Annotation of OpenXM/src/k097/lib/minimal/minimal-test.k, Revision 1.7
1.7 ! takayama 1: /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.6 2000/07/26 02:21:31 takayama Exp $ */
1.1 takayama 2: load["minimal.k"];
3: def sm1_resol1(p) {
4: sm1(" p resol1 /FunctionValue set ");
5: }
6:
7: def test8() {
8: local p,pp,ans,b,c,cc,ww,ww2;
9: f = "x^3-y^2*z^2";
10: p = Sannfs(f,"x,y,z");
11: ww = [["x",1,"y",1,"z",1,"Dx",1,"Dy",1,"Dz",1,"h",1],
12: ["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
13: ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
14: sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set ");
15: Sweyl("x,y,z",ww);
16: pp = Map(p,"Spoly");
17: /* return(pp); */
18: /* pp =
19: [y*Dy-z*Dz , -2*x*Dx-3*y*Dy+1 , 2*x*Dy*Dz^2-3*y*Dx^2 ,
20: 2*x*Dy^2*Dz-3*z*Dx^2 , 2*x*z*Dz^3-3*y^2*Dx^2+4*x*Dz^2 ]
21: */
22: ans = sm1_resol1([pp,"x,y,z",ww]);
23: /* Schreyer is in ans. */
24:
25: v = [x,y,z];
26: b = ans;
27: Println("------ ker=im for Schreyer ?------------------");
28: c = Skernel(b[0],v);
29: c = c[0];
30: sm1_pmat([c,b[1],v]);
31: cc = sm1_res_div(c,b[1],v);
32: sm1_pmat(sm1_gb(cc,v));
33: c = Skernel(b[1],v);
34: c = c[0];
35: cc = sm1_res_div(c,b[2],v);
36: sm1_pmat(sm1_gb(cc,v));
37: return(ans);
38: }
39: /*
40: a = test8();
41: SisComplex(a):
42: */
43:
44: def test8a() {
45: local p,pp,ans,b,c,cc,ww, ans_all;
46: f = "x^3-y^2*z^2";
47: p = Sannfs(f,"x,y,z");
48: sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set ");
49: ww = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
50: /* Removed "x",1, ... ===> It causes an error. I do not know the reason.*/
51: Sweyl("x,y,z",ww);
52: pp = Map(p,"Spoly");
53: /* return(pp); */
54: /* pp =
55: [y*Dy-z*Dz , -2*x*Dx-3*y*Dy+1 , 2*x*Dy*Dz^2-3*y*Dx^2 ,
56: 2*x*Dy^2*Dz-3*z*Dx^2 , 2*x*z*Dz^3-3*y^2*Dx^2+4*x*Dz^2 ]
57: */
58: ans_all = Sschreyer(pp);
59: ans = ans_all[0];
60: /* ans = sm1_resol1([pp,"x,y,z",ww]); */
61: /* Schreyer is in ans. */
62:
63: v = [x,y,z];
64: b = ans;
1.3 takayama 65: Println("------ ker=im for Schreyer ?----- wrong method!!!-----------");
1.1 takayama 66: c = Skernel(b[0],v);
67: c = c[0];
68: sm1_pmat([c,b[1],v]);
69: cc = sm1_res_div(c,b[1],v);
70: sm1_pmat(sm1_gb(cc,v));
71: c = Skernel(b[1],v);
72: c = c[0];
73: cc = sm1_res_div(c,b[2],v);
74: sm1_pmat(sm1_gb(cc,v));
75: return(ans);
76: }
77:
78: /* Comparing two constructions */
79: def test9() {
80: local p,pp,ans,b,c,cc,ww,ww2,ans_all,ans2;
81: f = "x^3-y^2*z^2";
82: p = Sannfs(f,"x,y,z");
83: ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
84: sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set ");
85: Sweyl("x,y,z",ww2);
