: G0 = elimination(G1,V);
2080: return G0;
2081: } else return [T,NV];
1.1 noro 2082: }
2083:
1.8 noro 2084: def radical_membership_sat(F,G,V) {
2085: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2086: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
2087: if ( type(L=getopt(dg)) == -1 ) L = 0;
2088: dp_ord(0);
2089: if ( L ) { DG = L[0]; Ind = L[1]; }
2090: else {
2091: DG = ltov(map(dp_ptod,G,V));
2092: if ( Mod ) DG = map(dp_mod,DG,Mod,[]);
2093: for ( Ind = [], I = length(G)-1; I >= 0; I-- ) Ind = cons(I,Ind);
2094: }
2095: DF = dp_ptod(F,V); DFI = dp_ptod(1,V);
2096: if ( Mod ) {
2097: DF = dp_mod(DF,Mod,[]); DFI = dp_mod(DFI,Mod,[]);
2098: setmod(Mod);
2099: }
2100: for ( I = 0; I < 3; I++ ) {
2101: DFI = Mod?dp_nf_mod(Ind,DF*DFI,DG,0,Mod):dp_nf(Ind,DF*DFI,DG,0);
2102: if ( !DFI ) return 0;
2103: }
2104: NV = ttttt;
2105: if ( IsGB )
2106: T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,[[0,1],[0,length(V)]]
2107: |gbblock=[[0,length(G)]]);
2108: else
2109: T = nd_gr(append(G,[NV*F-1]),cons(NV,V),Mod,[[0,1],[0,length(V)]]);
2110: if ( type(car(T)) == 1 ) return 0;
2111: G0 = elimination(T,V);
2112: return G0;
2113: }
2114:
1.1 noro 2115: def modular_radical_membership(F,G,V) {
2116: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2117: if ( Mod )
2118: return radical_membership(F,G,V|mod=Mod);
2119:
2120: F = gen_nf(F,G,V,0,0);
2121: if ( !F ) return 0;
2122: NV = ttttt;
2123: for ( J = 0; ; J++ ) {
2124: Mod = lprime(J);
2125: H = map(dp_hc,map(dp_ptod,G,V));
2126: for ( ; H != []; H = cdr(H) ) if ( !(car(H)%Mod) ) break;
2127: if ( H != [] ) continue;
2128:
2129: T = nd_f4(cons(NV*F-1,G),cons(NV,V),Mod,0);
2130: if ( type(car(T)) == 1 ) {
2131: I = radical_membership_rep(F,G,V,-1,0,Mod);
2132: I1 = radical_membership_rep(F,G,V,I,0,0);
2133: if ( I1 > 0 ) return 0;
2134: }
2135: return radical_membership(F,G,V);
2136: }
2137: }
2138:
2139: def radical_membership_rep(F,G,V,Max,Ord,Mod) {
2140: Ft = F;
2141: I = 1;
2142: while ( Max < 0 || I <= Max ) {
2143: Ft = gen_nf(Ft,G,V,Ord,Mod);
2144: if ( !Ft ) return I;
2145: Ft *= F;
2146: I++;
2147: }
2148: return -1;
2149: }
2150:
2151: def ideal_product(A,B,V)
2152: {
2153: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2154: dp_ord(0);
2155: DA = map(dp_ptod,A,V);
2156: DB = map(dp_ptod,B,V);
2157: DegA = map(dp_td,DA);
2158: DegB = map(dp_td,DB);
2159: for ( PA = [], T = A, DT = DegA; T != []; T = cdr(T), DT = cdr(DT) )
2160: PA = cons([car(T),car(DT)],PA);
2161: PA = reverse(PA);
2162: for ( PB = [], T = B, DT = DegB; T != []; T = cdr(T), DT = cdr(DT) )
2163: PB = cons([car(T),car(DT)],PB);
2164: PB = reverse(PB);
2165: R = [];
2166: for ( T = PA; T != []; T = cdr(T) )
2167: for ( S = PB; S != []; S = cdr(S) )
2168: R = cons([car(T)[0]*car(S)[0],car(T)[1]+car(S)[1]],R);
1.9 ohara 2169: T = qsort(R,noro_pd.comp_by_second);
1.1 noro 2170: T = map(first,T);
2171: Len = length(A)>length(B)?length(A):length(B);
2172: Len *= 2;
2173: L = sep_list(T,Len); B0 = L[0]; B1 = L[1];
2174: R = fast_gb(B0,V,Mod,0);
2175: while ( B1 != [] ) {
2176: print(length(B1));
2177: L = sep_list(B1,Len);
2178: B0 = L[0]; B1 = L[1];
2179: R = fast_gb(append(R,B0),V,Mod,0|gbblock=[[0,length(R)]],nora=1);
2180: }
2181: return R;
2182: }
2183:
2184: def saturation(GNV,F,V)
2185: {
