Annotation of OpenXM/src/k097/lib/minimal/minimal-test.k, Revision 1.18
1.18 ! takayama 1: /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.17 2000/08/10 02:59:08 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:
1.3 takayama 44: def test11() {
45: local a;
46: a = test_ann3("x^3-y^2*z^2");
47: return(a);
48: }
49: /* f should be a string. */
1.5 takayama 50: /* a=test_ann3("x^3+y^3+z^3");
51: It returns the following resolution in 1.5 hours. June 14, 2000.
52: [
53: [
54: [ x*Dx+y*Dy+z*Dz-3*h^2 ]
55: [ -z*Dy^2+y*Dz^2 ]
56: [ -z*Dx^2+x*Dz^2 ]
57: [ -y*Dx^2+x*Dy^2 ]
58: ]
59: [
60: [ 0 , -x , y , -z ]
61: [ z*Dx^2-x*Dz^2 , x*Dy , x*Dx+z*Dz-3*h^2 , z*Dy ]
62: [ y*Dx^2-x*Dy^2 , -x*Dz , y*Dz , x*Dx+y*Dy-3*h^2 ]
63: [ 0 , Dx^2 , -Dy^2 , Dz^2 ]
64: [ z*Dy^2-y*Dz^2 , x*Dx+y*Dy+z*Dz-2*h^2 , 0 , 0 ]
65: ]
66: [
67: [ -x*Dx+3*h^2 , y , -z , 0 , -x ]
68: [ Dy^3+Dz^3 , Dy^2 , -Dz^2 , x*Dx+y*Dy+z*Dz , -Dx^2 ]
69: ]
70: ]
71: */
1.3 takayama 72: def test_ann3(f) {
73: local a,v,ww2,ans2;
1.7 takayama 74: a = Sannfs3(f);
1.3 takayama 75: ans2 = a[0];
76: v = [x,y,z];
77: ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
78: Sweyl("x,y,z",ww2);
79: ans2 = ReParse(ans2);
80: r= IsExact_h(ans2,[x,y,z]);
81: Println(r);
1.9 takayama 82: return([r,ans2,a]);
1.3 takayama 83: }
84: def test11a() {
85: local a,v,ww2,ans2;
86: /* constructed by test11.
87: ans2 =
88: [[[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]] ,
89: [[3*Dx^2*h , 0 , Dy , -Dz] ,
90: [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] ,
91: [0 , 2*x*Dy^2*Dz-3*z*Dx^2*h , 0 , 2*x*Dx+3*z*Dz] ,
92: [2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0] ,
93: [0 , 0 , 0 , 0] ,
94: [2*x*Dy*Dz , 0 , z , -y] ,
95: [0 , 0 , 0 , 0] ,
96: [0 , 0 , 0 , 0] ,
97: [0 , 0 , 0 , 0]] ,
98: [[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
99: [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
100: [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
101: [-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] ,
102: [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
103: [3*y*z , z , y , -2*x*Dy*Dz , -3*z*Dy , 2*x*Dx , 2*x*z , -2*x*y , 0] ,
104: [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
105: [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
106: [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0]] ,
107: [[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
108: [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
109: [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0]]]
110: */
111: ans2 =
112: [[[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]] ,
113: [[3*Dx^2*h , 0 , Dy , -Dz] ,
114: [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] ,