86: pp = Map(p,"Spoly");
87: ans = sm1_resol1([pp,"x,y,z",ww2]);
88:
89: f = "x^3-y^2*z^2";
90: p = Sannfs(f,"x,y,z");
91: sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set ");
92: ww = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
93: Sweyl("x,y,z",ww);
94: pp = Map(p,"Spoly");
95: ans_all = Sschreyer(pp);
96: ans2 = ans_all[0];
97:
98: return([ans,ans2]);
1.2 takayama 99:
100: }
101:
1.3 takayama 102: /* Check if the complex by Sschreyer() is exact or not in our example? */
1.2 takayama 103: def test10() {
104: local p,pp,ans,b,c,cc,ww,ww2,ans_all,ans2, r;
105: f = "x^3-y^2*z^2";
106: p = Sannfs(f,"x,y,z");
107: ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
108: sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set ");
109: Sweyl("x,y,z",ww2);
110: pp = Map(p,"Spoly");
111: ans = sm1_resol1([pp,"x,y,z",ww2]);
112:
113: f = "x^3-y^2*z^2";
114: p = Sannfs(f,"x,y,z");
115: sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set ");
116: ww = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
117: Sweyl("x,y,z",ww);
118: pp = Map(p,"Spoly");
119: ans_all = Sschreyer(pp); /* Schreyer by LaScala-Stillman */
120: ans2 = ans_all[0];
121:
1.3 takayama 122: sm1(" /gb.verbose 1 def ");
123:
124: ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
125: Sweyl("x,y,z",ww2);
126: ans2 = ReParse(ans2);
127: r= IsExact_h(ans2,[x,y,z]);
1.2 takayama 128: Print(r);
129:
130: return([r,[ans,ans2]]);
1.1 takayama 131:
132: }
1.3 takayama 133:
134: def test11() {
135: local a;
136: a = test_ann3("x^3-y^2*z^2");
137: return(a);
138: }
139: /* f should be a string. */
1.5 takayama 140: /* a=test_ann3("x^3+y^3+z^3");
141: It returns the following resolution in 1.5 hours. June 14, 2000.
142: [
143: [
144: [ x*Dx+y*Dy+z*Dz-3*h^2 ]
145: [ -z*Dy^2+y*Dz^2 ]
146: [ -z*Dx^2+x*Dz^2 ]
147: [ -y*Dx^2+x*Dy^2 ]
148: ]
149: [
150: [ 0 , -x , y , -z ]
151: [ z*Dx^2-x*Dz^2 , x*Dy , x*Dx+z*Dz-3*h^2 , z*Dy ]
152: [ y*Dx^2-x*Dy^2 , -x*Dz , y*Dz , x*Dx+y*Dy-3*h^2 ]
153: [ 0 , Dx^2 , -Dy^2 , Dz^2 ]
154: [ z*Dy^2-y*Dz^2 , x*Dx+y*Dy+z*Dz-2*h^2 , 0 , 0 ]
155: ]
156: [
157: [ -x*Dx+3*h^2 , y , -z , 0 , -x ]
158: [ Dy^3+Dz^3 , Dy^2 , -Dz^2 , x*Dx+y*Dy+z*Dz , -Dx^2 ]
159: ]
160: ]
161: */
1.3 takayama 162: def test_ann3(f) {
163: local a,v,ww2,ans2;
1.7 ! takayama 164: a = Sannfs3(f);
1.3 takayama 165: ans2 = a[0];
166: v = [x,y,z];
167: ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
168: Sweyl("x,y,z",ww2);
169: ans2 = ReParse(ans2);
170: r= IsExact_h(ans2,[x,y,z]);
171: Println(r);
172: return([r,ans2]);
173: }
174: def test11a() {
175: local a,v,ww2,ans2;
176: /* constructed by test11.