2186: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2187: G = GNV[0]; NV = GNV[1];
2188: if ( Mod )
2189: G1 = nd_gr(cons(NV*F-1,G),cons(NV,V),Mod,[[0,1],[0,length(V)]]);
2190: else if ( Procs ) {
2191: Arg0 = ["nd_gr_trace",
2192: cons(NV*F-1,G),cons(NV,V),0,GBCheck,[[0,1],[0,length(V)]]];
2193: Arg1 = ["nd_gr_trace",
2194: cons(NV*F-1,G),cons(NV,V),1,GBCheck,[[0,1],[0,length(V)]]];
2195: G1 = competitive_exec(Procs,Arg0,Arg1);
2196: } else
2197: G1 = nd_gr(cons(NV*F-1,G),cons(NV,V),0,[[0,1],[0,length(V)]]);
2198: return elimination(G1,V);
2199: }
2200:
2201: def sat(G,F,V)
2202: {
2203: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2204: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
2205: NV = ttttt;
2206: if ( Mod )
2207: G1 = nd_gr(cons(NV*F-1,G),cons(NV,V),Mod,[[0,1],[0,length(V)]]);
2208: else if ( Procs ) {
2209: Arg0 = ["nd_gr_trace",
2210: cons(NV*F-1,G),cons(NV,V),0,GBCheck,[[0,1],[0,length(V)]]];
2211: Arg1 = ["nd_gr_trace",
2212: cons(NV*F-1,G),cons(NV,V),1,GBCheck,[[0,1],[0,length(V)]]];
2213: G1 = competitive_exec(Procs,Arg0,Arg1);
2214: } else {
2215: B1 = append(G,[NV*F-1]);
2216: V1 = cons(NV,V);
2217: Ord1 = [[0,1],[0,length(V)]];
2218: if ( IsGB )
2219: G1 = nd_gr(B1,V1,0,Ord1|gbblock=[[0,length(G)]]);
2220: else
2221: G1 = nd_gr(B1,V1,0,Ord1);
2222: }
2223: return elimination(G1,V);
2224: }
2225:
1.4 noro 2226: def isat(B,S,V)
2227: {
2228: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2229: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
2230: F = cdr(fctr(S));
2231: R = B;
2232: for ( T = F; T != []; T = cdr(T) )
2233: R = sat(R,car(T)[0],V|mod=Mod,isgb=IsGB);
2234: return R;
2235: }
2236:
1.11 noro 2237: /* buggy; do not use */
1.1 noro 2238: def satind(G,F,V)
2239: {
2240: if ( type(Block=getopt(gbblock)) == -1 ) Block = 0;
2241: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2242: NV = ttttt;
2243: N = length(V);
2244: B = append(G,[NV*F-1]);
2245: V1 = cons(NV,V);
2246: Ord1 = [[0,1],[0,N]];
2247: if ( Mod )
2248: if ( Block )
2249: D = nd_gr(B,V1,Mod,Ord1|nora=1,gentrace=1,gbblock=Block);
2250: else
2251: D = nd_gr(B,V1,Mod,Ord1|nora=1,gentrace=1);
2252: else
2253: if ( Block )
2254: D = nd_gr_trace(B,V1,SatHomo,GBCheck,Ord1
2255: |nora=1,gentrace=1,gbblock=Block);
2256: else
2257: D = nd_gr_trace(B,V1,SatHomo,GBCheck,Ord1
2258: |nora=1,gentrace=1);
2259: G1 = D[0];
2260: Len = length(G1);
2261: Deg = compute_deg(B,V1,NV,D);
2262: D1 = 0;
2263: R = [];
2264: M = length(B);
2265: for ( I = 0; I < Len; I++ ) {
2266: if ( !member(NV,vars(G1[I])) ) {
2267: for ( J = 1; J < M; J++ )
2268: D1 = MAX(D1,Deg[I][J]);
2269: R = cons(G1[I],R);
2270: }
2271: }
2272: return [reverse(R),D1];
2273: }
2274:
1.12 ! noro 2275: /* homogeneous case only */
! 2276:
1.11 noro 2277: def sat_ind_var(G,F,V)
2278: {
2279: if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
2280: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2281: V0 = append(setminus(V,[F]),[F]);
2282: G0 = nd_gr(G,V0,Mod,0);
2283: M = 0;
2284: for ( G1 = [], T = G0; T != []; T = cdr(T) ) {
2285: S = car(T);
2286: M1 = mindeg(S,F);
2287: S = sdiv(S,F^M1);
2288: G1 = cons(S,G1);
2289: if ( M1 > M ) M = M1;
2290: }
2291: G1 = nd_gr(G1,V,Mod,Ord);
2292: return [G1,M];
2293: }
2294:
1.1 noro 2295: def sat_ind(G,F,V)
2296: {
2297: if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