115: [0 , 2*x*Dy^2*Dz-3*z*Dx^2*h , 0 , 2*x*Dx+3*z*Dz] ,
116: [2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0] ,
117: [2*x*Dy*Dz , 0 , z , -y]],
118: [[-2*x*Dx-3*y*Dy-3*z*Dz-6*h^2 , -Dy , -Dz , 3*Dx^2*h , 3*Dy*Dz ] ,
119: [3*y*z , z , y , -2*x*Dy*Dz , 2*x*Dx]]];
120:
121: sm1_pmat( ans2[1]*ans2[0] );
122: sm1_pmat( ans2[2]*ans2[1] );
123: ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
124: Sweyl("x,y,z",ww2);
125: ans2 = ReParse(ans2);
126: r= IsExact_h(ans2,[x,y,z]);
127: Println(r);
128: return([r,ans2]);
129: }
130:
131: def test12() {
132: local a,v,ww2,ans2;
133: a = Sannfs3("x^3-y^2*z^2");
134: ans2 = a[0];
135: v = [x,y,z];
136: ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
1.4 takayama 137: Sweyl("x,y,z",ww2);
138: ans2 = ReParse(ans2); /* DO NOT FORGET! */
1.3 takayama 139: r= IsExact_h(ans2,[x,y,z]);
140: Println(r);
141: return([r,ans2]);
142: }
1.4 takayama 143:
144: def test13() {
145: Println("test13 try to construct a minimal free resolution");
146: Println("of a GKZ system [[1,2]]. 6/12, 2000.");
1.5 takayama 147: ans2 = GKZ([[1,2]],[0]);
148: /* Be careful!! It resets the grade to module1, not module1v */
1.4 takayama 149: ww2 = [["x1",-1,"x2",-1,"Dx1",1,"Dx2",1]];
150: Sweyl("x1,x2",ww2);
151: ans2 = ReParse(ans2[0]);
1.5 takayama 152: Println(ans2);
1.4 takayama 153: return(Sminimal(ans2));
154: }
155:
156: def test14() {
157: Println("test14 try to construct a minimal free resolution");
158: Println("of a GKZ system [[1,2,3]]. 6/12, 2000.");
1.6 takayama 159: ans2 = GKZ([[1,2,3]],[0]);
160: /* It stops by the strategy error.
161: July 26, 2000. It works fine after fixing a bug in resol.c */
1.4 takayama 162: ww2 = [["x1",-1,"x2",-1,"x3",-1,"Dx1",1,"Dx2",1,"Dx3",1]];
163: Sweyl("x1,x2,x3",ww2);
164: ans2 = ReParse(ans2[0]);
165: return(Sminimal(ans2));
166: }
167: def test14a() {
168: Println("test14a try to construct a minimal free resolution");
169: Println("of a GKZ system [[1,2,3]]. 6/12, 2000.");
170: Println("Without automatic homogenization.");
171: ww2 = [["x1",-1,"x2",-1,"x3",-1,"Dx1",1,"Dx2",1,"Dx3",1]];
172: Sweyl("x1,x2,x3",ww2);
173: ans2 = [x1*Dx1+2*x2*Dx2+3*x3*Dx3 , Dx1^2-Dx2*h , -Dx1*Dx2+Dx3*h ,
174: Dx2^2-Dx1*Dx3 ];
175: ans2 = ReParse(ans2);
1.8 takayama 176: return(Sminimal(ans2,["homogenized"]));
1.4 takayama 177: }
178:
179: def test15() {
180: Println("test15 try to construct a minimal free resolution");
181: Println("of a GKZ system [[1,2,3]] by the order filt. 6/12, 2000.");
182: ww2 = [["Dx1",1,"Dx2",1,"Dx3",1]];
1.7 takayama 183: ans2 = GKZ([[1,2,3]],[0]);
1.4 takayama 184: Sweyl("x1,x2,x3",ww2);
185: ans2 = ReParse(ans2[0]);
1.7 takayama 186: a = Sminimal(ans2);
187: Println("Minimal Resolution is "); sm1_pmat(a[0]);
188: Sweyl("x1,x2,x3");
