Annotation of OpenXM/src/k097/lib/restriction/demo.k, Revision 1.9
1.9 ! takayama 1: /* $OpenXM: OpenXM/src/k097/lib/restriction/demo.k,v 1.8 2001/09/20 00:48:17 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:
1.7 takayama 14: if (Boundp("NoX")) {
15: as = Asir.generate(false);
16: }else{
17: as = Asir.generate();
1.9 ! takayama 18: }
! 19:
! 20: def demoReduction(v) {
! 21: if (v == true) {
! 22: sm1(" [(Verbose) 1] system_variable [(DebugReductionRed) 1] system_variable Onverbose ");
! 23: }else{
! 24: sm1(" [(Verbose) 0] system_variable [(DebugReductionRed) 0] system_variable Offverbose ");
! 25: }
1.7 takayama 26: }
27:
1.1 takayama 28: asssssir = as;
29: demoSendAsirCommand(as);
30: RingD("x,y,z,s");
31:
32: def asirBfunction(a,f) {
33: local p,b;
34: p = ToString(f);
35: Println(p);
36: b = a.rpc("mybfct",[p]);
37: sm1(" b . /b set ");
38: return(b);
39: }
40:
41: def asirAnnfsXYZ(a,f) {
42: local p,b;
43: RingD("x,y,z,s"); /* Fix!! See the definition of myann() */
44: p = ToString(f);
45: b = a.rpc("myann",[p]);
46: return(b);
47: }
48:
1.3 takayama 49:
1.4 takayama 50: def asir_generic_bfct(a,ii,vv,dd,ww) {
1.3 takayama 51: local ans;
1.4 takayama 52: ans = a.rpc_str("mygeneric_bfct",[ii,vv,dd,ww]);
1.3 takayama 53: return(ans);
54: }
1.4 takayama 55: /* a=startAsir();
56: asir_generic_bfct(a,[Dx^2+Dy^2-1,Dx*Dy-4],[x,y],[Dx,Dy],[1,1]): */
57:
58: /* usage: misc/tmp/complex-ja.texi */
1.6 takayama 59: def ChangeRing(f) {
1.5 takayama 60: local r;
61: r = GetRing(f);
62: if (Tag(r) == 14) {
63: SetRing(r);
64: return(true);
65: }else{
66: return(false);
1.4 takayama 67: }
68: }
1.3 takayama 69:
70: def asir_BfRoots2(G) {
71: local bb,ans,ss;
72: sm1(" G flatten {dehomogenize} map /G set ");
1.6 takayama 73: ChangeRing(G);
1.4 takayama 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 ");
1.6 takayama 82: ChangeRing(G);
1.4 takayama 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:
1.8 takayama 89: def asir_BfRoots4(G) {
90: local bb,ans,ss;
91: sm1(" G flatten {dehomogenize} map /G set ");
92: ChangeRing(G);
93: ss = asir_generic_bfct(asssssir,G,[x,y,z,vv],[Dx,Dy,Dz,Dvv],[0,0,0,1]);
94: bb = [ss];
95: sm1(" bb 0 get findIntegralRoots { (universalNumber) dc } map /ans set ");
96: return([ans, bb]);
97: }
98:
1.1 takayama 99: def findMinSol(f) {
100: sm1(" f (string) dc findIntegralRoots 0 get (universalNumber) dc /FunctionValue set ");
101: }
102:
103: def asirAnnXYZ(a,f) {
104: local p,b,b0,k1;
105: RingD("x,y,z,s"); /* Fix!! See the definition of myann() */
106: p = ToString(f);
107: b = a.rpc("myann",[p]);
108: Print("Annhilating ideal with s is "); Println(b);
109: b0 = asirBfunction(a,f);
110: Print("bfunction is "); Println(b0);
111: k1 = findMinSol(b0);
112: Print("Minimal integral root is "); Println(k1);
113: sm1(" b { [[(s). k1 (string) dc .]] replace } map /b set ");
114: return(b);
115: }
116:
1.2 takayama 117:
1.1 takayama 118: def nonquasi2(p,q) {
119: local s,ans,f;
1.7 takayama 120:
121: sm1("0 set_timer "); sm1(" oxNoX ");
122: asssssir.OnTimer();
123:
