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Diff for /OpenXM/src/k097/lib/restriction/demo.k between version 1.1 and 1.8

version 1.1, 2000/12/14 13:18:41 version 1.8, 2001/09/20 00:48:17
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Line 1 
 /* $OpenXM$  */  /* $OpenXM: OpenXM/src/k097/lib/restriction/demo.k,v 1.7 2001/01/26 12:24:57 takayama Exp $  */
   
 load["restriction.k"];;  load["restriction.k"];;
 load("../ox/ox.k");;  load("../ox/ox.k");;
Line 6  load("../ox/ox.k");;
Line 6  load("../ox/ox.k");;
 def demoSendAsirCommand(a) {  def demoSendAsirCommand(a) {
   a.executeString("load(\"bfct\");");    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 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)))); }; ");    a.executeString(" def mybfct(F) { return(rtostr(bfct(eval_str(F)))); }; ");
     a.executeString(" def mygeneric_bfct(F,VV,DD,WW) { print([F,VV,DD,WW]); return(generic_bfct(F,VV,DD,WW));}; ");
 }  }
   
 as = startAsir();  if (Boundp("NoX")) {
     as = Asir.generate(false);
   }else{
     as = Asir.generate();
   }
   
 asssssir = as;  asssssir = as;
 demoSendAsirCommand(as);  demoSendAsirCommand(as);
 RingD("x,y,z,s");  RingD("x,y,z,s");
Line 31  def asirAnnfsXYZ(a,f) {
Line 38  def asirAnnfsXYZ(a,f) {
   return(b);    return(b);
 }  }
   
   
   def asir_generic_bfct(a,ii,vv,dd,ww) {
      local ans;
      ans = a.rpc_str("mygeneric_bfct",[ii,vv,dd,ww]);
      return(ans);
   }
   /* a=startAsir();
      asir_generic_bfct(a,[Dx^2+Dy^2-1,Dx*Dy-4],[x,y],[Dx,Dy],[1,1]): */
   
   /* usage: misc/tmp/complex-ja.texi */
   def ChangeRing(f) {
     local r;
     r = GetRing(f);
     if (Tag(r) == 14) {
       SetRing(r);
       return(true);
     }else{
       return(false);
     }
   }
   
   def asir_BfRoots2(G) {
      local bb,ans,ss;
      sm1(" G flatten {dehomogenize} map /G set ");
      ChangeRing(G);
      ss = asir_generic_bfct(asssssir,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 ");
      ChangeRing(G);
      ss = asir_generic_bfct(asssssir,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 asir_BfRoots4(G) {
      local bb,ans,ss;
      sm1(" G flatten {dehomogenize} map /G set ");
      ChangeRing(G);
      ss = asir_generic_bfct(asssssir,G,[x,y,z,vv],[Dx,Dy,Dz,Dvv],[0,0,0,1]);
      bb = [ss];
      sm1(" bb 0 get findIntegralRoots { (universalNumber) dc } map /ans set ");
      return([ans, bb]);
   }
   
 def findMinSol(f) {  def findMinSol(f) {
   sm1(" f (string) dc findIntegralRoots 0 get (universalNumber) dc /FunctionValue set ");    sm1(" f (string) dc findIntegralRoots 0 get (universalNumber) dc /FunctionValue set ");
 }  }
Line 49  def asirAnnXYZ(a,f) {
Line 106  def asirAnnXYZ(a,f) {
   return(b);    return(b);
 }  }
   
   
 def nonquasi2(p,q) {  def nonquasi2(p,q) {
   local s,ans,f;    local s,ans,f;
   
     sm1("0 set_timer "); sm1(" oxNoX ");
     asssssir.OnTimer();
   
   f = x^p+y^q+x*y^(q-1);    f = x^p+y^q+x*y^(q-1);
   Print("f=");Println(f);    Print("f=");Println(f);
   s = ToString(f);    s = ToString(f);
Line 65  def nonquasi2(p,q) {
Line 127  def nonquasi2(p,q) {
   Res = Sminimal(pp);    Res = Sminimal(pp);
   Res0 = Res[0];    Res0 = Res[0];
   Println("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);    Println("Step2: (-1,1)-minimal resolution (Res0) "); sm1_pmat(Res0);
   R = BfRoots1(Res0[0],"x,y");  /*  R = BfRoots1(Res0[0],"x,y"); */
     R = asir_BfRoots2(Res0[0]);
   Println("Step3: computing the cohomology of the truncated complex.");    Println("Step3: computing the cohomology of the truncated complex.");
   Print("Roots and b-function are "); Println(R);    Print("Roots and b-function are "); Println(R);
   R0 = R[0];    R0 = R[0];
   Ans=Srestall(Res0, ["x", "y"],  ["x", "y"], R0[Length(R0)-1]);    Ans=Srestall(Res0, ["x", "y"],  ["x", "y"], R0[Length(R0)-1]);
   