189: ans3 = ReParse(a[0]);
190: r= IsExact_h(ans3,[x1,x2,x3]);
191: Println(r);
192: return(a);
1.4 takayama 193: }
194:
195: def test15b() {
196: Println("test15b try to construct a minimal free resolution");
197: Println("of toric [[1,2,3]] by the order filt. 6/12, 2000.");
198: ww2 = [["Dx1",1,"Dx2",1,"Dx3",1]];
199: Sweyl("x1,x2,x3",ww2);
200: ans2 = [Dx1^2-Dx2*h , -Dx1*Dx2+Dx3*h , Dx2^2-Dx1*Dx3 ];
201: ans2 = ReParse(ans2);
1.8 takayama 202: return(Sminimal(ans2,["homogenized"]));
1.4 takayama 203: }
204:
1.7 takayama 205: def test15c() {
206: Println("test15c try to construct a minimal free resolution ");
207: Println("of a GKZ system [[1,2,3]] by -1,1");
208: ww2 = [["Dx1",1,"Dx2",1,"Dx3",1,"x1",-1,"x2",-1,"x3",-1]];
209: ans2 = GKZ([[1,2,3]],[0]);
210: Sweyl("x1,x2,x3",ww2);
211: ans2 = ReParse(ans2[0]);
212: a = Sminimal(ans2);
213: Println("Minimal Resolution is "); sm1_pmat(a[0]);
214: Sweyl("x1,x2,x3");
215: ans3 = ReParse(a[0]);
216: r= IsExact_h(ans3,[x1,x2,x3]);
217: Println(r);
218: return(a);
219: }
1.4 takayama 220: def test16() {
221: Println("test16 try to construct a minimal free resolution");
222: Println("of a GKZ system [[1,2,3,5]] by the order filt. 6/12, 2000.");
223: ww2 = [["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1]];
224: Sweyl("x1,x2,x3,x4",ww2);
225: ans2 = GKZ([[1,2,3,5]],[0]);
226: ans2 = ReParse(ans2[0]);
227: return(Sminimal(ans2));
228: }
229:
230: def test16b() {
231: Println("test16b try to construct a minimal free resolution");
232: Println("of a toric [[1,2,3,5]] by the order filt. 6/12, 2000.");
233: ww2 = [["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1]];
234: Sweyl("x1,x2,x3,x4",ww2);
235: ans2 = GKZ([[1,2,3,5]],[0]);
236: ans3 = Rest(ans2[0]);
237: ans3 = ReParse(ans3);
238: Println("Toric variety:");
239: Println(ans3);
240: return(Sminimal(ans3));
241: }
242:
1.9 takayama 243:
244: def test17() {
245: a=Sannfs3("x^3-y^2*z^2");
246: b=a[0]; w = ["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1];
247: Sweyl("x,y,z",[w]); b = Reparse(b);
248: c=Sinit_w(b,w);
249: Println("Resolution (b)----");
250: sm1_pmat(b);
251: Println("Initial (c)----");
252: sm1_pmat(c);
253: Println(IsExact_h(c,"x,y,z"));
254: }
1.10 takayama 255:
256: def test_if_v_strict(resmat,w,v) {
1.12 takayama 257: local b,c,g;
1.10 takayama 258: Sweyl(v,[w]); b = Reparse(resmat);
1.13 takayama 259: Println("Degree shifts ");
260: Println(SgetShifts(b,w));
1.9 takayama 261: c=Sinit_w(b,w);
262: Println("Resolution (b)----");
263: sm1_pmat(b);
264: Println("Initial (c)----");
1.12 takayama 265: sm1_pmat(c);
1.10 takayama 266: Println("Exactness of the resolution ---");
1.12 takayama 267: Println(IsExact_h(b,v));
1.10 takayama 268: Println("Exactness of the initial complex.---");