2298: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2299: NV = ttttt;
2300: F = gen_nf(F,G,V,Ord,Mod);
2301: for ( I = 0, GI = G; ; I++ ) {
2302: G1 = colon(GI,F,V|mod=Mod,ord=Ord);
2303: if ( ideal_inclusion(G1,GI,V,Ord|mod=Mod) ) {
2304: return [GI,I];
2305: }
2306: else GI = G1;
2307: }
2308: }
2309:
2310: def colon(G,F,V)
2311: {
2312: if ( type(Ord=getopt(ord)) == -1 ) Ord = 0;
2313: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2314: if ( type(IsGB=getopt(isgb)) == -1 ) IsGB = 0;
2315: F = gen_nf(F,G,V,Ord,Mod);
2316: if ( !F ) return [1];
2317: if ( IsGB )
2318: T = ideal_intersection(G,[F],V,Ord|gbblock=[[0,length(G)]],mod=Mod);
2319: else
2320: T = ideal_intersection(G,[F],V,Ord|mod=Mod);
1.4 noro 2321: Gen = Mod?map(sdivm,T,F,Mod):map(ptozp,map(sdiv,T,F));
2322: return nd_gr(Gen,V,Mod,Ord);
1.1 noro 2323: }
2324:
2325: #if 1
2326: def ideal_colon(G,F,V)
2327: {
2328: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2329: G = nd_gr(G,V,Mod,0);
2330: C = [1];
2331: TV = ttttt;
1.9 ohara 2332: F = qsort(F,noro_pd.comp_tdeg);
1.1 noro 2333: for ( T = F; T != []; T = cdr(T) ) {
2334: S = colon(G,car(T),V|isgb=1,mod=Mod);
2335: if ( type(S[0])!= 1 ) {
2336: C = nd_gr(append(vtol(ltov(C)*TV),vtol(ltov(S)*(1-TV))),
2337: cons(TV,V),Mod,[[0,1],[Ord,length(V)]]|gbblock=[[0,length(C)]]);
2338: C = elimination(C,V);
2339: }
2340: }
2341: return C;
2342: }
2343: #else
2344: def ideal_colon(G,F,V)
2345: {
2346: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2347: G = nd_gr(G,V,Mod,0);
2348: for ( T = F, L = []; T != []; T = cdr(T) ) {
2349: C = colon(G,car(T),V|isgb=1,mod=Mod);
2350: if ( type(C[0]) != 1 ) L = cons(C,L);
2351: }
2352: L = reverse(L);
2353: return ideal_list_intersection(L,V,0|mod=Mod);
2354: }
2355:
2356: #endif
2357:
2358: def member(A,L)
2359: {
2360: for ( ; L != []; L = cdr(L) )
2361: if ( car(L) == A ) return 1;
2362: return 0;
2363: }
2364:
2365: def mingen(B,V) {
2366: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2367: Data = nd_gr(B,V,Mod,O|gentrace=1,gensyz=1);
1.4 noro 2368: G = Data[0]; STrace = Data[6];
1.1 noro 2369: N = length(G);
1.4 noro 2370: S = compute_gbsyz(N,V,STrace,Mod);
2371: for ( T = S, R = []; T != []; T = cdr(T) ) {
2372: for ( A = car(T); A1 = dp_rest(A); A = A1);
2373: if ( type(dp_hc(A)) ==1 ) R = cons(dp_etov(A)[0],R);
2374: }
2375: for ( I = 0, U = []; I < N; I++ ) if ( !member(I,R) ) U = cons(G[I],U);
1.1 noro 2376: return U;
2377: }
2378:
1.4 noro 2379: def compute_gbsyz(N,V,Trace,Mod)
1.1 noro 2380: {
2381: P = vector(N);
1.4 noro 2382: for ( I = 0; I < N; I++ ) P[I] = dp_ptod(x^I,[x]);
2383: for ( U = [], T = Trace; T != []; T = cdr(T) ) {
1.1 noro 2384: Ti = car(T);
2385: if ( Ti[0] != -1 ) error("Input is not a GB");
1.4 noro 2386: R = recompute_trace(Ti[1],P,V,Mod);
2387: U = cons(R,U);
1.1 noro 2388: }
2389: return reverse(U);
2390: }
2391:
1.4 noro 2392: def recompute_trace(Ti,P,V,Mod)
1.1 noro 2393: {
2394: for ( Num = 0, Den = 1; Ti != []; Ti = cdr(Ti) ) {
1.4 noro 2395: Sj = car(Ti); Dj = Sj[0]; Ij =Sj[1]; Mj = dp_dtop(Sj[2],V); Cj = Sj[3];
1.1 noro 2396: /* Num/Den <- (Dj*Num+Den*Mj*P[Ij])/(Den*Cj) */
1.4 noro 2397: if ( Dj ) Num = (Dj*Num+Den*Mj*P[Ij]);
1.1 noro 2398: Den *= Cj;
2399: }
1.4 noro 2400: return Num;
1.1 noro 2401: }
2402:
2403: def ideal_sat(G,F,V)
