=================================================================== RCS file: /home/cvs/OpenXM/src/k097/lib/minimal/minimal-test.k,v retrieving revision 1.9 retrieving revision 1.17 diff -u -p -r1.9 -r1.17 --- OpenXM/src/k097/lib/minimal/minimal-test.k 2000/08/01 03:42:35 1.9 +++ 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 1.8 2000/07/31 01:21:41 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 "); @@ -252,38 +252,215 @@ def test17() { sm1_pmat(c); Println(IsExact_h(c,"x,y,z")); } -def test17b() { - a=Sannfs3("x^3-y^2*z^2"); - b=a[0]; w = ["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]; - Sweyl("x,y,z",[w]); b = Reparse(b); + +def test_if_v_strict(resmat,w,v) { + local b,c,g; + Sweyl(v,[w]); b = Reparse(resmat); + Println("Degree shifts "); + Println(SgetShifts(b,w)); c=Sinit_w(b,w); Println("Resolution (b)----"); sm1_pmat(b); Println("Initial (c)----"); sm1_pmat(c); - Println(IsExact_h(c,"x,y,z")); + Println("Exactness of the resolution ---"); + Println(IsExact_h(b,v)); + Println("Exactness of the initial complex.---"); + Println(IsExact_h(c,v)); g = Sinvolutive(b[0],w); - Println("Involutive basis ---"); - sm1_pmat(g); + /* Println("Involutive basis ---"); + sm1_pmat(g); + Println(Sinvolutive(c[0],w)); + sm1(" /gb.verbose 1 def "); */ Println("Is same ideal?"); - Println(IsSameIdeal_h(g,c[0],"x,y")); + Println(IsSameIdeal_h(g,c[0],v)); +} +def test17b() { + a=Sannfs3("x^3-y^2*z^2"); + b=a[0]; w = ["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]; + test_if_v_strict(b,w,"x,y,z"); + return(a); } def test18() { a=Sannfs2("x^3-y^2"); b=a[0]; w = ["x",-1,"y",-1,"Dx",1,"Dy",1]; - Sweyl("x,y",[w]); b = Reparse(b); - c=Sinit_w(b,w); - Println("Resolution (b)----"); - sm1_pmat(b); - Println("Initial (c)----"); - sm1_pmat(c); - g = Sinvolutive(b[0],w); - Println("Involutive basis ---"); - sm1_pmat(g); - Println("Is same ideal?"); - Println(IsSameIdeal_h(g,c[0],"x,y")); - + test_if_v_strict(b,w,"x,y"); + return(a); } + +def test19() { + Println("test19 try to construct a minimal free resolution and check if it is v-strict."); + Println("of a GKZ system [[1,2,3]] by -1,1"); + ww2 = ["Dx1",1,"Dx2",1,"Dx3",1,"x1",-1,"x2",-1,"x3",-1]; + ans2 = GKZ([[1,2,3]],[0]); + Sweyl("x1,x2,x3",[ww2]); + ans2 = ReParse(ans2[0]); + a = Sminimal(ans2); + Println("Minimal Resolution is "); sm1_pmat(a[0]); + b = a[0]; + test_if_v_strict(b,ww2,"x1,x2,x3"); + return(a); +} + +/* Need more than 100M memory. 291, 845, 1266, 1116, 592 : Schreyer frame. + I've not yet tried to finish the computation. */ +def test20() { + w = ["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1,"x1",-1,"x2",-1,"x3",-1,"x4",-1]; + ans2 = GKZ([[1,1,1,1],[0,1,3,4]],[0,0]); + Sweyl("x1,x2,x3,x4",[w]); + ans2 = ReParse(ans2[0]); + a = Sminimal(ans2); + Println("Minimal Resolution is "); sm1_pmat(a[0]); + b = a[0]; + /* test_if_v_strict(b,w,"x1,x2,x3,x4"); */ + return(a); +} +def test20b() { + w = ["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1,"x1",-1,"x2",-1,"x3",-1,"x4",-1]; + ans2 = GKZ([[1,1,1,1],[0,1,3,4]],[1,2]); + Sweyl("x1,x2,x3,x4",[w]); + ans2 = ReParse(ans2[0]); + a = Sminimal(ans2); + Println("Minimal Resolution is "); sm1_pmat(a[0]); + b = a[0]; + /* test_if_v_strict(b,w,"x1,x2,x3,x4"); */ + return(a); +} + +def test21() { + a=Sannfs3("x^3-y^2*z^2+y^2+z^2"); + /* a=Sannfs3("x^3-y-z"); for debug */ + b=a[0]; w = ["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]; + test_if_v_strict(b,w,"x,y,z"); + Println("Degree shifts of Schreyer resolution ----"); + 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",-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); +} + +