1.12 takayama 269: Println(IsExact_h(c,v));
1.9 takayama 270: g = Sinvolutive(b[0],w);
1.10 takayama 271: /* Println("Involutive basis ---");
1.11 takayama 272: sm1_pmat(g);
1.12 takayama 273: Println(Sinvolutive(c[0],w));
1.11 takayama 274: sm1(" /gb.verbose 1 def "); */
1.9 takayama 275: Println("Is same ideal?");
1.12 takayama 276: Println(IsSameIdeal_h(g,c[0],v));
1.10 takayama 277: }
278: def test17b() {
279: a=Sannfs3("x^3-y^2*z^2");
1.11 takayama 280: b=a[0]; w = ["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1];
1.10 takayama 281: test_if_v_strict(b,w,"x,y,z");
282: return(a);
1.9 takayama 283: }
284:
285: def test18() {
286: a=Sannfs2("x^3-y^2");
287: b=a[0]; w = ["x",-1,"y",-1,"Dx",1,"Dy",1];
1.10 takayama 288: test_if_v_strict(b,w,"x,y");
289: return(a);
1.9 takayama 290: }
1.4 takayama 291:
1.10 takayama 292: def test19() {
293: Println("test19 try to construct a minimal free resolution and check if it is v-strict.");
294: Println("of a GKZ system [[1,2,3]] by -1,1");
295: ww2 = ["Dx1",1,"Dx2",1,"Dx3",1,"x1",-1,"x2",-1,"x3",-1];
296: ans2 = GKZ([[1,2,3]],[0]);
297: Sweyl("x1,x2,x3",[ww2]);
298: ans2 = ReParse(ans2[0]);
299: a = Sminimal(ans2);
300: Println("Minimal Resolution is "); sm1_pmat(a[0]);
301: b = a[0];
302: test_if_v_strict(b,ww2,"x1,x2,x3");
303: return(a);
304: }
305:
1.13 takayama 306: /* Need more than 100M memory. 291, 845, 1266, 1116, 592 : Schreyer frame.
307: I've not yet tried to finish the computation. */
1.10 takayama 308: def test20() {
309: w = ["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1,"x1",-1,"x2",-1,"x3",-1,"x4",-1];
310: ans2 = GKZ([[1,1,1,1],[0,1,3,4]],[0,0]);
311: Sweyl("x1,x2,x3,x4",[w]);
312: ans2 = ReParse(ans2[0]);
313: a = Sminimal(ans2);
314: Println("Minimal Resolution is "); sm1_pmat(a[0]);
315: b = a[0];
316: /* test_if_v_strict(b,w,"x1,x2,x3,x4"); */
317: return(a);
318: }
319: def test20b() {
320: w = ["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1,"x1",-1,"x2",-1,"x3",-1,"x4",-1];
321: ans2 = GKZ([[1,1,1,1],[0,1,3,4]],[1,2]);
322: Sweyl("x1,x2,x3,x4",[w]);
323: ans2 = ReParse(ans2[0]);
324: a = Sminimal(ans2);
325: Println("Minimal Resolution is "); sm1_pmat(a[0]);
326: b = a[0];
327: /* test_if_v_strict(b,w,"x1,x2,x3,x4"); */
328: return(a);
329: }
1.13 takayama 330:
331: def test21() {
332: a=Sannfs3("x^3-y^2*z^2+y^2+z^2");
333: /* a=Sannfs3("x^3-y-z"); for debug */
334: b=a[0]; w = ["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1];
335: test_if_v_strict(b,w,"x,y,z");
336: Println("Degree shifts of Schreyer resolution ----");
1.18 ! takayama 337: Println(SgetShifts(Reparse(a[3]),w));
1.13 takayama 338: return(a);
339: }
1.15 takayama 340: def test21b() {
