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monomial_l.tst @ 09f10e

spielwiese

Last change on this file since 09f10e was cee23a8, checked in by Hans Schoenemann <hannes@…>, 14 years ago
monomial.lib ->monomialideal.lib git-svn-id: file:///usr/local/Singular/svn/trunk@13306 2c84dea3-7e68-4137-9b89-c4e89433aadc
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1	LIB "tst.lib";
2	tst_init();
3
4	LIB "monomialideal.lib";
5
6	// EX. 1:
7	ring r4=0,x(1..4),dp;
8	ideal i=x(1)^3x(2)x(3),x(1)x(2)x(3)x(4),x(2)^2x(3)^2x(4)^2,x(2)^2x(4)^4,x(3)^3*x(4);
9	isMonomial(i);
10	isprimeMon(i);
11	isprimaryMon(i);
12	isirreducibleMon(i);
13	isartinianMon(i);
14	isgenericMon(i);
15
16	list pd=primdecMon(i);
17	list id=irreddecMon(i);
18	list id1=irreddecMon(i,"vas");
19
20	list id2=irreddecMon(i,"gz");
21
22	list id3=irreddecMon(i,"ad");
23
24	list id4=irreddecMon(i,"for");
25
26	list id5=irreddecMon(i,"mil");
27
28	list id6=irreddecMon(i,"lr");
29
30	list id8=irreddecMon(i,"sr");
31
32	size(pd);size(id);size(id1);size(id2);size(id3);size(id4);size(id5);size(id6);size(id8);
33
34	areEqual(id,id1);areEqual(id,id2);areEqual(id,id3);areEqual(id,id4);areEqual(id,id5);areEqual(id,id6);areEqual(id,id8);
35
36	//
37	//
38	// EX. 2:
39	ring r5=0,(x,y,z,t,w),dp;
40	ideal I=y2t,x2y-x2z+yt2,x2y2,xyztw,x3z2,y5+xz3w-x2zw2,x7-yt2w4;
41	ideal i=simplify(lead(std(I)),1);
42	isMonomial(i);
43	isprimeMon(i);
44	isprimaryMon(i);
45	isirreducibleMon(i);
46	isartinianMon(i);
47	isgenericMon(i);
48
49	list pd=primdecMon(i);
50
51	list id=irreddecMon(i);
52
53	// list id1=irreddecMon(i,"vas");
54	list id2=irreddecMon(i,"gz");
55
56	list id3=irreddecMon(i,"ad");
57
58	list id4=irreddecMon(i,"for");
59
60	// list id5=irreddecMon(i,"mil");
61	list id6=irreddecMon(i,"lr");
62
63	list id8=irreddecMon(i,"sr");
64
65	size(pd);size(id);size(id2);size(id3);size(id4);size(id6);size(id8);
66
67	areEqual(id,id2);areEqual(id,id3);areEqual(id,id4);areEqual(id,id6);areEqual(id,id8);
68
69	//
70	//
71	// EX 3:
72	ring r6=0,x(0..5),dp;
73	ideal I=x(2)^2-x(4)x(5),x(1)x(2)-x(0)x(5),x(0)x(2)-x(1)*x(4),
74	x(1)^2-x(3)x(5),x(0)x(1)-x(2)x(3),x(0)^2-x(3)x(4);
75	ideal i=simplify(lead(std(I)),1);
76	isMonomial(i);
77	isprimeMon(i);
78	isprimaryMon(i);
79	isirreducibleMon(i);
80	isartinianMon(i);
81	isgenericMon(i);
82
83	list pd=primdecMon(i);
84
85	list id=irreddecMon(i);
86
87	list id1=irreddecMon(i,"vas");
88
89	list id2=irreddecMon(i,"gz");
90
91	list id3=irreddecMon(i,"ad");
92
93	list id4=irreddecMon(i,"for");
94
95	list id5=irreddecMon(i,"mil");
96
97	list id6=irreddecMon(i,"lr");
98
99	list id8=irreddecMon(i,"sr");
100
101	size(pd);size(id);size(id1);size(id2);size(id3);size(id4);size(id5);size(id6);size(id8);
102
103	areEqual(id,id1);areEqual(id,id2);areEqual(id,id3);areEqual(id,id4);areEqual(id,id5);areEqual(id,id6);areEqual(id,id8);
104
105	//
106	//
107	// EX 4
108	//