2404: {
2405: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2406: G = nd_gr(G,V,Mod,0);
2407: for ( T = F, L = []; T != []; T = cdr(T) )
2408: L = cons(sat(G,car(T),V|mod=Mod),L);
2409: L = reverse(L);
2410: return ideal_list_intersection(L,V,0|mod=Mod);
2411: }
2412:
2413: def ideal_inclusion(F,G,V,O)
2414: {
2415: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2416: for ( T = F; T != []; T = cdr(T) )
2417: if ( gen_nf(car(T),G,V,O,Mod) ) return 0;
2418: return 1;
2419: }
2420:
2421: /* remove redundant components */
2422:
2423: def qd_simp_comp(QP,V)
2424: {
2425: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2426: R = ltov(QP);
2427: N = length(R);
2428: for ( I = 0; I < N; I++ ) {
2429: if ( R[I] ) {
2430: QI = R[I][0]; PI = R[I][1];
2431: for ( J = I+1; J < N; J++ )
2432: if ( R[J] && gen_gb_comp(PI,R[J][1],Mod) ) {
2433: QI = ideal_intersection(QI,R[J][0],V,0|mod=Mod);
2434: R[J] = 0;
2435: }
2436: R[I] = [QI,PI];
2437: }
2438: }
2439: for ( I = N-1, S = []; I >= 0; I-- )
2440: if ( R[I] ) S = cons(R[I],S);
2441: return S;
2442: }
2443:
2444: def qd_remove_redundant_comp(G,Iso,Emb,V,Ord)
2445: {
2446: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2447: IsoInt = ideal_list_intersection(map(first,Iso),V,Ord|mod=Mod);
2448: Emb = qd_simp_comp(Emb,V|mod=Mod);
2449: Emb = reverse(qsort(Emb));
2450: A = ltov(Emb); N = length(A);
2451: Pre = IsoInt; Post = vector(N+1);
2452: for ( Post[N] = IsoInt, I = N-1; I >= 1; I-- )
2453: Post[I] = ideal_intersection(Post[I+1],A[I][0],V,Ord|mod=Mod);
2454: for ( I = 0; I < N; I++ ) {
2455: print(".",2);
2456: Int = ideal_intersection(Pre,Post[I+1],V,Ord|mod=Mod);
2457: if ( gen_gb_comp(Int,G,Mod) ) A[I] = 0;
2458: else
2459: Pre = ideal_intersection(Pre,A[I][0],V,Ord|mod=Mod);
2460: }
2461: for ( T = [], I = 0; I < N; I++ )
2462: if ( A[I] ) T = cons(A[I],T);
2463: return reverse(T);
2464: }
2465:
2466: def pd_simp_comp(PL,V)
2467: {
2468: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2469: if ( type(First=getopt(first)) == -1 ) First = 0;
2470: A = ltov(PL); N = length(A);
2471: if ( N == 1 ) return PL;
2472: for ( I = 0; I < N; I++ ) {
2473: if ( !A[I] ) continue;
2474: AI = First?A[I][0]:A[I];
2475: for ( J = 0; J < N; J++ ) {
2476: if ( J == I || !A[J] ) continue;
2477: AJ = First?A[J][0]:A[J];
2478: if ( gen_gb_comp(AI,AJ,Mod) || ideal_inclusion(AI,AJ,V,Ord|mod=Mod) )
2479: A[J] = 0;
2480: }
2481: }
2482: for ( I = 0, T = []; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
2483: return reverse(T);
2484: }
2485:
2486: def pd_remove_redundant_comp(G,P,V,Ord)
2487: {
2488: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2489: if ( type(First=getopt(first)) == -1 ) First = 0;
2490: if ( length(P) == 1 ) return P;
2491:
2492: A = ltov(P); N = length(A);
2493: for ( I = 0; I < N; I++ ) {
2494: if ( !A[I] ) continue;
2495: for ( J = I+1; J < N; J++ )
2496: if ( A[J] &&
2497: gen_gb_comp(First?A[I][0]:A[I],First?A[J][0]:A[J],Mod) ) A[J] = 0;
2498: }
2499: for ( I = 0, T = []; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
2500: A = ltov(reverse(T)); N = length(A);
2501: Pre = [1]; Post = vector(N+1);
2502: for ( Post[N] = [1], I = N-1; I >= 1; I-- )
2503: Post[I] = ideal_intersection(Post[I+1],First?A[I][0]:A[I],V,Ord|mod=Mod);
2504: for ( I = 0; I < N; I++ ) {
