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sheafcoh_l.tst @ 19609c

spielwiese

Last change on this file since 19609c was dc94f9, checked in by Hans Schönemann <hannes@…>, 19 years ago
hannes/lossen: sheafcoh_.* git-svn-id: file:///usr/local/Singular/svn/trunk@8269 2c84dea3-7e68-4137-9b89-c4e89433aadc
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File size: 7.6 KB

Line
1	LIB "tst.lib";
2	tst_init();
3
4	LIB "sheafcoh.lib";
5
6	// Kohomologie der Strukturgarbe von P^7:
7	//----------------------------------------
8	ring r=0,x(1..8),dp;
9	module M=0;
10	def A=sheafCoh(0,-10,5);
11	def B=sheafCohBGG(0,-10,3);
12	displayCohom(A,-10,5,7);
13	displayCohom(B,-10,3,7);
14	kill r;
15
16	// Kohomologie der Idealgarbe der Veronese Flaeche in $\P^3$:
17	//------------------------------------------------------------
18	ring S = 32003, x(0..4), dp;
19	module MI=maxideal(1);
20	attrib(MI,"isHomog",intvec(-1));
21	resolution kos = nres(MI,0);
22	print(betti(kos),"betti");
23	matrix alpha0 = random(32002,10,3);
24	module pres = module(alpha0)+kos[3];
25	attrib(pres,"isHomog",intvec(1,1,1,1,1,1,1,1,1,1));
26	resolution fcokernel = mres(pres,0);
27	print(betti(fcokernel),"betti");
28	module dir = transpose(pres);
29	attrib(dir,"isHomog",intvec(-1,-1,-1,-2,-2,-2,
30	-2,-2,-2,-2,-2,-2,-2));
31	resolution fdir = mres(dir,2);
32	print(betti(fdir),"betti");
33	ideal I = groebner(flatten(fdir[2]));
34	resolution FI = mres(I,0);
35	print(betti(FI),"betti");
36	module F=FI[2];
37	A=sheafCoh(F,-6,6);
38	B=sheafCohBGG(F,-6,6);
39
40	dimH(3,F,-4);
41	dimH(1,F,1);
42
43	kill S;
44
45	// Kohomologie der Idealgarbe einer Flaeche in $\P^4$:
46	//------------------------------------------------------------
47	ring S = 32003, x(0..4), dp;
48	resolution kos = nres(maxideal(1),0);
49	betti(kos);
50	matrix kos5 = kos[5];
51	matrix tphi = transpose(dsum(kos5,kos5));
52	matrix kos3 = kos[3];
53	matrix psi = dsum(kos3,kos3);
54	matrix beta1 = random(32002,20,2);
55	matrix tbeta1tilde = transpose(psi*beta1);
56	matrix tbeta0 = lift(tphi,tbeta1tilde);
57	matrix kos4 = kos[4];
58	matrix tkos4pluskos4 = transpose(dsum(kos4,kos4));
59	matrix tgammamin1 = random(32002,20,1);
60	matrix tgamma0 = tkos4pluskos4*tgammamin1;
61	matrix talpha0 = concat(tbeta0,tgamma0);
62	matrix zero[20][1];
63	matrix tpsi = transpose(psi);
64	matrix tpresg = concat(tpsi,zero);
65	matrix pres = module(transpose(talpha0))
66	+ module(transpose(tpresg));
67	module dir = transpose(pres);
68	dir = prune(dir);
69	homog(dir);
70	intvec deg_dir = attrib(dir,"isHomog");
71	attrib(dir,"isHomog",deg_dir-2); // set degrees
72	resolution fdir = mres(prune(dir),2);
73	print(betti(fdir),"betti");
74	ideal I = groebner(flatten(fdir[2]));
75	resolution FI = mres(I,0);
76
77	module F=FI[2];
78	def A1=sheafCoh(F,-4,6);
79	A1=sheafCoh(F,-3,6,"sres");
80	def A2=sheafCohBGG(F,-4,6);
81
82	kill S;
83
84	// Kohomologie des Morrocks-Mumford-Buendels (Macaulay-Beispiel von Wolfram):
85	// ----------------------------------------------------------------------------
86
87	ring R=0,x(0..4),dp;
88
89	matrix FHM[19][35] =
90	-x(2), 0, -x(1), -x(4), 0, 0, 0, 0, 0, 0, 0,
91	0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
92	0, 0, -x(0), 0, 0, 0, 0, 0, -x(4), 0,
