Annotation of OpenXM/src/k097/lib/restriction/demo.k, Revision 1.6
1.6 ! takayama 1: /* $OpenXM: OpenXM/src/k097/lib/restriction/demo.k,v 1.5 2000/12/28 00:08:14 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 */
1.6 ! takayama 46: def ChangeRing(f) {
1.5 takayama 47: local r;
48: r = GetRing(f);
49: if (Tag(r) == 14) {
50: SetRing(r);
51: return(true);
52: }else{
53: return(false);
1.4 takayama 54: }
55: }
1.3 takayama 56:
57: def asir_BfRoots2(G) {
58: local bb,ans,ss;
59: sm1(" G flatten {dehomogenize} map /G set ");
1.6 ! takayama 60: ChangeRing(G);
1.4 takayama 61: ss = asir_generic_bfct(asssssir,G,[x,y],[Dx,Dy],[1,1]);
1.3 takayama 62: bb = [ss];
63: sm1(" bb 0 get findIntegralRoots { (universalNumber) dc } map /ans set ");
64: return([ans, bb]);
65: }
66: def asir_BfRoots3(G) {
67: local bb,ans,ss;
68: sm1(" G flatten {dehomogenize} map /G set ");
1.6 ! takayama 69: ChangeRing(G);
1.4 takayama 70: ss = asir_generic_bfct(asssssir,G,[x,y,z],[Dx,Dy,Dz],[1,1,1]);
1.3 takayama 71: bb = [ss];
72: sm1(" bb 0 get findIntegralRoots { (universalNumber) dc } map /ans set ");
73: return([ans, bb]);
74: }
75:
1.1 takayama 76: def findMinSol(f) {
77: sm1(" f (string) dc findIntegralRoots 0 get (universalNumber) dc /FunctionValue set ");
78: }
79:
80: def asirAnnXYZ(a,f) {
81: local p,b,b0,k1;
82: RingD("x,y,z,s"); /* Fix!! See the definition of myann() */
83: p = ToString(f);
84: b = a.rpc("myann",[p]);
85: Print("Annhilating ideal with s is "); Println(b);
86: b0 = asirBfunction(a,f);
87: Print("bfunction is "); Println(b0);
88: k1 = findMinSol(b0);
89: Print("Minimal integral root is "); Println(k1);
90: sm1(" b { [[(s). k1 (string) dc .]] replace } map /b set ");
91: return(b);
92: }
93:
1.2 takayama 94:
1.1 takayama 95: def nonquasi2(p,q) {
96: local s,ans,f;
97: f = x^p+y^q+x*y^(q-1);
98: Print("f=");Println(f);
99: s = ToString(f);
100: sm1(" Onverbose ");
101: ans = asirAnnfsXYZ(asssssir,f);
102: sm1(" ans 0 get (ring) dc ring_def ");
103: sm1("[ ans { [[(s). (-1).]] replace } map ] /II set ");
104: Println("Step 1: Annhilating ideal (II)"); Println(II);
105: sm1(" II 0 get { [(x) (y) (Dx) (Dy) ] laplace0 } map /II set ");
106: Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]);
107: pp = Map(II,"Spoly");
108: Res = Sminimal(pp);
109: Res0 = Res[0];
110: Println("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
1.3 takayama 111: /* R = BfRoots1(Res0[0],"x,y"); */
112: R = asir_BfRoots2(Res0[0]);
1.1 takayama 113: Println("Step3: computing the cohomology of the truncated complex.");
114: Print("Roots and b-function are "); Println(R);
115: R0 = R[0];
116: Ans=Srestall(Res0, ["x", "y"], ["x", "y"], R0[Length(R0)-1]);
117: Print("Answer is "); Println(Ans[0]);
1.2 takayama 118: return(Ans);
119: }
120:
121: def asirAnn0XYZ(a,f) {
122: local p,b,b0;
123: RingD("x,y,z,s"); /* Fix!! See the definition of myann() */
124: p = ToString(f);
125: b = a.rpc("myann0",[p]);
126: Print("Annhilating ideal of f^r is "); Println(b);
127: return(b);
128: }
129:
130: def DeRham2WithAsir(f) {
131: local s;
132: s = ToString(f);
133: II = asirAnn0XYZ(asssssir,f);
134: Print("Step 1: Annhilating ideal (II)"); Println(II);
135: sm1(" II { [(x) (y) (Dx) (Dy) ] laplace0 } map /II set ");
136: Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]);
137: pp = Map(II,"Spoly");
138: Res = Sminimal(pp);
139: Res0 = Res[0];
140: Print("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
1.3 takayama 141: /* R = BfRoots1(Res0[0],"x,y"); */
142: R = asir_BfRoots2(Res0[0]);
1.2 takayama 143: Println("Step3: computing the cohomology of the truncated complex.");
144: Print("Roots and b-function are "); Println(R);
145: R0 = R[0];
146: Ans=Srestall(Res0, ["x", "y"], ["x", "y"],R0[Length(R0)-1] );
147: Print("Answer is ");Println(Ans[0]);
148: return(Ans);
149: }
150: def DeRham3WithAsir(f) {
151: local s;
152: s = ToString(f);
153: II = asirAnn0XYZ(asssssir,f);
154: Print("Step 1: Annhilating ideal (II)"); Println(II);
155: sm1(" II { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /II set ");
156: Sweyl("x,y,z",[["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]]);
157: pp = Map(II,"Spoly");
158: Res = Sminimal(pp);
159: Res0 = Res[0];
160: Print("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
1.4 takayama 161: /* R = BfRoots1(Res0[0],"x,y,z"); */
1.3 takayama 162: R = asir_BfRoots3(Res0[0]);
1.2 takayama 163: Println("Step3: computing the cohomology of the truncated complex.");
164: Print("Roots and b-function are "); Println(R);
165: R0 = R[0];
166: Ans=Srestall(Res0, ["x", "y", "z"], ["x", "y", "z"],R0[Length(R0)-1] );
167: Print("Answer is ");Println(Ans[0]);
1.1 takayama 168: return(Ans);
169: }
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