=================================================================== RCS file: /home/cvs/OpenXM/src/k097/lib/minimal/minimal-test.k,v retrieving revision 1.13 retrieving revision 1.17 diff -u -p -r1.13 -r1.17 --- OpenXM/src/k097/lib/minimal/minimal-test.k 2000/08/02 03:23:36 1.13 +++ OpenXM/src/k097/lib/minimal/minimal-test.k 2000/08/10 02:59:08 1.17 @@ -1,4 +1,4 @@ -/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.12 2000/08/01 08:51:02 takayama Exp $ */ +/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.16 2000/08/09 03:45:27 takayama Exp $ */ load["minimal.k"]; def sm1_resol1(p) { sm1(" p resol1 /FunctionValue set "); @@ -337,11 +337,130 @@ def test21() { Println(SgetShifts(Reparse(a[4,0]),w)); return(a); } +def test21b() { + local i,j,n,sss, maxR, ttt,ans,p; + Println("The dimensions of linear spaces -----"); + /* sss is the SgetShifts of the Schreyer resol. */ + sss= + [[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] , + [ -1, -1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3 ] , + [ 0, 1, -1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 3, 2, 2, 1, 4, 3, 3, 2, 0, 2, 1, 3, 2, 2, 1, 2, 2, 2, 2, 2, 1, 0, 1, 2, 2, 2, 2, 3, 2, 2, 3, 1, 3, 3, 3, 3, 4 ] , + [ 1, 0, 2, 3, 2, 3, 1, 1, 1, 2, 1, 2, 2, 2, 0, 3, 1, 3, 2, 3, 4 ] , + [ 1, 1 ] ] ; + maxR = 2; /* Maximal root of the b-function. */ + n = Length(sss); + for (i=0; i<n; i++) { + ttt = sss[i]; + ans = 0; + for (j=0; j<Length(ttt); j++) { + p = ttt[j] + maxR + 3; /* degree */ + if (p >= 0) { + ans = ans + CancelNumber(p*(p-1)*(p-2)/(3*2*1)); + /* Add the number of monomials */ + } + } + Print(ans); Print(", "); + } + Println(" "); +} def test22() { a=Sannfs3("x^3+y^3+z^3"); - b=a[0]; w = ["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]; + b=a[0]; w = ["x",-1,"y",-2,"z",-3,"Dx",1,"Dy",2,"Dz",3]; test_if_v_strict(b,w,"x,y,z"); return(a); } + +def FillFromLeft(mat,p,z) { + local m,n,i,j,aa; + m = Length(mat); n = Length(mat[0]); + aa = NewMatrix(m,n+p); + for (i=0; i<m; i++) { + for (j=0; j<p; j++) { + aa[i,j] = z; /* zero */ + } + for (j=0; j<n; j++) { + aa[i,j+p] = mat[i,j]; + } + } + return(aa); +} + +def FillFromRight(mat,p,z) { + local m,n,i,j,aa; + m = Length(mat); n = Length(mat[0]); + aa = NewMatrix(m,n+p); + for (i=0; i<m; i++) { + for (j=n; j<n+p; j++) { + aa[i,j] = z; /* zero */ + } + for (j=0; j<n; j++) { + aa[i,j] = mat[i,j]; + } + } + return(aa); +} + +def test23() { + w = ["Dx1",1,"Dx2",1,"Dx3",1,"x1",-1,"x2",-1,"x3",-1]; + Sweyl("x1,x2,x3",[w]); + d2 = [[Dx1^2-Dx2*h] , [-Dx1*Dx2+Dx3*h] , [Dx2^2-Dx1*Dx3] ]; + d1 = [[-Dx2, -Dx1, -h],[Dx3,Dx2,Dx1]]; + LL = x1*Dx1 + 2*x2*Dx2+3*x3*Dx3; + /* It is exact for LL = Dx1 + 2*Dx2+3*Dx3; */ + u1 = [[LL+4*h^2,Poly("0")],[Poly("0"),LL+5*h^2]]; + u2 = [[LL+2*h^2,Poly("0"),Poly("0")], + [Poly("0"),LL+3*h^2,Poly("0")], + [Poly("0"),Poly("0"),LL+4*h^2]]; + u3 = [[LL]]; + Println("Checking if it is a double complex. "); + Println("u^2 d^2 - d^2 u^3"); + sm1_pmat(u2*d2 - d2*u3); + Println("u^1 d^1 - d^1 u^2"); + sm1_pmat(u1*d1 - d1*u2); + aa = [ + Join(u3,d2), + Join(FillFromLeft(u2,1,Poly("0"))-FillFromRight(d2,3,Poly("0")), + FillFromLeft(d1,1,Poly("0"))), + FillFromLeft(u1,3,Poly("0"))-FillFromRight(d1,2,Poly("0")) + ]; + Println([ aa[1]*aa[0], aa[2]*aa[1] ]); + r= IsExact_h(aa,[x1,x2,x3]); + Println(r); + /* sm1_pmat(aa); */ + return(aa); +} + + +def test24() { + local Res, Eqs, ww,a; + ww = ["x",-1,"y",-1,"Dx",1,"Dy",1]; + Println("Example of V-minimal <> minimal "); + Sweyl("x,y", [ww]); + Eqs = [Dx-(x*Dx+y*Dy), + Dy-(x*Dx+y*Dy)]; + sm1(" Eqs dehomogenize /Eqs set"); + Res = Sminimal(Eqs); + Sweyl("x,y", [ww]); + a = Reparse(Res[0]); + sm1_pmat(a); + Println("Initial of the complex is "); + sm1_pmat( Sinit_w(a,ww) ); + return(Res); +} + +def test24b() { + local Res, Eqs, ww ; + ww = ["x",-1,"y",-1,"Dx",1,"Dy",1]; + Println("Construction of minimal "); + Sweyl("x,y", [ww]); + Eqs = [Dx-(x*Dx+y*Dy), + Dy-(x*Dx+y*Dy)]; + sm1(" Eqs dehomogenize /Eqs set"); + Res = Sminimal(Eqs,["Sordinary"]); + sm1_pmat(Res[0]); + return(Res); +} + +