     Println("Timing data: sm1 "); sm1(" 1 set_timer ");
     Print("     ox_asir [CPU,GC]:  ");Println(asssssir.OffTimer());
   
   Print("Answer is "); Println(Ans[0]);    Print("Answer is "); Println(Ans[0]);
   return(Ans);    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;
   
     sm1("0 set_timer "); sm1(" oxNoX ");
     asssssir.OnTimer();
   
     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] );
   
     Println("Timing data: sm1 "); sm1(" 1 set_timer ");
     Print("     ox_asir [CPU,GC]:  ");Println(asssssir.OffTimer());
   
     Print("Answer is ");Println(Ans[0]);
     return(Ans);
   }
   def DeRham3WithAsir(f) {
     local s;
   
     sm1("0 set_timer "); sm1(" oxNoX ");
     asssssir.OnTimer();
   
     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] );
   
     Println("Timing data: sm1 "); sm1(" 1 set_timer ");
     Print("     ox_asir [CPU,GC]:  ");Println(asssssir.OffTimer());
   
     Print("Answer is ");Println(Ans[0]);
     return(Ans);
   }
   
   /*  test data
   
      NoX=true;
      nonquasi2(4,5);
      nonquasi2(4,6);
      nonquasi2(4,7);
      nonquasi2(4,8);
      nonquasi2(4,9);
      nonquasi2(4,10);
   
      nonquasi2(5,6);
      nonquasi2(6,7);
      nonquasi2(7,8);
      nonquasi2(8,9);
      nonquasi2(9,10);
   */
   
      P2 = [
        "x^3-y^2",
        "y^2-x^3-x-1",
        "y^2-x^5-x-1",
        "y^2-x^7-x-1",
        "y^2-x^9-x-1",
        "y^2-x^11-x-1"
      ];
   
      P3 = [
        "x^3-y^2*z^2",
        "x^2*z+y^3+y^2*z+z^3",
        "y*z^2+x^3+x^2*y^2+y^6",
        "x*z^2+x^2*y+x*y^3+y^5"
      ];
   
   
   def diff_tmp(ff,xx) {
     local g;
     g = xx*ff;
     return( Replace(g,[[xx,Poly("0")],[h,Poly("1")]]));
   }
   
   def Localize3WithAsir(I,f) {
     local s;
   
     sm1("0 set_timer "); sm1(" oxNoX ");
     asssssir.OnTimer();
   
     RingD("x,y,z,vv");
     /* BUG: use of RingD("x,y,z,v") causes an expected error.
       [x2,x3,x4,x4] in mygeneric_bfct.  (should be [x2,x3,x4,x5]).
     */
     f = ReParse(f);
     I = ReParse(I);
     /* Test data. */
     /*
     f = x^3-y^2*z^2;
     I = [f^2*Dx-3*x^2, f^2*Dy-2*y*z^2, f^2*Dz-2*y^2*z];
   
     f = x^3-y^2;
     I = [f^2*Dx-diff_tmp(f,Dx), f^2*Dy-diff_tmp(f,Dy), Dz];
     */
   
     r1 = Dx-vv^2*diff_tmp(f,Dx)*Dvv;
     r2 = Dy-vv^2*diff_tmp(f,Dy)*Dvv;
     r3 = Dz-vv^2*diff_tmp(f,Dz)*Dvv;
     II = ReParse(I);
     sm1(" II { [[(Dx). r1] [(Dy). r2] [(Dz). r3]] replace } map dehomogenize /II set ");
   
     Print("Step 1: phi(J)"); Println(II);
     II = Join(II,[vv*f-1]);
     Print("Step 2: <phi(J),vf-1>"); Println(II);
   
     Println("Step3: computing the integral.");
     sm1(" II  { [(x) (y) (z) (vv) (Dx) (Dy) (Dz) (Dvv)] laplace0 } map /JJ set ");
     Sweyl("x,y,z,vv",[["vv",-1,"Dvv",1]]);
     pp = Map(JJ,"Spoly");
     R = asir_BfRoots4(pp);
     Print("Roots and b-function are "); Println(R);
   
     R0 = R[0];
     k1 = R0[Length(R0)-1];
     sm1(" [(parse) (intw.sm1) pushfile] extension /intw.verbose 1 def ");
     sm1(" [II [(vv) (x) (y) (z)] [(vv) -1 (Dvv) 1] k1 (integer) dc] integral-k1 /Ans set ");
   
     Println("Timing data: sm1 "); sm1(" 1 set_timer ");
     Print("     ox_asir [CPU,GC]:  ");Println(asssssir.OffTimer());
   
     Print("Answer is ");Println(Ans);
     return(Ans);
   }
   
   
   def Ltest2() {
     RingD("x,y,z");
     f = x^3-y^2;
     I = [f^2*Dx-diff_tmp(f,Dx), f^2*Dy-diff_tmp(f,Dy), Dz];
     return( Localize3WithAsir(I,f) );
 }  }
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