Annotation of OpenXM/src/k097/lib/restriction/demo.k, Revision 1.4
1.4 ! takayama 1: /* $OpenXM: OpenXM/src/k097/lib/restriction/demo.k,v 1.3 2000/12/27 08:09:27 takayama Exp $ */
1.1 takayama 2:
3: load["restriction.k"];;
4: load("../ox/ox.k");;
5:
6: def demoSendAsirCommand(a) {
7: a.executeString("load(\"bfct\");");
8: a.executeString(" def myann(F) { B=ann(eval_str(F)); print(B); return(map(dp_ptod,B,[hoge,x,y,z,s,hh,ee,dx,dy,dz,ds,dhh])); }; ");
1.2 takayama 9: a.executeString(" def myann0(F) { B=ann0(eval_str(F)); print(B); return(map(dp_ptod,B[1],[hoge,x,y,z,s,hh,ee,dx,dy,dz,ds,dhh])); }; ");
1.1 takayama 10: a.executeString(" def mybfct(F) { return(rtostr(bfct(eval_str(F)))); }; ");
1.4 ! takayama 11: a.executeString(" def mygeneric_bfct(F,VV,DD,WW) { print([F,VV,DD,WW]); return(generic_bfct(F,VV,DD,WW));}; ");
1.1 takayama 12: }
13:
14: as = startAsir();
15: asssssir = as;
16: demoSendAsirCommand(as);
17: RingD("x,y,z,s");
18:
19: def asirBfunction(a,f) {
20: local p,b;
21: p = ToString(f);
22: Println(p);
23: b = a.rpc("mybfct",[p]);
24: sm1(" b . /b set ");
25: return(b);
26: }
27:
28: def asirAnnfsXYZ(a,f) {
29: local p,b;
30: RingD("x,y,z,s"); /* Fix!! See the definition of myann() */
31: p = ToString(f);
32: b = a.rpc("myann",[p]);
33: return(b);
34: }
35:
1.3 takayama 36:
1.4 ! takayama 37: def asir_generic_bfct(a,ii,vv,dd,ww) {
1.3 takayama 38: local ans;
1.4 ! takayama 39: ans = a.rpc_str("mygeneric_bfct",[ii,vv,dd,ww]);
1.3 takayama 40: return(ans);
41: }
1.4 ! takayama 42: /* a=startAsir();
! 43: asir_generic_bfct(a,[Dx^2+Dy^2-1,Dx*Dy-4],[x,y],[Dx,Dy],[1,1]): */
! 44:
! 45: /* usage: misc/tmp/complex-ja.texi */
! 46: def changeRing(F) {
! 47: local n,i,f;
! 48: if (IsArray(F)) {
! 49: n = Length(F);
! 50: for (i=0; i<n; i++) {
! 51: if (IsArray(F[i])) {
! 52: if (changeRing(F)) return(true);
! 53: }else if (IsPolynomial(F[i])) {
! 54: if (F[i] != Poly("0")) {
! 55: f = F[i];
! 56: sm1(" f (ring) dc ring_def ");
! 57: return(true);
! 58: }
! 59: }
! 60: }
! 61: }else if (IsPolynomial(F)) {
! 62: if (F != Poly("0")) {
! 63: sm1(" F (ring) dc ring_def ");
! 64: return(true);
! 65: }
! 66: }
! 67: return(false);
! 68: }
1.3 takayama 69:
70: def asir_BfRoots2(G) {
71: local bb,ans,ss;
72: sm1(" G flatten {dehomogenize} map /G set ");
1.4 ! takayama 73: changeRing(G);
! 74: ss = asir_generic_bfct(asssssir,G,[x,y],[Dx,Dy],[1,1]);
1.3 takayama 75: bb = [ss];
76: sm1(" bb 0 get findIntegralRoots { (universalNumber) dc } map /ans set ");
77: return([ans, bb]);
78: }
79: def asir_BfRoots3(G) {
80: local bb,ans,ss;
81: sm1(" G flatten {dehomogenize} map /G set ");
1.4 ! takayama 82: changeRing(G);
! 83: ss = asir_generic_bfct(asssssir,G,[x,y,z],[Dx,Dy,Dz],[1,1,1]);
1.3 takayama 84: bb = [ss];
85: sm1(" bb 0 get findIntegralRoots { (universalNumber) dc } map /ans set ");
86: return([ans, bb]);
87: }
88:
1.1 takayama 89: def findMinSol(f) {
90: sm1(" f (string) dc findIntegralRoots 0 get (universalNumber) dc /FunctionValue set ");
91: }
92:
93: def asirAnnXYZ(a,f) {
94: local p,b,b0,k1;
95: RingD("x,y,z,s"); /* Fix!! See the definition of myann() */
96: p = ToString(f);
97: b = a.rpc("myann",[p]);
98: Print("Annhilating ideal with s is "); Println(b);
99: b0 = asirBfunction(a,f);