93	0, -x(3), -x(2), 0,
94
95	0, 0, x(0), 0, 0, 0, 0, 0, -x(3), 0, 0, 0,
96	0, 0, -x(1), 0, 0, 0, 0, x(4), 0, 0,
97	0, 0, 0, 0, 0, 0, 0, 0, -x(3), -x(2),
98	0, 0, 0,
99
100	0, x(3), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
101	0, 0, 0, 0, 0, 0, 0, 0, x(2), 0,
102	0, x(1), 0, 0, 0, 0, -x(0), 0, 0, -x(4),
103	0, 0, -x(3),
104
105	0, 0, 0, -x(2), -x(3), 0, -x(3), 0, 0, 0, 0,
106	-x(1), 0, 0, x(0), 0, 0, 0, 0, 0,
107	-x(4), 0, 0, 0, 0, 0, 0, 0, 0, -x(2),
108	0, 0, 0, 0, 0,
109
110	x(4), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
111	x(0), 0, 0, 0, 0, 0, 0, -x(3), x(2), 0,
112	0, 0, 0, 0, 0, 0, 0, -x(1), 0, 0,
113	0, 0, x(4), 0,
114
115	x(1), 0, 0, 0, 0, 0, 0, 0, 0, x(2), 0, 0,
116	0, 0, 0, 0, 0, 0, 0, 0, -x(0), 0,
117	0, 0, x(4), 0, 0, -x(3), 0, 0, 0, 0,
118	0, 0, 0,
119
120	0, 0, 0, x(0), 0, 0, 0, 0, 0, -x(4), x(2), 0,
121	-x(4), 0, 0, -x(3), 0, 0, 0, -x(1), 0, 0,
122	0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
123	0, 0, 0,
124
125	0, x(4), -x(3), 0, -x(2), 0, 0, 0, 0, -x(0), 0,
126	0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
127	0, -x(3), 0, 0, 0, -x(1), 0, 0, 0, 0,
128	0, 0, 0, -x(4),
129
130	0, -x(2), 0, 0, 0, 0, 0, 0, x(4), 0, -x(1),
131	x(3), 0, 0, 0, 0, 0, 0, 0, 0, 0,
132	0, 0, 0, -x(0), 0, 0, 0, 0, 0, 0,
133	0, 0, 0, 0,
134
135	0, 0, 0, 0, x(0), 0, 0, 0, 0, 0, 0, 0,
136	0, 0, 0, -x(2), 0, 0, -x(1), 0, 0,
137	-x(1), 0, 0, 0, 0, 0, -x(4), 0, 0, 0,
138	x(3), 0, 0, 0,
139
140	0, 0, -x(4), 0, 0, -x(1), 0, 0, 0, 0, 0, 0,
141	0, -x(1), 0, x(0), 0, 0, 0, 0, 0, 0,
142	-x(4), 0, -x(3), 0, 0, 0, -x(2), 0, 0, 0,
143	0, 0, 0,
144
145	0, x(1), 0, x(3), 0, x(2), 0, 0, 0, 0, 0, 0,
146	0, x(2), 0, 0, 0, 0, x(0), 0, 0, 0,
147	0, 0, 0, -x(4), 0, 0, 0, 0, 0, 0,
148	0, 0, 0,
149
150	-x(3), 0, 0, 0, x(1), x(4), x(1), 0, x(0), 0, 0,
151	0, 0, 0, 0, 0, 0, -x(2), 0, 0, 0,
152	0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
153	0, 0, 0, 0,
154
155	0, 0, 0, 0, 0, 0, 0, x(3), x(2), -x(1), 0, 0,
156	-x(1), 0, 0, 0, -x(0), 0, -x(4), 0, 0,
157	-x(4), 0, x(3), 0, 0, 0, 0, 0, 0, x(2),
158	0, 0, 0, 0,
159
160	0, 0, 0, 0, 0, x(0), 0, -x(2), 0, 0, -x(3), 0,
161	0, 0, -x(4), 0, 0, 0, 0, 0, 0, 0,
162	0, -x(2), 0, 0, 0, x(1), 0, 0, 0, 0,
163	0, 0, 0,
164
165	0, 0, 0, 0, 0, 0, 0, 0, 0, x(2)*x(4), 0, 0,
166	0, 0, 0, x(2)x(3), 0, 0, x(1)x(3), 0, 0,
167	0, 0, 0, x(4)^2, 0, 0, 0, x(1)^2, 0, 0,
168	0, 0, -x(1)*x(4), 0,
169
170	0, 0, 0, 0, 0, 0, 0, 0, x(3)*x(4), 0, 0,
171	x(3)^2, 0, 0, x(1)*x(4), 0, 0, 0, 0, 0,
172	x(2)^2, 0, 0, x(1)*x(2), 0, 0, 0, 0, 0, 0,
173	0, 0, 0, 0, -x(2)*x(3),
174
175	0, 0, 0, 0, 0, 0, x(4)^2, 0, 0, 0, x(0)*x(4),
176	0, x(3)^2, 0, x(2)x(3), 0, -x(1)x(4), x(1)*x(3), 0, 0,
177	0, x(2)^2, 0, 0, x(1)x(2), -x(0)x(3), x(0)*x(2), 0,
178	x(3)x(4), x(1)^2, 0, x(0)x(1), -x(2)*x(4), x(0)^2, 0,
179
180	0, 0, 0, 0, 0, 0, 0, x(4)^2, 0, 0, 0,
181	x(2)x(4), 0, x(3)^2, 0, x(1)x(4), x(2)x(3), -x(0)x(4), 0,
182	x(0)x(3), x(1)x(3), 0, x(2)^2, 0, 0, x(1)x(2), -x(3)x(4),
183	x(0)x(2), 0, 0, x(1)^2, 0, x(0)x(1), 0, x(0)^2;
184
185
186	def M=module(FHM);
187	attrib(M,"isHomog",intvec(4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3));
188	A1=sheafCohBGG(M,-10,7);
189	A2=sheafCoh(M,-4,3);
190
191	tst_status(1);$
192

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