1.18 ! takayama 341: local i,j,n,sss, maxR, ttt,ans,p, euler;
1.15 takayama 342: Println("The dimensions of linear spaces -----");
343: /* sss is the SgetShifts of the Schreyer resol. */
1.18 ! takayama 344: sss=[ [ 0 ] , [ 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 2 , 1 , 3 , 2 ] , [ 1 , 1 , 1 , 2 , 3 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 2 , 2 , 2 , 3 , 2 , 3 , 3 , 3 , 4 , 3 , 3 , 4 , 3 , 3 , 4 , 3 , 3 , 4 , 4 , 4 , 4 , 4 , 5 , 4 , 4 , 3 , 5 , 5 , 5 , 5 , 4 ] , [ 1 , 3 , 1 , 3 , 3 , 1 , 2 , 2 , 3 , 2 , 3 , 2 , 3 , 5 , 4 , 4 , 3 , 6 , 5 , 4 , 3 , 2 , 3 , 3 , 5 , 4 , 3 , 2 , 4 , 4 , 4 , 4 , 5 , 3 , 2 , 3 , 3 , 4 , 4 , 4 , 5 , 4 , 4 , 5 , 3 , 5 , 4 , 5 , 5 , 6 ] , [ 3 , 1 , 4 , 5 , 4 , 5 , 2 , 3 , 2 , 4 , 3 , 4 , 3 , 3 , 2 , 4 , 3 , 5 , 4 , 5 , 6 ] , [ 2 , 3 ] ] ;
! 345: maxR = 2; /* Maximal root of the b-function. */
1.15 takayama 346: n = Length(sss);
1.18 ! takayama 347: euler = 0;
1.15 takayama 348: for (i=0; i<n; i++) {
349: ttt = sss[i];
350: ans = 0;
351: for (j=0; j<Length(ttt); j++) {
352: p = ttt[j] + maxR + 3; /* degree */
353: if (p >= 0) {
354: ans = ans + CancelNumber(p*(p-1)*(p-2)/(3*2*1));
355: /* Add the number of monomials */
356: }
357: }
358: Print(ans); Print(", ");
1.18 ! takayama 359: euler = euler+(-1)^i*ans;
1.15 takayama 360: }
361: Println(" ");
1.18 ! takayama 362: Print("Euler number is : "); Println(euler);
! 363: }
! 364: def test21c() {
! 365: local i,j,n,sss, maxR, ttt,ans,p, euler;
! 366: Println("The dimensions of linear spaces -----");
! 367: /* sss is the SgetShifts of the minimal resol. */
! 368: sss= [ [ 0 ] , [ 2 , 2 , 2 , 2 , 2 , 2 , 2 ] , [ 1 , 2 , 2 , 2 , 2 , 3 , 4 , 4 , 4 , 4 ] , [ 1 , 3 , 4 , 6 ] ];
! 369: maxR = 2; /* Maximal root of the b-function. */
! 370: n = Length(sss);
! 371: euler = 0;
! 372: for (i=0; i<n; i++) {
! 373: ttt = sss[i];
! 374: ans = 0;
! 375: for (j=0; j<Length(ttt); j++) {
! 376: p = ttt[j] + maxR + 3; /* degree */
! 377: if (p >= 0) {
! 378: ans = ans + CancelNumber(p*(p-1)*(p-2)/(3*2*1));
! 379: /* Add the number of monomials */
! 380: }
! 381: }
! 382: Print(ans); Print(", ");
! 383: euler = euler+(-1)^i*ans;
! 384: }
! 385: Println(" ");
! 386: Print("Euler number is : "); Println(euler);
1.15 takayama 387: }
1.13 takayama 388: def test22() {
389: a=Sannfs3("x^3+y^3+z^3");
1.14 takayama 390: b=a[0]; w = ["x",-1,"y",-2,"z",-3,"Dx",1,"Dy",2,"Dz",3];
1.13 takayama 391: test_if_v_strict(b,w,"x,y,z");
392: return(a);
393: }
1.16 takayama 394:
395: def FillFromLeft(mat,p,z) {
396: local m,n,i,j,aa;
397: m = Length(mat); n = Length(mat[0]);
398: aa = NewMatrix(m,n+p);
399: for (i=0; i<m; i++) {
400: for (j=0; j<p; j++) {
401: aa[i,j] = z; /* zero */
402: }
403: for (j=0; j<n; j++) {
404: aa[i,j+p] = mat[i,j];
