File: [local] / OpenXM / src / k097 / lib / restriction / demo.k (download)
Revision 1.3, Wed Dec 27 08:09:27 2000 UTC (23 years, 8 months ago) by takayama
Branch: MAIN
Changes since 1.2: +47 -4
lines
DeRham2WithAsir, DeRham3WithAsir, nonquasi2 call generic_bfct() of asir
to compute b-function for restriction. It is much faster than calling bfm.
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/* $OpenXM: OpenXM/src/k097/lib/restriction/demo.k,v 1.3 2000/12/27 08:09:27 takayama Exp $ */
load["restriction.k"];;
load("../ox/ox.k");;
def demoSendAsirCommand(a) {
a.executeString("load(\"bfct\");");
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])); }; ");
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])); }; ");
a.executeString(" def mybfct(F) { return(rtostr(bfct(eval_str(F)))); }; ");
}
as = startAsir();
asssssir = as;
demoSendAsirCommand(as);
RingD("x,y,z,s");
def asirBfunction(a,f) {
local p,b;
p = ToString(f);
Println(p);
b = a.rpc("mybfct",[p]);
sm1(" b . /b set ");
return(b);
}
def asirAnnfsXYZ(a,f) {
local p,b;
RingD("x,y,z,s"); /* Fix!! See the definition of myann() */
p = ToString(f);
b = a.rpc("myann",[p]);
return(b);
}
def asir_rpc_old(argv_rpc_asir) {
sm1(" oxasir.ccc [ ] eq {
(Starting ox_asir server.) message
ox_asirConnectMethod
} { } ifelse ");
sm1(" oxasir.ccc argv_rpc_asir asir /FunctionValue set ");
}
def asir_define_own_functions() {
asir_rpc_old(["igcd",2,3]);
sm1(" oxasir.ccc (def mygeneric_bfct(Id,V,DV,W) {
return( rtostr(generic_bfct(Id,V,DV,W)));
}) oxsubmit ");
}
def asir_generic_bfct(ii,vv,dd,ww) {
local ans;
ans = asir_rpc_old(["mygeneric_bfct",ii,vv,dd,ww]);
return(ans);
}
/* asir_generic_bfct([Dx^2+Dy^2-1,Dx*Dy-4],[x,y],[Dx,Dy],[1,1]): */
def asir_BfRoots2(G) {
local bb,ans,ss;
sm1(" G flatten {dehomogenize} map /G set ");
asir_define_own_functions();
ss = asir_generic_bfct(G,[x,y],[Dx,Dy],[1,1]);
bb = [ss];
sm1(" bb 0 get findIntegralRoots { (universalNumber) dc } map /ans set ");
return([ans, bb]);
}
def asir_BfRoots3(G) {
local bb,ans,ss;
sm1(" G flatten {dehomogenize} map /G set ");
asir_define_own_functions();
ss = asir_generic_bfct(G,[x,y,z],[Dx,Dy,Dz],[1,1,1]);
bb = [ss];
sm1(" bb 0 get findIntegralRoots { (universalNumber) dc } map /ans set ");
return([ans, bb]);
}
def findMinSol(f) {
sm1(" f (string) dc findIntegralRoots 0 get (universalNumber) dc /FunctionValue set ");
}
def asirAnnXYZ(a,f) {
local p,b,b0,k1;
RingD("x,y,z,s"); /* Fix!! See the definition of myann() */
p = ToString(f);
b = a.rpc("myann",[p]);
Print("Annhilating ideal with s is "); Println(b);
b0 = asirBfunction(a,f);
Print("bfunction is "); Println(b0);
k1 = findMinSol(b0);
Print("Minimal integral root is "); Println(k1);
sm1(" b { [[(s). k1 (string) dc .]] replace } map /b set ");
return(b);
}
def nonquasi2(p,q) {
local s,ans,f;
f = x^p+y^q+x*y^(q-1);
Print("f=");Println(f);
s = ToString(f);
sm1(" Onverbose ");
ans = asirAnnfsXYZ(asssssir,f);
sm1(" ans 0 get (ring) dc ring_def ");
sm1("[ ans { [[(s). (-1).]] replace } map ] /II set ");
Println("Step 1: Annhilating ideal (II)"); Println(II);
sm1(" II 0 get { [(x) (y) (Dx) (Dy) ] laplace0 } map /II set ");
Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]);
pp = Map(II,"Spoly");
Res = Sminimal(pp);
Res0 = Res[0];
Println("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
/* R = BfRoots1(Res0[0],"x,y"); */
R = asir_BfRoots2(Res0[0]);
Println("Step3: computing the cohomology of the truncated complex.");
Print("Roots and b-function are "); Println(R);
R0 = R[0];
Ans=Srestall(Res0, ["x", "y"], ["x", "y"], R0[Length(R0)-1]);
Print("Answer is "); Println(Ans[0]);
return(Ans);
}
def asirAnn0XYZ(a,f) {
local p,b,b0;
RingD("x,y,z,s"); /* Fix!! See the definition of myann() */
p = ToString(f);
b = a.rpc("myann0",[p]);
Print("Annhilating ideal of f^r is "); Println(b);
return(b);
}
def DeRham2WithAsir(f) {
local s;
s = ToString(f);
II = asirAnn0XYZ(asssssir,f);
Print("Step 1: Annhilating ideal (II)"); Println(II);
sm1(" II { [(x) (y) (Dx) (Dy) ] laplace0 } map /II set ");
Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]);
pp = Map(II,"Spoly");
Res = Sminimal(pp);
Res0 = Res[0];
Print("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
/* R = BfRoots1(Res0[0],"x,y"); */
R = asir_BfRoots2(Res0[0]);
Println("Step3: computing the cohomology of the truncated complex.");
Print("Roots and b-function are "); Println(R);
R0 = R[0];
Ans=Srestall(Res0, ["x", "y"], ["x", "y"],R0[Length(R0)-1] );
Print("Answer is ");Println(Ans[0]);
return(Ans);
}
def DeRham3WithAsir(f) {
local s;
s = ToString(f);
II = asirAnn0XYZ(asssssir,f);
Print("Step 1: Annhilating ideal (II)"); Println(II);
sm1(" II { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /II set ");
Sweyl("x,y,z",[["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]]);
pp = Map(II,"Spoly");
Res = Sminimal(pp);
Res0 = Res[0];
Print("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
/* R = BfRoots1(Res0[0],"x,y,z"); */
R = asir_BfRoots3(Res0[0]);
Println("Step3: computing the cohomology of the truncated complex.");
Print("Roots and b-function are "); Println(R);
R0 = R[0];
Ans=Srestall(Res0, ["x", "y", "z"], ["x", "y", "z"],R0[Length(R0)-1] );
Print("Answer is ");Println(Ans[0]);
return(Ans);
}