177: ans2 =
178: [[[y*Dy-z*Dz] , [-2*x*Dx-3*z*Dz+h^2] , [2*x*Dy*Dz^2-3*y*Dx^2*h] , [2*x*Dy^2*Dz-3*z*Dx^2*h]] ,
179: [[3*Dx^2*h , 0 , Dy , -Dz] ,
180: [6*x*Dy*Dz^2-9*y*Dx^2*h , -2*x*Dy*Dz^2+3*y*Dx^2*h , -2*x*Dx-3*y*Dy , 0] ,
181: [0 , 2*x*Dy^2*Dz-3*z*Dx^2*h , 0 , 2*x*Dx+3*z*Dz] ,
182: [2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0] ,
183: [0 , 0 , 0 , 0] ,
184: [2*x*Dy*Dz , 0 , z , -y] ,
185: [0 , 0 , 0 , 0] ,
186: [0 , 0 , 0 , 0] ,
187: [0 , 0 , 0 , 0]] ,
188: [[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
189: [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
190: [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
191: [-2*x*Dx-3*y*Dy-3*z*Dz-6*h^2 , -Dy , -Dz , 3*Dx^2*h , 3*Dy^2 , 3*Dy*Dz , -2*x*Dy , 2*x*Dz , 0] ,
192: [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
193: [3*y*z , z , y , -2*x*Dy*Dz , -3*z*Dy , 2*x*Dx , 2*x*z , -2*x*y , 0] ,
194: [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
195: [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
196: [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0]] ,
197: [[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
198: [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
199: [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0]]]
200: */
201: ans2 =
202: [[[y*Dy-z*Dz] , [-2*x*Dx-3*z*Dz+h^2] , [2*x*Dy*Dz^2-3*y*Dx^2*h] , [2*x*Dy^2*Dz-3*z*Dx^2*h]] ,
203: [[3*Dx^2*h , 0 , Dy , -Dz] ,
204: [6*x*Dy*Dz^2-9*y*Dx^2*h , -2*x*Dy*Dz^2+3*y*Dx^2*h , -2*x*Dx-3*y*Dy , 0] ,
205: [0 , 2*x*Dy^2*Dz-3*z*Dx^2*h , 0 , 2*x*Dx+3*z*Dz] ,
206: [2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0] ,
207: [2*x*Dy*Dz , 0 , z , -y]],
208: [[-2*x*Dx-3*y*Dy-3*z*Dz-6*h^2 , -Dy , -Dz , 3*Dx^2*h , 3*Dy*Dz ] ,
209: [3*y*z , z , y , -2*x*Dy*Dz , 2*x*Dx]]];
210:
211: sm1_pmat( ans2[1]*ans2[0] );
212: sm1_pmat( ans2[2]*ans2[1] );
213: ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
214: Sweyl("x,y,z",ww2);
215: ans2 = ReParse(ans2);
216: r= IsExact_h(ans2,[x,y,z]);
217: Println(r);
218: return([r,ans2]);
219: }
220:
221: def test12() {
222: local a,v,ww2,ans2;
223: a = Sannfs3("x^3-y^2*z^2");
224: ans2 = a[0];
225: v = [x,y,z];
226: ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
1.4 takayama 227: Sweyl("x,y,z",ww2);
228: ans2 = ReParse(ans2); /* DO NOT FORGET! */
1.3 takayama 229: r= IsExact_h(ans2,[x,y,z]);
230: Println(r);
231: return([r,ans2]);
232: }
1.4 takayama 233:
234: def test13() {
235: Println("test13 try to construct a minimal free resolution");
236: Println("of a GKZ system [[1,2]]. 6/12, 2000.");
1.5 takayama 237: ans2 = GKZ([[1,2]],[0]);
238: /* Be careful!! It resets the grade to module1, not module1v */
1.4 takayama 239: ww2 = [["x1",-1,"x2",-1,"Dx1",1,"Dx2",1]];
240: Sweyl("x1,x2",ww2);
241: ans2 = ReParse(ans2[0]);
1.5 takayama 242: Println(ans2);
1.4 takayama 243: return(Sminimal(ans2));
244: }
245:
246: def test14() {
247: Println("test14 try to construct a minimal free resolution");
248: Println("of a GKZ system [[1,2,3]]. 6/12, 2000.");
1.6 takayama 249: ans2 = GKZ([[1,2,3]],[0]);
250: /* It stops by the strategy error.