100: Print("bfunction is "); Println(b0);
101: k1 = findMinSol(b0);
102: Print("Minimal integral root is "); Println(k1);
103: sm1(" b { [[(s). k1 (string) dc .]] replace } map /b set ");
104: return(b);
105: }
106:
1.2 takayama 107:
1.1 takayama 108: def nonquasi2(p,q) {
109: local s,ans,f;
110: f = x^p+y^q+x*y^(q-1);
111: Print("f=");Println(f);
112: s = ToString(f);
113: sm1(" Onverbose ");
114: ans = asirAnnfsXYZ(asssssir,f);
115: sm1(" ans 0 get (ring) dc ring_def ");
116: sm1("[ ans { [[(s). (-1).]] replace } map ] /II set ");
117: Println("Step 1: Annhilating ideal (II)"); Println(II);
118: sm1(" II 0 get { [(x) (y) (Dx) (Dy) ] laplace0 } map /II set ");
119: Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]);
120: pp = Map(II,"Spoly");
121: Res = Sminimal(pp);
122: Res0 = Res[0];
123: Println("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
1.3 takayama 124: /* R = BfRoots1(Res0[0],"x,y"); */
125: R = asir_BfRoots2(Res0[0]);
1.1 takayama 126: Println("Step3: computing the cohomology of the truncated complex.");
127: Print("Roots and b-function are "); Println(R);
128: R0 = R[0];
129: Ans=Srestall(Res0, ["x", "y"], ["x", "y"], R0[Length(R0)-1]);
130: Print("Answer is "); Println(Ans[0]);
1.2 takayama 131: return(Ans);
132: }
133:
134: def asirAnn0XYZ(a,f) {
135: local p,b,b0;
136: RingD("x,y,z,s"); /* Fix!! See the definition of myann() */
137: p = ToString(f);
138: b = a.rpc("myann0",[p]);
139: Print("Annhilating ideal of f^r is "); Println(b);
140: return(b);
141: }
142:
143: def DeRham2WithAsir(f) {
144: local s;
145: s = ToString(f);
146: II = asirAnn0XYZ(asssssir,f);
147: Print("Step 1: Annhilating ideal (II)"); Println(II);
148: sm1(" II { [(x) (y) (Dx) (Dy) ] laplace0 } map /II set ");
149: Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]);
150: pp = Map(II,"Spoly");
151: Res = Sminimal(pp);
152: Res0 = Res[0];
153: Print("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
1.3 takayama 154: /* R = BfRoots1(Res0[0],"x,y"); */
155: R = asir_BfRoots2(Res0[0]);
1.2 takayama 156: Println("Step3: computing the cohomology of the truncated complex.");
157: Print("Roots and b-function are "); Println(R);
158: R0 = R[0];
159: Ans=Srestall(Res0, ["x", "y"], ["x", "y"],R0[Length(R0)-1] );
160: Print("Answer is ");Println(Ans[0]);
161: return(Ans);
162: }
163: def DeRham3WithAsir(f) {
164: local s;
165: s = ToString(f);
166: II = asirAnn0XYZ(asssssir,f);
167: Print("Step 1: Annhilating ideal (II)"); Println(II);
168: sm1(" II { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /II set ");
169: Sweyl("x,y,z",[["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]]);
170: pp = Map(II,"Spoly");
171: Res = Sminimal(pp);
172: Res0 = Res[0];
173: Print("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
1.4 ! takayama 174: /* R = BfRoots1(Res0[0],"x,y,z"); */
1.3 takayama 175: R = asir_BfRoots3(Res0[0]);
1.2 takayama 176: Println("Step3: computing the cohomology of the truncated complex.");
177: Print("Roots and b-function are "); Println(R);
178: R0 = R[0];
179: Ans=Srestall(Res0, ["x", "y", "z"], ["x", "y", "z"],R0[Length(R0)-1] );
180: Print("Answer is ");Println(Ans[0]);
1.1 takayama 181: return(Ans);
182: }
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