2505: Int = ideal_intersection(Pre,Post[I+1],V,Ord|mod=Mod);
2506: if ( gen_gb_comp(Int,G,Mod) ) A[I] = 0;
2507: else
2508: Pre = ideal_intersection(Pre,First?A[I][0]:A[I],V,Ord|mod=Mod);
2509: }
2510: for ( T = [], I = 0; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
2511: return reverse(T);
2512: }
2513:
1.7 noro 2514: def remove_identical_comp(L)
2515: {
2516: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2517: if ( length(L) == 1 ) return L;
2518:
2519: A = ltov(L); N = length(A);
2520: for ( I = 0; I < N; I++ ) {
2521: if ( !A[I] ) continue;
2522: for ( J = I+1; J < N; J++ )
2523: if ( A[J] &&
2524: gen_gb_comp(A[I],A[J],Mod) ) A[J] = 0;
2525: }
2526: for ( I = 0, T = []; I < N; I++ ) if ( A[I] ) T = cons(A[I],T);
2527: return reverse(T);
2528: }
2529:
1.1 noro 2530: /* polynomial operations */
2531:
2532: def ppart(F,V,Mod)
2533: {
2534: if ( !Mod )
2535: G = nd_gr([F],[V],0,0);
2536: else
2537: G = dp_gr_mod_main([F],[V],0,Mod,0);
2538: return G[0];
2539: }
2540:
2541:
2542: def sq(F,Mod)
2543: {
2544: if ( !F ) return 0;
2545: A = cdr(gen_fctr(F,Mod));
2546: for ( R = 1; A != []; A = cdr(A) )
2547: R *= car(car(A));
2548: return R;
2549: }
2550:
2551: def lcfactor(G,V,O,Mod)
2552: {
2553: O0 = dp_ord(); dp_ord(O);
2554: C = [];
2555: for ( T = G; T != []; T = cdr(T) ) {
2556: C1 = dp_hc(dp_ptod(car(T),V));
2557: S = gen_fctr(C1,Mod);
2558: for ( S = cdr(S); S != []; S = cdr(S) )
2559: if ( !member(S[0][0],C) ) C = cons(S[0][0],C);
2560: }
2561: dp_ord(O0);
2562: return C;
2563: }
2564:
2565: def gen_fctr(F,Mod)
2566: {
2567: if ( Mod ) return modfctr(F,Mod);
2568: else return fctr(F);
2569: }
2570:
2571: def gen_mptop(F)
2572: {
2573: if ( !F ) return F;
2574: else if ( type(F)==1 )
2575: if ( ntype(F)==5 ) return mptop(F);
2576: else return F;
2577: else {
2578: V = var(F);
2579: D = deg(F,V);
2580: for ( R = 0, I = 0; I <= D; I++ )
2581: if ( C = coef(F,I,V) ) R += gen_mptop(C)*V^I;
2582: return R;
2583: }
2584: }
2585:
2586: def gen_nf(F,G,V,Ord,Mod)
2587: {
2588: if ( !Mod ) return p_nf(F,G,V,Ord);
2589:
2590: setmod(Mod);
2591: dp_ord(Ord); DF = dp_mod(dp_ptod(F,V),Mod,[]);
2592: N = length(G); DG = newvect(N);
2593: for ( I = N-1, IL = []; I >= 0; I-- ) {
2594: DG[I] = dp_mod(dp_ptod(G[I],V),Mod,[]);
2595: IL = cons(I,IL);
2596: }
2597: T = dp_nf_mod(IL,DF,DG,1,Mod);
2598: for ( R = 0; T; T = dp_rest(T) )
2599: R += gen_mptop(dp_hc(T))*dp_dtop(dp_ht(T),V);
2600: return R;
2601: }
2602:
2603: /* Ti = [D,I,M,C] */
2604:
2605: def compute_deg0(Ti,P,V,TV)
2606: {
2607: N = length(P[0]);
2608: Num = vector(N);
2609: for ( I = 0; I < N; I++ ) Num[I] = -1;
2610: for ( ; Ti != []; Ti = cdr(Ti) ) {
2611: Sj = car(Ti);
2612: Dj = Sj[0];
2613: Ij =Sj[1];
2614: Mj = deg(type(Sj[2])==9?dp_dtop(Sj[2],V):Sj[2],TV);
2615: Pj = P[Ij];
2616: if ( Dj )
2617: for ( I = 0; I < N; I++ )
2618: if ( Pj[I] >= 0 ) {
2619: T = Mj+Pj[I];
2620: Num[I] = MAX(Num[I],T);
2621: }
2622: }
2623: return Num;
2624: }
2625:
2626: def compute_deg(B,V,TV,Data)
2627: {
2628: GB = Data[0];
2629: Homo = Data[1];
2630: Trace = Data[2];
2631: IntRed = Data[3];
2632: Ind = Data[4];
2633: DB = map(dp_ptod,B,V);
2634: if ( Homo ) {
2635: DB = map(dp_homo,DB);
2636: V0 = append(V,[hhh]);
2637: } else
2638: V0 = V;
2639: Perm = Trace[0]; Trace = cdr(Trace);
2640: for ( I = length(Perm)-1, T = Trace; T != []; T = cdr(T) )