1.1 takayama 124: f = x^p+y^q+x*y^(q-1);
125: Print("f=");Println(f);
126: s = ToString(f);
127: sm1(" Onverbose ");
128: ans = asirAnnfsXYZ(asssssir,f);
129: sm1(" ans 0 get (ring) dc ring_def ");
130: sm1("[ ans { [[(s). (-1).]] replace } map ] /II set ");
131: Println("Step 1: Annhilating ideal (II)"); Println(II);
132: sm1(" II 0 get { [(x) (y) (Dx) (Dy) ] laplace0 } map /II set ");
133: Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]);
134: pp = Map(II,"Spoly");
135: Res = Sminimal(pp);
136: Res0 = Res[0];
137: Println("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
1.3 takayama 138: /* R = BfRoots1(Res0[0],"x,y"); */
139: R = asir_BfRoots2(Res0[0]);
1.1 takayama 140: Println("Step3: computing the cohomology of the truncated complex.");
141: Print("Roots and b-function are "); Println(R);
142: R0 = R[0];
143: Ans=Srestall(Res0, ["x", "y"], ["x", "y"], R0[Length(R0)-1]);
1.7 takayama 144:
145: Println("Timing data: sm1 "); sm1(" 1 set_timer ");
146: Print(" ox_asir [CPU,GC]: ");Println(asssssir.OffTimer());
147:
1.1 takayama 148: Print("Answer is "); Println(Ans[0]);
1.2 takayama 149: return(Ans);
150: }
151:
152: def asirAnn0XYZ(a,f) {
153: local p,b,b0;
154: RingD("x,y,z,s"); /* Fix!! See the definition of myann() */
155: p = ToString(f);
156: b = a.rpc("myann0",[p]);
157: Print("Annhilating ideal of f^r is "); Println(b);
158: return(b);
159: }
160:
161: def DeRham2WithAsir(f) {
162: local s;
1.7 takayama 163:
164: sm1("0 set_timer "); sm1(" oxNoX ");
165: asssssir.OnTimer();
166:
1.2 takayama 167: s = ToString(f);
168: II = asirAnn0XYZ(asssssir,f);
169: Print("Step 1: Annhilating ideal (II)"); Println(II);
170: sm1(" II { [(x) (y) (Dx) (Dy) ] laplace0 } map /II set ");
171: Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]);
172: pp = Map(II,"Spoly");
173: Res = Sminimal(pp);
174: Res0 = Res[0];
175: Print("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
1.3 takayama 176: /* R = BfRoots1(Res0[0],"x,y"); */
177: R = asir_BfRoots2(Res0[0]);
1.2 takayama 178: Println("Step3: computing the cohomology of the truncated complex.");
179: Print("Roots and b-function are "); Println(R);
180: R0 = R[0];
181: Ans=Srestall(Res0, ["x", "y"], ["x", "y"],R0[Length(R0)-1] );
1.7 takayama 182:
183: Println("Timing data: sm1 "); sm1(" 1 set_timer ");
184: Print(" ox_asir [CPU,GC]: ");Println(asssssir.OffTimer());
185:
1.2 takayama 186: Print("Answer is ");Println(Ans[0]);
187: return(Ans);
188: }
189: def DeRham3WithAsir(f) {
190: local s;
1.7 takayama 191:
192: sm1("0 set_timer "); sm1(" oxNoX ");
193: asssssir.OnTimer();
194:
1.2 takayama 195: s = ToString(f);
196: II = asirAnn0XYZ(asssssir,f);
197: Print("Step 1: Annhilating ideal (II)"); Println(II);
198: sm1(" II { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /II set ");
199: Sweyl("x,y,z",[["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]]);
200: pp = Map(II,"Spoly");
201: Res = Sminimal(pp);
202: Res0 = Res[0];
203: Print("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
1.4 takayama 204: /* R = BfRoots1(Res0[0],"x,y,z"); */
