Annotation of OpenXM/src/k097/lib/restriction/restriction.k, Revision 1.3
1.3 ! takayama 1: /* $OpenXM: OpenXM/src/k097/lib/restriction/restriction.k,v 1.2 2013/01/24 00:27:54 takayama Exp $ */
1.1 takayama 2: load["lib/minimal/minimal-test.k"];;
3: Load_sm1(["Srestall_s.sm1","lib/restriction/Srestall_s.sm1"],"Srestall_s.sm1.loaded");
4:
5: def Srestall(gg,ttxx,tt,k1) {
6: local cohom, gg, ttxx, tt, k1, cohom0, cohomd,ans;
7: sm1("gg dehomogenize /gg set");
8: gg = ToString_array(gg);
9: sm1(" [(x) ring_of_differential_operators [[(x) 1]] weight_vector 0] define_ring ]");
10: sm1("[(Homogenize_vec) 1] system_variable");
11: Println([Tag(gg),Tag(ttxx),Tag(tt)]);
12: sm1("gg ttxx tt k1 (integer) dc Srestall1 /cohom0 set");
13: sm1(" cohom0 {deRham.simp} map /cohomd set ");
14: ans = [cohomd,cohom0];
15: return(ans);
16: }
17: HelpAdd(["Srestall",
18: [ "Srestall(gg,v,rv,k1) evaluates the dimensions of all restictions of",
19: "gg along the list of variables rv. Here, v is a list of variables and",
20: " k1 is the maximal integral root of the b-function of gg.",
21: "Srestall uses the function Sminimal to get a (-w,w)-minimal free resolution.",
22: "cf. Bfroots1(ii,vv)"
23: ]]);
24:
25: def DeRham2(f) {
26: local s;
27: s = ToString(f);
28: II = Sannfs(f,"x,y");
29: Println("Step 1: Annhilating ideal (II)"); Println(II);
30: sm1(" II 0 get { [(x) (y) (Dx) (Dy) ] laplace0 } map /II set ");
31: Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]);
32: pp = Map(II,"Spoly");
33: Res = Sminimal(pp);
34: Res0 = Res[0];
35: Println("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
36: R = BfRoots1(Res0[0],"x,y");
37: Println("Step3: computing the cohomology of the truncated complex.");
38: Print("Roots and b-function are "); Println(R);
39: R0 = R[0];
40: Ans=Srestall(Res0, ["x", "y"], ["x", "y"],R0[Length(R0)-1]);
41: Print("Answer is "); Println(Ans[0]);
42: return(Ans);
43: }
44:
45: def DeRham3(f) {
46: local s;
47: s = ToString(f);
48: II = Sannfs(f,"x,y,z");
49: Print("Step 1: Annhilating ideal (II)"); Println(II);
50: sm1(" II 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /II set ");
51: Sweyl("x,y,z",[["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]]);
52: pp = Map(II,"Spoly");
53: Res = Sminimal(pp);
54: Res0 = Res[0];
55: Print("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
56: R = BfRoots1(Res0[0],"x,y,z");
57: Println("Step3: computing the cohomology of the truncated complex.");
58: Print("Roots and b-function are "); Println(R);
59: R0 = R[0];
60: Ans=Srestall(Res0, ["x", "y", "z"], ["x", "y", "z"],R0[Length(R0)-1] );
61: Print("Answer is ");Println(Ans[0]);
62: return(Ans);
63: }
64:
65: def DeRham1(f) {
66: local s;
67: s = ToString(f);
68: II = Sannfs(f,"x");
69: Println("Step 1: Annhilating ideal (II)"); Println(II);
70: sm1(" II 0 get { [(x) (Dx) ] laplace0 } map /II set ");
71: Sweyl("x",[["x",-1,"Dx",1]]);
72: pp = Map(II,"Spoly");
73: Res = Sminimal(pp);
74: Res0 = Res[0];
75: Println("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
76: R = BfRoots1(Res0[0],"x");
77: Println("Step3: computing the cohomology of the truncated complex.");
78: Print("Roots and b-function are "); Println(R);
79: R0 = R[0];
80: Ans=Srestall(Res0, ["x"], ["x"],R0[Length(R0)-1]);
81: Print("Answer is "); Println(Ans[0]);
82: return(Ans);
83: }
84:
85: /* Demo for non-quasi */
86: def nonquasi(p,q) {
87: local s,ans,f;