405: }
406: }
407: return(aa);
408: }
409:
410: def FillFromRight(mat,p,z) {
411: local m,n,i,j,aa;
412: m = Length(mat); n = Length(mat[0]);
413: aa = NewMatrix(m,n+p);
414: for (i=0; i<m; i++) {
415: for (j=n; j<n+p; j++) {
416: aa[i,j] = z; /* zero */
417: }
418: for (j=0; j<n; j++) {
419: aa[i,j] = mat[i,j];
420: }
421: }
422: return(aa);
423: }
424:
425: def test23() {
426: w = ["Dx1",1,"Dx2",1,"Dx3",1,"x1",-1,"x2",-1,"x3",-1];
427: Sweyl("x1,x2,x3",[w]);
428: d2 = [[Dx1^2-Dx2*h] , [-Dx1*Dx2+Dx3*h] , [Dx2^2-Dx1*Dx3] ];
429: d1 = [[-Dx2, -Dx1, -h],[Dx3,Dx2,Dx1]];
430: LL = x1*Dx1 + 2*x2*Dx2+3*x3*Dx3;
431: /* It is exact for LL = Dx1 + 2*Dx2+3*Dx3; */
432: u1 = [[LL+4*h^2,Poly("0")],[Poly("0"),LL+5*h^2]];
433: u2 = [[LL+2*h^2,Poly("0"),Poly("0")],
434: [Poly("0"),LL+3*h^2,Poly("0")],
435: [Poly("0"),Poly("0"),LL+4*h^2]];
436: u3 = [[LL]];
437: Println("Checking if it is a double complex. ");
438: Println("u^2 d^2 - d^2 u^3");
439: sm1_pmat(u2*d2 - d2*u3);
440: Println("u^1 d^1 - d^1 u^2");
441: sm1_pmat(u1*d1 - d1*u2);
442: aa = [
443: Join(u3,d2),
444: Join(FillFromLeft(u2,1,Poly("0"))-FillFromRight(d2,3,Poly("0")),
445: FillFromLeft(d1,1,Poly("0"))),
446: FillFromLeft(u1,3,Poly("0"))-FillFromRight(d1,2,Poly("0"))
447: ];
448: Println([ aa[1]*aa[0], aa[2]*aa[1] ]);
449: r= IsExact_h(aa,[x1,x2,x3]);
450: Println(r);
451: /* sm1_pmat(aa); */
452: return(aa);
453: }
454:
455:
1.17 takayama 456: def test24() {
457: local Res, Eqs, ww,a;
458: ww = ["x",-1,"y",-1,"Dx",1,"Dy",1];
459: Println("Example of V-minimal <> minimal ");
460: Sweyl("x,y", [ww]);
461: Eqs = [Dx-(x*Dx+y*Dy),
462: Dy-(x*Dx+y*Dy)];
463: sm1(" Eqs dehomogenize /Eqs set");
464: Res = Sminimal(Eqs);
465: Sweyl("x,y", [ww]);
466: a = Reparse(Res[0]);
467: sm1_pmat(a);
468: Println("Initial of the complex is ");
469: sm1_pmat( Sinit_w(a,ww) );
470: return(Res);
471: }
472:
473: def test24b() {
474: local Res, Eqs, ww ;
475: ww = ["x",-1,"y",-1,"Dx",1,"Dy",1];
476: Println("Construction of minimal ");
477: Sweyl("x,y", [ww]);
478: Eqs = [Dx-(x*Dx+y*Dy),
479: Dy-(x*Dx+y*Dy)];
480: sm1(" Eqs dehomogenize /Eqs set");
481: Res = Sminimal(Eqs,["Sordinary"]);
482: sm1_pmat(Res[0]);
483: return(Res);
484: }
1.16 takayama 485:
1.18 ! takayama 486: def test25() {
! 487: w = ["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1,"Dx5",1,"Dx6",1,
! 488: "x1",-1,"x2",-1,"x3",-1,"x4",-1,"x5",-1,"x6",-1];
! 489: ans2 = GKZ([[1,1,1,1,1,1],
! 490: [0,0,0,1,1,1],
! 491: [0,1,0,0,1,0],
! 492: [0,0,1,0,0,1]],[0,0,0,0]);;
! 493: Sweyl("x1,x2,x3,x4,x5,x6",[w]);
! 494: ans2 = ReParse(ans2[0]);
! 495: a = Sminimal(ans2);
! 496: }
1.16 takayama 497:
1.13 takayama 498:
1.3 takayama 499:
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