251: July 26, 2000. It works fine after fixing a bug in resol.c */
1.4 takayama 252: ww2 = [["x1",-1,"x2",-1,"x3",-1,"Dx1",1,"Dx2",1,"Dx3",1]];
253: Sweyl("x1,x2,x3",ww2);
254: ans2 = ReParse(ans2[0]);
255: return(Sminimal(ans2));
256: }
257: def test14a() {
258: Println("test14a try to construct a minimal free resolution");
259: Println("of a GKZ system [[1,2,3]]. 6/12, 2000.");
260: Println("Without automatic homogenization.");
261: ww2 = [["x1",-1,"x2",-1,"x3",-1,"Dx1",1,"Dx2",1,"Dx3",1]];
262: Sweyl("x1,x2,x3",ww2);
263: ans2 = [x1*Dx1+2*x2*Dx2+3*x3*Dx3 , Dx1^2-Dx2*h , -Dx1*Dx2+Dx3*h ,
264: Dx2^2-Dx1*Dx3 ];
265: ans2 = ReParse(ans2);
266: return(Sminimal(ans2,"homogenized"));
267: }
268:
269: def test15() {
270: Println("test15 try to construct a minimal free resolution");
271: Println("of a GKZ system [[1,2,3]] by the order filt. 6/12, 2000.");
272: ww2 = [["Dx1",1,"Dx2",1,"Dx3",1]];
1.7 ! takayama 273: ans2 = GKZ([[1,2,3]],[0]);
1.4 takayama 274: Sweyl("x1,x2,x3",ww2);
275: ans2 = ReParse(ans2[0]);
1.7 ! takayama 276: a = Sminimal(ans2);
! 277: Println("Minimal Resolution is "); sm1_pmat(a[0]);
! 278: Sweyl("x1,x2,x3");
! 279: ans3 = ReParse(a[0]);
! 280: r= IsExact_h(ans3,[x1,x2,x3]);
! 281: Println(r);
! 282: return(a);
1.4 takayama 283: }
284:
285: def test15b() {
286: Println("test15b try to construct a minimal free resolution");
287: Println("of toric [[1,2,3]] by the order filt. 6/12, 2000.");
288: ww2 = [["Dx1",1,"Dx2",1,"Dx3",1]];
289: Sweyl("x1,x2,x3",ww2);
290: ans2 = [Dx1^2-Dx2*h , -Dx1*Dx2+Dx3*h , Dx2^2-Dx1*Dx3 ];
291: ans2 = ReParse(ans2);
292: return(Sminimal(ans2,"homogenized"));
293: }
294:
1.7 ! takayama 295: def test15c() {
! 296: Println("test15c try to construct a minimal free resolution ");
! 297: Println("of a GKZ system [[1,2,3]] by -1,1");
! 298: ww2 = [["Dx1",1,"Dx2",1,"Dx3",1,"x1",-1,"x2",-1,"x3",-1]];
! 299: ans2 = GKZ([[1,2,3]],[0]);
! 300: Sweyl("x1,x2,x3",ww2);
! 301: ans2 = ReParse(ans2[0]);
! 302: a = Sminimal(ans2);
! 303: Println("Minimal Resolution is "); sm1_pmat(a[0]);
! 304: Sweyl("x1,x2,x3");
! 305: ans3 = ReParse(a[0]);
! 306: r= IsExact_h(ans3,[x1,x2,x3]);
! 307: Println(r);
! 308: return(a);
! 309: }
1.4 takayama 310: def test16() {
311: Println("test16 try to construct a minimal free resolution");
312: Println("of a GKZ system [[1,2,3,5]] by the order filt. 6/12, 2000.");
313: ww2 = [["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1]];
314: Sweyl("x1,x2,x3,x4",ww2);
315: ans2 = GKZ([[1,2,3,5]],[0]);
316: ans2 = ReParse(ans2[0]);
317: return(Sminimal(ans2));
318: }
319:
320: def test16b() {
321: Println("test16b try to construct a minimal free resolution");
322: Println("of a toric [[1,2,3,5]] by the order filt. 6/12, 2000.");
323: ww2 = [["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1]];
324: Sweyl("x1,x2,x3,x4",ww2);
325: ans2 = GKZ([[1,2,3,5]],[0]);
326: ans3 = Rest(ans2[0]);
327: ans3 = ReParse(ans3);
328: Println("Toric variety:");
329: Println(ans3);
330: return(Sminimal(ans3));
331: }
332:
333:
334:
1.3 takayama 335:
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