88: f = x^p+y^q+x*y^(q-1);
89: Print("f=");Println(f);
90: s = ToString(f);
91: sm1(" Onverbose ");
92: sm1(" s [(s) (x) (y)] genericAnn /ans set ");
93: sm1(" ans 0 get (ring) dc ring_def ");
94: sm1("[ ans { [[(s). (-1).]] replace } map ] /II set ");
95: Println("Step 1: Annhilating ideal (II)"); Println(II);
96: sm1(" II 0 get { [(x) (y) (Dx) (Dy) ] laplace0 } map /II set ");
97: Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]);
98: pp = Map(II,"Spoly");
99: Res = Sminimal(pp);
100: Res0 = Res[0];
101: Println("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
102: R = BfRoots1(Res0[0],"x,y");
103: Println("Step3: computing the cohomology of the truncated complex.");
104: Print("Roots and b-function are "); Println(R);
105: R0 = R[0];
106: Ans=Srestall(Res0, ["x", "y"], ["x", "y"], R0[Length(R0)-1]);
107: Print("Answer is "); Println(Ans[0]);
108: return(Ans);
109: }
110:
1.3 ! takayama 111: /* should be moved to slib.k */
! 112: def UseSmallD() {
! 113: sm1("[(Strict)] system_variable /aaa.strict set ");
! 114: sm1("[(Strict) 0] system_variable ");
! 115: /* kan96xx/Doc/callsm1.sm1 */
! 116: sm1("/@@@.Dsymbol (d) def /aaaDsymbol (d) def ");
! 117: sm1("/@@@.Esymbol (ee0) def ");
! 118: sm1("/@@@.Hsymbol (hh) def ");
! 119: sm1("[(Strict) aaa.strict] system_variable ");
! 120: }
! 121: HelpAdd(["UseSmallD",
! 122: [ "UseSmallD() changes the Dsymbol to d and E,H symbols to ee0,hh",
! 123: "@@@.Dsymbol can be refered by aaaDsymbol."
! 124: ]]);
! 125:
1.2 takayama 126: def t_addD(v) {
1.3 ! takayama 127: sm1(" /aaaDsymbol @@@.Dsymbol def ");
! 128: return(AddString([aaaDsymbol,ToString(v)])); /* add x->Dx */
1.2 takayama 129: }
130: def Sintegration(gg,v,intv) {
131: local i,vstr,n,dv,wv,vall;
132: II=Map(gg,"ToString");
133: v = Map(v,"ToString");
134: intv = Map(intv,"ToString");
135: vstr=" "; n=Length(v);
136: for (i=0; i<n-1; i++) {
137: vstr=AddString([vstr,v[i],","]);
138: }
139: vstr=AddString([vstr,v[n-1]]);
140: dv=Map(v,"t_addD");
141: wv=[ ];
142: for (i=0; i<n; i++) { wv = Join(wv,[v[i],-1]); }
143: for (i=0; i<n; i++) { wv = Join(wv,[dv[i],1]); }
144: /* Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]); */
145: Sweyl(vstr,[wv]);
146: II=Map(II,"Poly");
147: /* sm1(" II 0 get { [(x) (y) (Dx) (Dy) ] laplace0 } map /II set "); */
148: vall = Join(v,dv);
149: sm1(" II { vall laplace0 } map /II set ");
150: pp = Map(II,"Spoly");
151: Println("Step1: Laplace transform "); Println(pp);
152: Res = Sminimal(pp);
153: Res0 = Res[0];
154: Println("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
155: /* R = BfRoots1(Res0[0],"x,y"); */
156: R = BfRoots1(Res0[0],vstr);
157: Println("Step3: computing the cohomology of the truncated complex.");
158: Print("Roots and b-function are "); Println(R);
159: R0 = R[0];
160: /* Ans=Srestall(Res0, ["x", "y"], ["x", "y"],R0[Length(R0)-1]); */
161: Ans=Srestall(Res0, v, intv,R0[Length(R0)-1]);
162: Print("Answer is "); Println(Ans[0]);
163: return(Ans);
164: }
165: HelpAdd(["Sintegration",
166: [ "Sintegration(gg,v,intv) evaluates the dimensions of all integrations of",
167: "gg along the list of variables intv. Here, v is a list of variables.",
168: "Interation variables intv must be in the first part of v.",
169: "Sintegration uses the function Srestall.",
170: "Example: RingD(\"x,t\"); Sintegration([Dt-(3*t^2-x),Dx+t],[t,x],[t]):"
171: ]]);
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