109	ring R4=0,(x,y,z,t),dp;
110	// Ex.2.5 in [Bermejo-Gimenez], Proc.Amer.Math.Soc. 128(5):
111	ideal I = x17y14-y31, x20y13, x60-y36z24-x20z20t20;
112	ideal i=simplify(lead(std(I)),1);
113	isMonomial(i);
114	isprimeMon(i);
115	isprimaryMon(i);
116	isirreducibleMon(i);
117	isartinianMon(i);
118	isgenericMon(i);
119
120	list pd=primdecMon(i);
121
122	list id=irreddecMon(i);
123
124	list id1=irreddecMon(i,"vas");
125
126	list id2=irreddecMon(i,"gz");
127
128	list id3=irreddecMon(i,"ad");
129
130	list id4=irreddecMon(i,"for");
131
132	list id5=irreddecMon(i,"mil");
133
134	list id6=irreddecMon(i,"lr");
135
136	list id8=irreddecMon(i,"sr");
137
138	size(pd);size(id);size(id1);size(id2);size(id3);size(id4);size(id5);size(id6);size(id8);
139
140	areEqual(id,id1);areEqual(id,id2);areEqual(id,id3);areEqual(id,id4);areEqual(id,id5);areEqual(id,id6);areEqual(id,id8);
141
142	//
143	//
144	// EX 5
145	// Ex.2.9 in [Bermejo-Gimenez], Proc.Amer.Math.Soc. 128(5):
146	int k=315;
147	I=x17y14-y31,x20y13,x60-y36z24-x20z20t20,y41z^k-y40z^(k+1);
148	i=simplify(lead(std(I)),1);
149	isMonomial(i);
150	isprimeMon(i);
151	isprimaryMon(i);
152	isirreducibleMon(i);
153	isartinianMon(i);
154	isgenericMon(i);
155
156	pd=primdecMon(i);
157
158	id=irreddecMon(i);
159
160	id1=irreddecMon(i,"vas");
161
162	id2=irreddecMon(i,"gz");
163
164	id3=irreddecMon(i,"ad");
165
166	id4=irreddecMon(i,"for");
167
168	id5=irreddecMon(i,"mil");
169
170	id6=irreddecMon(i,"lr");
171
172	id8=irreddecMon(i,"sr");
173
174	size(pd);size(id);size(id1);size(id2);size(id3);size(id4);size(id5);size(id6);size(id8);
175
176	areEqual(id,id1);areEqual(id,id2);areEqual(id,id3);areEqual(id,id4);areEqual(id,id5);areEqual(id,id6);areEqual(id,id8);
177
178	//
179	//
180	// EX 6
181	// Example in Rk.2.10 in [Bermejo-Gimenez], ProcAMS 128(5):
182	I=x2-3xy+5xt,xy-3y2+5yt,xz-3yz,2xt-yt,y2-yz-2yt;
183	i=simplify(lead(std(I)),1);
184	isMonomial(i);
185	isprimeMon(i);
186	isprimaryMon(i);
187	isirreducibleMon(i);
188	isartinianMon(i);
189	isgenericMon(i);
190
191	pd=primdecMon(i);
192
193	id=irreddecMon(i);
194
195	id1=irreddecMon(i,"vas");
196
197	id2=irreddecMon(i,"gz");
198
199	id3=irreddecMon(i,"ad");
200
201	id4=irreddecMon(i,"for");
202
203	id5=irreddecMon(i,"mil");
204
205	id6=irreddecMon(i,"lr");
206
207	id8=irreddecMon(i,"sr");
208
209	size(pd);size(id);size(id1);size(id2);size(id3);size(id4);size(id5);size(id6);size(id8);
210
211	areEqual(id,id1);areEqual(id,id2);areEqual(id,id3);areEqual(id,id4);areEqual(id,id5);areEqual(id,id6);areEqual(id,id8);
212
213	//
214	//
215	// EX 7
216	I=y4-t3z, x3t-y2z2, x3y2-t2z3, x6-tz5;
217	i=simplify(lead(std(I)),1);
218	isMonomial(i);
219	isprimeMon(i);
220	isprimaryMon(i);
221	isirreducibleMon(i);
222	isartinianMon(i);
223	isgenericMon(i);
224
225	pd=primdecMon(i);
226
227	id=irreddecMon(i);
228
229	id1=irreddecMon(i,"vas");
230
231	id2=irreddecMon(i,"gz");
232