2641: if ( (J=car(T)[0]) > I ) I = J;
2642: N = I+1;
2643: N0 = length(B);
2644: P = vector(N);
2645: for ( T = Perm, I = 0; T != []; T = cdr(T), I++ ) {
2646: Pi = car(T);
2647: C = vector(N0);
2648: for ( J = 0; J < N0; J++ ) C[J] = -1;
2649: C[Pi[1]] = 0;
2650: P[Pi[0]] = C;
2651: }
2652: for ( T = Trace; T != []; T = cdr(T) ) {
2653: Ti = car(T); P[Ti[0]] = compute_deg0(Ti[1],P,V0,TV);
2654: }
2655: M = length(Ind);
2656: for ( T = IntRed; T != []; T = cdr(T) ) {
2657: Ti = car(T); P[Ti[0]] = compute_deg0(Ti[1],P,V,TV);
2658: }
2659: R = [];
2660: for ( J = 0; J < M; J++ ) {
2661: U = P[Ind[J]];
2662: R = cons(U,R);
2663: }
2664: return reverse(R);
2665: }
2666:
2667: /* set theoretic functions */
2668:
2669: def member(A,S)
2670: {
2671: for ( ; S != []; S = cdr(S) )
2672: if ( car(S) == A ) return 1;
2673: return 0;
2674: }
2675:
2676: def elimination(G,V) {
2677: for ( R = [], T = G; T != []; T = cdr(T) )
2678: if ( setminus(vars(car(T)),V) == [] ) R =cons(car(T),R);
2679: return R;
2680: }
2681:
2682: def setintersection(A,B)
2683: {
2684: for ( L = []; A != []; A = cdr(A) )
2685: if ( member(car(A),B) )
2686: L = cons(car(A),L);
2687: return L;
2688: }
2689:
2690: def setminus(A,B) {
2691: for ( T = reverse(A), R = []; T != []; T = cdr(T) ) {
2692: for ( S = B, M = car(T); S != []; S = cdr(S) )
2693: if ( car(S) == M ) break;
2694: if ( S == [] ) R = cons(M,R);
2695: }
2696: return R;
2697: }
2698:
2699: def sep_list(L,N)
2700: {
2701: if ( length(L) <= N ) return [L,[]];
2702: R = [];
2703: for ( T = L, I = 0; I < N; I++, T = cdr(T) )
2704: R = cons(car(T),R);
2705: return [reverse(R),T];
2706: }
2707:
2708: def first(L)
2709: {
2710: return L[0];
2711: }
2712:
2713: def second(L)
2714: {
2715: return L[1];
2716: }
2717:
2718: def third(L)
2719: {
2720: return L[2];
2721: }
2722:
2723: def first_second(L)
2724: {
2725: return [L[0],L[1]];
2726: }
2727:
2728: def comp_tord(A,B)
2729: {
2730: DA = dp_ht(A);
2731: DB = dp_ht(B);
2732: if ( DA > DB ) return 1;
2733: else if ( DA < DB ) return -1;
2734: else return 0;
2735: }
2736:
2737: def comp_tdeg(A,B)
2738: {
2739: DA = tdeg(A);
2740: DB = tdeg(B);
2741: if ( DA > DB ) return 1;
2742: else if ( DA < DB ) return -1;
2743: else return 0;
2744: }
2745:
2746: def comp_tdeg_first(A,B)
2747: {
2748: DA = tdeg(A[0]);
2749: DB = tdeg(B[0]);
2750: if ( DA > DB ) return 1;
2751: else if ( DA < DB ) return -1;
2752: else return 0;
2753: }
2754:
2755: def comp_third_tdeg(A,B)
2756: {
2757: if ( A[2] > B[2] ) return 1;
2758: if ( A[2] < B[2] ) return -1;
2759: DA = tdeg(A[0]);
2760: DB = tdeg(B[0]);
2761: if ( DA > DB ) return 1;
2762: else if ( DA < DB ) return -1;
2763: else return 0;
2764: }
2765:
2766: def tdeg(P)
2767: {
2768: dp_ord(0);
2769: return dp_td(dp_ptod(P,vars(P)));
2770: }
2771:
2772: def comp_by_ord(A,B)
2773: {
2774: if ( dp_ht(A) > dp_ht(B) ) return 1;
2775: else if ( dp_ht(A) < dp_ht(B) ) return -1;
2776: else return 0;
2777: }
2778:
2779: def comp_by_second(A,B)
2780: {
2781: if ( A[1] > B[1] ) return 1;
2782: else if ( A[1] < B[1] ) return -1;
2783: else return 0;
2784: }
2785:
2786: def get_lc(F)
2787: {
2788: if ( type(F)==1 ) return F;
2789: V = var(F);
2790: D = deg(F,V);
2791: return get_lc(coef(F,D,V));
2792: }
2793:
2794: def tomonic(F,Mod)
2795: {
2796: C = get_lc(F);