1.3 takayama 205: R = asir_BfRoots3(Res0[0]);
1.2 takayama 206: Println("Step3: computing the cohomology of the truncated complex.");
207: Print("Roots and b-function are "); Println(R);
208: R0 = R[0];
209: Ans=Srestall(Res0, ["x", "y", "z"], ["x", "y", "z"],R0[Length(R0)-1] );
1.7 takayama 210:
211: Println("Timing data: sm1 "); sm1(" 1 set_timer ");
212: Print(" ox_asir [CPU,GC]: ");Println(asssssir.OffTimer());
213:
1.2 takayama 214: Print("Answer is ");Println(Ans[0]);
1.1 takayama 215: return(Ans);
216: }
1.7 takayama 217:
218: /* test data
219:
220: NoX=true;
221: nonquasi2(4,5);
222: nonquasi2(4,6);
223: nonquasi2(4,7);
224: nonquasi2(4,8);
225: nonquasi2(4,9);
226: nonquasi2(4,10);
227:
228: nonquasi2(5,6);
229: nonquasi2(6,7);
230: nonquasi2(7,8);
231: nonquasi2(8,9);
232: nonquasi2(9,10);
233: */
234:
235: P2 = [
236: "x^3-y^2",
237: "y^2-x^3-x-1",
238: "y^2-x^5-x-1",
239: "y^2-x^7-x-1",
240: "y^2-x^9-x-1",
241: "y^2-x^11-x-1"
242: ];
243:
244: P3 = [
245: "x^3-y^2*z^2",
246: "x^2*z+y^3+y^2*z+z^3",
247: "y*z^2+x^3+x^2*y^2+y^6",
248: "x*z^2+x^2*y+x*y^3+y^5"
249: ];
250:
251:
1.8 takayama 252: def diff_tmp(ff,xx) {
253: local g;
254: g = xx*ff;
255: return( Replace(g,[[xx,Poly("0")],[h,Poly("1")]]));
256: }
257:
258: def Localize3WithAsir(I,f) {
259: local s;
1.7 takayama 260:
1.8 takayama 261: sm1("0 set_timer "); sm1(" oxNoX ");
262: asssssir.OnTimer();
263:
264: RingD("x,y,z,vv");
265: /* BUG: use of RingD("x,y,z,v") causes an expected error.
266: [x2,x3,x4,x4] in mygeneric_bfct. (should be [x2,x3,x4,x5]).
267: */
268: f = ReParse(f);
269: I = ReParse(I);
270: /* Test data. */
271: /*
272: f = x^3-y^2*z^2;
273: I = [f^2*Dx-3*x^2, f^2*Dy-2*y*z^2, f^2*Dz-2*y^2*z];
274:
275: f = x^3-y^2;
276: I = [f^2*Dx-diff_tmp(f,Dx), f^2*Dy-diff_tmp(f,Dy), Dz];
277: */
278:
279: r1 = Dx-vv^2*diff_tmp(f,Dx)*Dvv;
280: r2 = Dy-vv^2*diff_tmp(f,Dy)*Dvv;
281: r3 = Dz-vv^2*diff_tmp(f,Dz)*Dvv;
282: II = ReParse(I);
283: sm1(" II { [[(Dx). r1] [(Dy). r2] [(Dz). r3]] replace } map dehomogenize /II set ");
284:
285: Print("Step 1: phi(J)"); Println(II);
286: II = Join(II,[vv*f-1]);
287: Print("Step 2: <phi(J),vf-1>"); Println(II);
288:
289: Println("Step3: computing the integral.");
290: sm1(" II { [(x) (y) (z) (vv) (Dx) (Dy) (Dz) (Dvv)] laplace0 } map /JJ set ");
291: Sweyl("x,y,z,vv",[["vv",-1,"Dvv",1]]);
292: pp = Map(JJ,"Spoly");
293: R = asir_BfRoots4(pp);
294: Print("Roots and b-function are "); Println(R);
295:
296: R0 = R[0];
297: k1 = R0[Length(R0)-1];
298: sm1(" [(parse) (intw.sm1) pushfile] extension /intw.verbose 1 def ");
299: sm1(" [II [(vv) (x) (y) (z)] [(vv) -1 (Dvv) 1] k1 (integer) dc] integral-k1 /Ans set ");
300:
301: Println("Timing data: sm1 "); sm1(" 1 set_timer ");
302: Print(" ox_asir [CPU,GC]: ");Println(asssssir.OffTimer());
303:
304: Print("Answer is ");Println(Ans);
305: return(Ans);
306: }
307:
308:
309: def Ltest2() {
310: RingD("x,y,z");
311: f = x^3-y^2;
312: I = [f^2*Dx-diff_tmp(f,Dx), f^2*Dy-diff_tmp(f,Dy), Dz];
313: return( Localize3WithAsir(I,f) );
314: }
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