233	id3=irreddecMon(i,"ad");
234
235	id4=irreddecMon(i,"for");
236
237	id5=irreddecMon(i,"mil");
238
239	id6=irreddecMon(i,"lr");
240
241	id8=irreddecMon(i,"sr");
242
243	size(pd);size(id);size(id1);size(id2);size(id3);size(id4);size(id5);size(id6);size(id8);
244
245	areEqual(id,id1);areEqual(id,id2);areEqual(id,id3);areEqual(id,id4);areEqual(id,id5);areEqual(id,id6);areEqual(id,id8);
246
247	//
248	//
249	// EX 8
250	ring R5=0,(x,y,z,t,w),dp;
251	ideal I = xy-zw,x3-yw2,x2z-y2w,y3-xz2,-y2z3+xw4+tw4+w5,-yz4+x2w3+xtw3+xw4,
252	-z5+x2tw2+x2w3+yw4;
253	ideal i=simplify(lead(std(I)),1);
254	isMonomial(i);
255	isprimeMon(i);
256	isprimaryMon(i);
257	isirreducibleMon(i);
258	isartinianMon(i);
259	isgenericMon(i);
260
261	list pd=primdecMon(i);
262
263	list id=irreddecMon(i);
264
265	list id1=irreddecMon(i,"vas");
266
267	list id2=irreddecMon(i,"gz");
268
269	list id3=irreddecMon(i,"ad");
270
271	list id4=irreddecMon(i,"for");
272
273	list id5=irreddecMon(i,"mil");
274
275	list id6=irreddecMon(i,"lr");
276
277	list id8=irreddecMon(i,"sr");
278
279	size(pd);size(id);size(id1);size(id2);size(id3);size(id4);size(id5);size(id6);size(id8);
280
281	areEqual(id,id1);areEqual(id,id2);areEqual(id,id3);areEqual(id,id4);areEqual(id,id5);areEqual(id,id6);areEqual(id,id8);
282
283	//
284	//
285	// EX 9
286	// Next example is the defining ideal of the 2nd. Veronesean of P3, a variety
287	// in P8 which is arithmetically Cohen-Macaulay:
288	ring r14=0,(a,b,c,d,x(0..9)),dp;
289	ideal i= x(0)-ab,x(1)-ac,x(2)-ad,x(3)-bc,x(4)-bd,x(5)-cd,
290	x(6)-a2,x(7)-b2,x(8)-c2,x(9)-d2;
291	ideal ei=eliminate(i,abcd);
292	ring r10=0,x(0..9),dp;
293	ideal I=imap(r14,ei);
294	ideal i=simplify(lead(std(I)),1);
295	isMonomial(i);
296	isprimeMon(i);
297	isprimaryMon(i);
298	isirreducibleMon(i);
299	isartinianMon(i);
300	isgenericMon(i);
301
302	list pd=primdecMon(i);
303
304	list id=irreddecMon(i);
305
306	list id1=irreddecMon(i,"vas");
307
308	list id2=irreddecMon(i,"gz");
309
310	list id3=irreddecMon(i,"ad");
311
312	list id4=irreddecMon(i,"for");
313
314	list id5=irreddecMon(i,"mil");
315
316	list id6=irreddecMon(i,"lr");
317
318	list id8=irreddecMon(i,"sr");
319
320	size(pd);size(id);size(id1);size(id2);size(id3);size(id4);size(id5);size(id6);size(id8);
321
322	areEqual(id,id1);areEqual(id,id2);areEqual(id,id3);areEqual(id,id4);areEqual(id,id5);areEqual(id,id6);areEqual(id,id8);
323
324	//
325	//
326	// EX 10:
327	ring r7=0,(x,y,z,t,u,a,b),dp;
328	ideal i=u-b40,t-a40,x-a23b17,y-a22b18+ab39,z-a25b15;
329	ideal ei=eliminate(i,ab); // It takes a few seconds to compute the ideal
330	ring rr5=0,(x,y,z,t,u),dp;
331	ideal I=imap(r7,ei);
332	ideal i=simplify(lead(std(I)),1);
333	isMonomial(i);
334	isprimeMon(i);
335	isprimaryMon(i);
336	isirreducibleMon(i);
337	isartinianMon(i);
338	isgenericMon(i);
339
340	list pd=primdecMon(i);
341
342	list id=irreddecMon(i);
343