2797: IC = inv(C,Mod);
2798: return (IC*F)%Mod;
2799: }
2800:
2801: def gen_gb_comp(A,B,Mod)
2802: {
2803: if ( !Mod ) return gb_comp(A,B);
2804: LA = length(A); LB = length(B);
2805: if ( LA != LB ) return 0;
2806: A = map(tomonic,A,Mod);
2807: B = map(tomonic,B,Mod);
2808: A = qsort(A); B = qsort(B);
2809: if ( A != B ) return 0;
2810: return 1;
2811: }
2812:
2813: def prod(L)
2814: {
2815: for ( R = 1; L != []; L = cdr(L) )
2816: R *= car(L);
2817: return R;
2818: }
2819:
2820: def monodec0(B,V)
2821: {
2822: M = monodec(B,V);
2823: return map(vars,M);
2824: }
2825:
2826: def monodec(B,V)
2827: {
2828: B = map(sq,B,0);
2829: G = nd_gr_postproc(B,V,0,0,0);
2830: V = vars(G);
2831: N = length(V);
2832: if ( N == 0 ) return G == [] ? [[]] : [];
2833: if ( N == 1 ) return G;
2834: if ( N < 20 ) {
2835: T = dp_mono_raddec(G,V);
2836: return map(prod,T);
2837: }
2838: X = car(V); W = cdr(V);
2839: D0 = monodec(map(subst,B,X,0),W);
2840: T0 = map(dp_ptod,D0,W);
2841: D1 = monodec(map(subst,B,X,1),W);
2842: T1 = map(dp_ptod,D1,W);
1.4 noro 2843: #if 0
1.1 noro 2844: for ( T = T1; T != []; T = cdr(T) ) {
2845: for ( M = car(T), S1 = [], S = T0; S != []; S = cdr(S) )
2846: if ( !dp_redble(car(S),M) ) S1= cons(car(S),S1);
2847: T0 = S1;
2848: }
1.4 noro 2849: #else
2850: T0 = dp_mono_reduce(T0,T1);
2851: #endif
1.1 noro 2852: D0 = map(dp_dtop,T0,W);
2853: D0 = vtol(X*ltov(D0));
2854: return append(D0,D1);
2855: }
2856:
2857: def separator(P,V)
2858: {
2859: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
2860: N = length(P);
1.4 noro 2861: dp_ord(0);
2862: DP = vector(N);
1.9 ohara 2863: for ( I = 0; I < N; I++ ) DP[I] = qsort(ltov(map(dp_ptod,P[I][0],V)),noro_pd.comp_tord);
1.4 noro 2864: if ( Mod )
2865: for ( I = 0; I < N; I++ ) DP[I] = map(dp_mod,DP[I],Mod,[]);
2866: Ind = vector(N);
2867: for ( I = 0; I < N; I++ ) {
2868: for ( K = [], J = length(DP[I])-1; J >= 0; J-- ) K = cons(J,K);
2869: Ind[I] = K;
2870: }
2871: S = vector(N);
2872: for ( I = 0; I < N; I++ ) S[I] = 1;
1.1 noro 2873: for ( I = 0; I < N; I++ ) {
1.4 noro 2874: print(".",2);
1.1 noro 2875: for ( J = 0; J < N; J++ ) {
2876: if ( J == I ) continue;
1.4 noro 2877: T = DP[I]; L = length(T);
2878: if ( Mod ) {
2879: for ( K = 0; K < L; K++ )
2880: if ( dp_nf_mod(Ind[J],T[K],DP[J],0,Mod) ) break;
2881: } else {
2882: for ( K = 0; K < L; K++ )
2883: if ( dp_nf(Ind[J],T[K],DP[J],0) ) break;
2884: }
2885: S[J] = lcm(S[J],dp_dtop(T[K],V));
1.1 noro 2886: }
2887: }
1.4 noro 2888: print("");
1.1 noro 2889: return S;
2890: }
2891:
2892: def prepost(PL,V)
1.4 noro 2893: {
2894: if ( type(Mod=getopt(mod)) == -1 ) Mod = 0;
1.1 noro 2895: A = ltov(PL); N = length(A);
2896: Pre = vector(N);
2897: Post = vector(N);
2898: R = vector(N);
2899: Pre[0] = [1];
2900: print("pre ",2);
2901: for ( I = 1; I < N; I++, print(".",2) )
1.4 noro 2902: Pre[I] = ideal_intersection_m(Pre[I-1],A[I-1],V,0|mod=Mod);
1.1 noro 2903: print("done");
2904: print("post ",2);
2905: Post[N-1] = [1];
2906: for ( I = N-2; I >= 0; I--, print(".",2) )
1.4 noro 2907: Post[I] = ideal_intersection_m(Post[I+1],A[I+1],V,0|mod=Mod);
1.1 noro 2908: print("done");
2909: print("int ",2);
2910: for ( I = 0; I < N; I++, print(".",2) )
1.4 noro 2911: R[I] = ideal_intersection_m(Pre[I],Post[I],V,0|mod=Mod);
1.1 noro 2912: print("done");
2913: return R;
2914: }
2915:
2916: /* XXX */
2917:
2918: def call_func(Arg)
2919: {
2920: F = car(Arg);
2921: return call(strtov(F),cdr(Arg));
2922: }
2923:
1.8 noro 2924: def call_func_serial(Arg,Serial)
2925: {
2926: F = car(Arg);
2927: return [call(strtov(F),cdr(Arg)),Serial];
2928: }
2929:
1.1 noro 2930: def competitive_exec(P,Arg0,Arg1)
2931: {
2932: P0 = P[0]; P1 = P[1];
2933: ox_cmo_rpc(P0,"noro_pd.call_func",Arg0|sync=1);
2934: ox_cmo_rpc(P1,"noro_pd.call_func",Arg1|sync=1);
2935: F = ox_select(P);
2936: R = ox_get(F[0]);
2937: if ( length(F) == 2 ) {
2938: ox_get(F[1]);
2939: } else {
2940: U = setminus(P,F);
2941: ox_reset(U[0]);
2942: }
2943: return R;
2944: }
2945:
2946:
2947: def nd_gr_rat(B,V,PV,Ord1,Ord)
2948: {
2949: G = nd_gr(B,append(V,PV),0,Ord1);
2950: G1 = nd_gr_postproc(G,V,0,Ord,0);
2951: return G1;
2952: }
2953:
2954: /* Task[i] = [fname,[arg0,...,argn]] */
2955:
2956: def para_exec(Proc,Task) {
2957: Free = Proc;
2958: N = length(Task);
2959: R = [];
1.8 noro 2960: print([N],2); print("->",2);
2961: Serial = 0;
1.1 noro 2962: while ( N ) {
2963: while ( Task != [] && Free != [] ) {
2964: T = car(Task); Task = cdr(Task);
1.8 noro 2965: ox_rpc(car(Free),"noro_pd.call_func_serial",T,Serial++);
1.1 noro 2966: ox_push_cmd(car(Free),258); Free = cdr(Free);
2967: }
2968: Finish0 = Finish = ox_select(Proc);
2969: for ( ; Finish != []; Finish = cdr(Finish) ) {
2970: print(".",2);
2971: L = ox_get(car(Finish));
2972: R = cons(L,R);
2973: N--;
2974: }
1.8 noro 2975: print([N],2);
1.1 noro 2976: Free = append(Free,Finish0);
2977: }
2978: print("");
1.9 ohara 2979: R = qsort(R,noro_pd.comp_by_second);
1.8 noro 2980: R = map(first,R);
2981: return R;
1.1 noro 2982: }
1.4 noro 2983:
2984: def redbase(B,V,Mod,Ord)
2985: {
2986: M = nd_gr_postproc(B,V,Mod,Ord,0);
2987: dp_ord(Ord);
2988: DM = ltov(map(dp_ptod,M,V));
2989: if ( Mod ) DM = map(dp_mod,DM,Mod,[]);
2990: N = length(DM);
2991: for ( Ind = [], I = N-1; I >= 0; I-- ) Ind = cons(I,Ind);
2992: for ( T = B, R = vtol(DM); T != []; T = cdr(T) ) {
2993: D = dp_ptod(car(T),V);
2994: if ( Mod ) D = dp_mod(D,Mod,[]);
2995: D = Mod?dp_nf_mod(Ind,D,DM,1,Mod):dp_nf(Ind,D,DM,1);
2996: if ( D ) R = cons(D,R);
2997: }
1.9 ohara 2998: D = qsort(R,noro_pd.comp_tord);
1.4 noro 2999: return map(dp_dtop,D,V);
3000: }
3001:
3002: def witness(A,B,V)
3003: {
3004: G = nd_gr(B,V,0,Mod);
3005: L = length(A);
3006: QL = []; PL = [];
3007: for ( I = L-1; I >= 0; I-- ) {
3008: QL = append(map(first,A[I]),QL);
3009: PL = append(map(second,A[I]),PL);
3010: }
3011: N = length(QL);
3012: Qhat = prepost(QL,V);
3013: for ( I = 0, W = []; I < N; I++ ) {
3014: for ( T = Qhat[I]; T != []; T = cdr(T) )
3015: if ( gen_nf(car(T),QL[I],V,0,Mod) ) break;
3016: Ai = car(T);
3017: Ji = colon(G,Ai,V|isgb=1,mod=Mod);
3018: Ji = nd_gr(Ji,V,Mod,0);
3019: if ( gen_gb_comp(Ji,PL[I],Mod) ) Bi = 1;
3020: else {
3021: Ki = ideal_colon(Ji,PL[I],V|mod=Mod);
3022: for ( T = Ki; T != []; T = cdr(T) )
3023: if ( gen_nf(car(T),Ji,V,0,Mod) ) break;
3024: Bi = car(T);
3025: }
3026: W = cons(Ai*Bi,W);
3027: Li = colon(G,W[0],V|isgb=1,mod=Mod);
3028: Li = nd_gr(Li,V,Mod,0);
3029: if ( !gen_gb_comp(Li,PL[I],Mod) )
3030: error("afo");
3031: }
3032: return reverse(W);
3033: }
1.1 noro 3034: endmodule$
3035: end$
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