344	list id1=irreddecMon(i,"vas");
345
346	list id2=irreddecMon(i,"gz");
347
348	list id3=irreddecMon(i,"ad");
349
350	list id4=irreddecMon(i,"for");
351
352	list id5=irreddecMon(i,"mil");
353
354	list id6=irreddecMon(i,"lr");
355
356	list id8=irreddecMon(i,"sr");
357
358	size(pd);size(id);size(id1);size(id2);size(id3);size(id4);size(id5);size(id6);size(id8);
359
360	areEqual(id,id1);areEqual(id,id2);areEqual(id,id3);areEqual(id,id4);areEqual(id,id5);areEqual(id,id6);areEqual(id,id8);
361
362	//
363	//
364	// EX 11:
365	ring r11=0,(x(0..8),s,t),dp;
366	ideal i=x(0)-st24,x(1)-s2t23,x(2)-s3t22,x(3)-s9t16,x(4)-s11t14,x(5)-s18t7,
367	x(6)-s24t,x(7)-t25,x(8)-s25;
368	ideal ei=eliminate(i,st);
369	ring r9=0,x(0..8),dp;
370	ideal I=imap(r11,ei);
371	ideal i=simplify(lead(std(I)),1);
372	isMonomial(i);
373	isprimeMon(i);
374	isprimaryMon(i);
375	isirreducibleMon(i);
376	isartinianMon(i);
377	isgenericMon(i);
378
379	list pd=primdecMon(i);
380
381	list id=irreddecMon(i);
382
383	// list id1=irreddecMon(i,"vas");
384	list id2=irreddecMon(i,"gz");
385
386	list id3=irreddecMon(i,"ad");
387
388	list id4=irreddecMon(i,"for");
389
390	// list id5=irreddecMon(i,"mil");
391	list id6=irreddecMon(i,"lr");
392
393	list id8=irreddecMon(i,"sr");
394
395	size(pd);size(id);size(id2);size(id3);size(id4);size(id6);size(id8);
396	// TARDA UN POCO PERO LO HACE
397	;
398
399	areEqual(id,id2);areEqual(id,id3);areEqual(id,id4);areEqual(id,id6);areEqual(id,id8);
400
401	//
402	//
403	// EX 12:
404	ring r18=0,(s,t,u,x(0..14)),dp;
405	ideal i=x(0)-s3t6u6,x(1)-s5t5u5,x(2)-t9s6,x(3)-st4u10,x(4)-s2t12u,x(5)-t14u,
406	x(6)-s8t7,x(7)-s4t6u5,x(8)-t13su,x(9)-s4t9u2,x(10)-stu13,x(11)-s5t7u3,
407	x(12)-s15,x(13)-t15,x(14)-u15;
408	ideal ei=eliminate(i,stu);
409	ring r15=0,x(0..14),dp;
410	ideal I=imap(r18,ei);
411	ideal i=simplify(lead(std(I)),1);
412	size(i);
413
414	isMonomial(i);
415	isprimeMon(i);
416	isprimaryMon(i);
417	isirreducibleMon(i);
418	isartinianMon(i);
419	isgenericMon(i);
420
421	list pd=primdecMon(i); size(pd); // 2 SEGUNDOS CON "add", 4 componentes
422	;
423
424	list id=irreddecMon(i); size(id); // 1 SEGUNDO CON "add", 180 componentes
425	;
426
427	list id1=irreddecMon(i,"sr"); // 103 SEC. CON "sr", coincide con la anterior
428	size(id1); areEqual(id,id1);
429
430	list id2=irreddecMon(i,"for"); // 19 SEC. CON "for", coincide con la anterior
431	size(id2); areEqual(id,id2);
432
433	// HE PARADO LOS CALCULOS CON "gz" Y CON "ad", NO HE PROBADO LOS OTROS
434	//
435	//
436
437	list pdg=primdecGTZ(i); // 39 SEC. CON EL METODO GENERAL DE DESCOMP. PRIMARIA
438	size(pdg);
439
440	//
441	//
442	// EX 13:
443	ring s8=0,(x(0..5),s,t),dp;
444	ideal i=x(0)-st24,x(1)-s2t23,x(2)-s3t22,x(3)-s9t16,x(4)-s11t14,x(5)-s18t7;
445	ideal ei=eliminate(i,st);
446	ring s6=0,x(0..5),dp;
447	ideal I=imap(s8,ei);
448	ideal i=simplify(lead(std(I)),1);
449	isMonomial(i);
450	isprimeMon(i);
451	isprimaryMon(i);
452	isirreducibleMon(i);
453	isartinianMon(i);
454	isgenericMon(i);
455
456	list pd=primdecMon(i);
457
458	list id=irreddecMon(i);
459
460	list id1=irreddecMon(i,"vas");
461
462	list id2=irreddecMon(i,"gz");
463
464	list id3=irreddecMon(i,"ad");
465
466	list id4=irreddecMon(i,"for");
467
468	list id5=irreddecMon(i,"mil");
469
470	list id6=irreddecMon(i,"lr");
471
472	list id8=irreddecMon(i,"sr");
473
474	size(pd);size(id);size(id1);size(id2);size(id3);size(id4);size(id5);size(id6);size(id8);
475
476	areEqual(id,id2);areEqual(id,id1);areEqual(id,id3);areEqual(id,id4);areEqual(id,id5);areEqual(id,id6);areEqual(id,id8);
477
478	//
479	//
480	// EX 14:
481	ring s15=0,(s,t,u,x(0..11)),dp;
482	ideal i=x(0)-s3t6u6,x(1)-s5t5u5,x(2)-t9s6,x(3)-st4u10,x(4)-s2t12u,x(5)-t14u,
483	x(6)-s8t7,x(7)-s4t6u5,x(8)-t13su,x(9)-s4t9u2,x(10)-stu13,x(11)-s5t7u3;
484	ideal ei=eliminate(i,stu);
485	ring s12=0,x(0..11),dp;
486	ideal I=imap(s15,ei);
487	ideal i=simplify(lead(std(I)),1);
488	size(i);
489
490	isMonomial(i);
491	isprimeMon(i);
492	isprimaryMon(i);
493	isirreducibleMon(i);
494	isartinianMon(i);
495	isgenericMon(i);
496
497	list pd=primdecMon(i); size(pd); // 1 SEGUNDOS CON "add", 9 componentes
498	;
499
500	list id=irreddecMon(i); size(id); // 0 SEGUNDO CON "add", 112 componentes
501	;
502
503	list id1=irreddecMon(i,"sr"); // 46 SEC. CON "sr", coincide con la anterior
504	size(id1); areEqual(id,id1);
505
506	list id2=irreddecMon(i,"for"); //7 SEC. CON "for", coincide con la anterior
507	size(id2); areEqual(id,id2);
508
509	//
510	//
511	// EX 15:
512	setring s15;
513	i=x(0)-st6u8,x(1)-s5t3u7,x(2)-t11u4,x(3)-s9t4u2,x(4)-s2t7u6,x(5)-s7t7u,
514	x(6)-s10t5,x(7)-s4t6u5,x(8)-s13tu,x(9)-s14u,x(10)-st2u12,x(11)-s3t9u3;
515	ei=eliminate(i,stu);
516	setring s12;
517	ideal II=imap(s15,ei);
518	ideal ii=simplify(lead(std(II)),1);
519	size(ii);
520
521	isMonomial(ii);
522	isprimeMon(ii);
523	isprimaryMon(ii);
524	isirreducibleMon(ii);
525	isartinianMon(ii);
526	isgenericMon(ii);
527
528	list ppdd=primdecMon(ii); size(ppdd); // 0 SEGUNDOS CON "add", 10 componentes
529	;
530
531	list iidd=irreddecMon(ii); size(iidd); // 1 SEGUNDO CON "add", 111 componentes
532	;
533
534	list pdg=primdecGTZ(ii); // 9 SEC. CON EL METODO GENERAL DE DESCOMP. PRIMARIA
535	size(pdg);
536
537	// COMPARAMOS AHORA LOS RADICALES DE LAS COMPONENTES PRIMARIAS OBTENIDAS POR EL
538	// METODO GENERAL (rad2) Y POR EL METODO ESPECIFICO add (rad1)
539	list rad1=radicalMon(ppdd[1]),radicalMon(ppdd[2]),radicalMon(ppdd[3]),radicalMon(ppdd[4]),radicalMon(ppdd[5]),
540	radicalMon(ppdd[6]),radicalMon(ppdd[7]),radicalMon(ppdd[8]),radicalMon(ppdd[9]),radicalMon(ppdd[10]);
541	list rad2=pdg[1][2],pdg[2][2],pdg[3][2],pdg[4][2],pdg[5][2],pdg[6][2],pdg[7][2],pdg[8][2],pdg[9][2],pdg[10][2];
542
543	areEqual(rad1,rad2);
544
545
546	tst_status(1);$

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