=================================================================== RCS file: /home/cvs/OpenXM/src/k097/lib/minimal/minimal-test.k,v retrieving revision 1.2 retrieving revision 1.9 diff -u -p -r1.2 -r1.9 --- OpenXM/src/k097/lib/minimal/minimal-test.k 2000/06/08 08:37:53 1.2 +++ OpenXM/src/k097/lib/minimal/minimal-test.k 2000/08/01 03:42:35 1.9 @@ -1,86 +1,9 @@ -/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.1 2000/05/24 15:31:28 takayama Exp $ */ +/* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.8 2000/07/31 01:21:41 takayama Exp $ */ load["minimal.k"]; -def test5() { - local a,b,c,cc,v; - a = Sannfs3_laScala2("x^3-y^2*z^2"); - b = a[0]; - v = [x,y,z]; - c = Skernel(b[0],v); - c = c[0]; - sm1_pmat([c,b[1],v]); - Println("-----------------------------------"); - cc = sm1_res_div(c,b[1],v); - sm1_pmat(sm1_gb(cc,v)); - c = Skernel(b[1],v); - c = c[0]; - cc = sm1_res_div(c,b[2],v); - sm1_pmat(sm1_gb(cc,v)); - return(a); -} -def test6() { - local a,b,c,cc,v; - a = Sannfs3("x^3-y^2*z^2"); - b = a[0]; - v = [x,y,z]; - c = Skernel(b[0],v); - c = c[0]; - sm1_pmat([c,b[1],v]); - Println("-------ker = im for minimal ?---------------------"); - cc = sm1_res_div(c,b[1],v); - sm1_pmat(sm1_gb(cc,v)); - c = Skernel(b[1],v); - c = c[0]; - cc = sm1_res_div(c,b[2],v); - sm1_pmat(sm1_gb(cc,v)); - Println("------ ker=im for Schreyer ?------------------"); - b = a[3]; - c = Skernel(b[0],v); - c = c[0]; - sm1_pmat([c,b[1],v]); - cc = sm1_res_div(c,b[1],v); - sm1_pmat(sm1_gb(cc,v)); - c = Skernel(b[1],v); - c = c[0]; - cc = sm1_res_div(c,b[2],v); - sm1_pmat(sm1_gb(cc,v)); - return(a); -} - -/* May 23, Tue */ -def test7() { - local a,b,c,cc,v; - a = Sannfs3_laScala2("x^3-y^2*z^2"); - b = a[0]; - v = [x,y,z]; - c = Skernel(b[0],v); - c = c[0]; - sm1_pmat([c,b[1],v]); - Println("-------ker = im for minimal ?---------------------"); - cc = sm1_res_div(c,b[1],v); - sm1_pmat(sm1_gb(cc,v)); - c = Skernel(b[1],v); - c = c[0]; - cc = sm1_res_div(c,b[2],v); - sm1_pmat(sm1_gb(cc,v)); - Println("------ ker=im for Schreyer ?------------------"); - b = a[3]; - c = Skernel(b[0],v); - c = c[0]; - sm1_pmat([c,b[1],v]); - cc = sm1_res_div(c,b[1],v); - sm1_pmat(sm1_gb(cc,v)); - c = Skernel(b[1],v); - c = c[0]; - cc = sm1_res_div(c,b[2],v); - sm1_pmat(sm1_gb(cc,v)); - return(a); -} - def sm1_resol1(p) { sm1(" p resol1 /FunctionValue set "); } - def test8() { local p,pp,ans,b,c,cc,ww,ww2; f = "x^3-y^2*z^2"; @@ -118,87 +41,249 @@ def test8() { SisComplex(a): */ -def test8a() { - local p,pp,ans,b,c,cc,ww, ans_all; - f = "x^3-y^2*z^2"; - p = Sannfs(f,"x,y,z"); - sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set "); - ww = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]]; - /* Removed "x",1, ... ===> It causes an error. I do not know the reason.*/ - Sweyl("x,y,z",ww); - pp = Map(p,"Spoly"); - /* return(pp); */ - /* pp = - [y*Dy-z*Dz , -2*x*Dx-3*y*Dy+1 , 2*x*Dy*Dz^2-3*y*Dx^2 , - 2*x*Dy^2*Dz-3*z*Dx^2 , 2*x*z*Dz^3-3*y^2*Dx^2+4*x*Dz^2 ] - */ - ans_all = Sschreyer(pp); - ans = ans_all[0]; - /* ans = sm1_resol1([pp,"x,y,z",ww]); */ - /* Schreyer is in ans. */ - +def test11() { + local a; + a = test_ann3("x^3-y^2*z^2"); + return(a); +} +/* f should be a string. */ +/* a=test_ann3("x^3+y^3+z^3"); +It returns the following resolution in 1.5 hours. June 14, 2000. + [ + [ + [ x*Dx+y*Dy+z*Dz-3*h^2 ] + [ -z*Dy^2+y*Dz^2 ] + [ -z*Dx^2+x*Dz^2 ] + [ -y*Dx^2+x*Dy^2 ] + ] + [ + [ 0 , -x , y , -z ] + [ z*Dx^2-x*Dz^2 , x*Dy , x*Dx+z*Dz-3*h^2 , z*Dy ] + [ y*Dx^2-x*Dy^2 , -x*Dz , y*Dz , x*Dx+y*Dy-3*h^2 ] + [ 0 , Dx^2 , -Dy^2 , Dz^2 ] + [ z*Dy^2-y*Dz^2 , x*Dx+y*Dy+z*Dz-2*h^2 , 0 , 0 ] + ] + [ + [ -x*Dx+3*h^2 , y , -z , 0 , -x ] + [ Dy^3+Dz^3 , Dy^2 , -Dz^2 , x*Dx+y*Dy+z*Dz , -Dx^2 ] + ] + ] +*/ +def test_ann3(f) { + local a,v,ww2,ans2; + a = Sannfs3(f); + ans2 = a[0]; v = [x,y,z]; - b = ans; - Println("------ ker=im for Schreyer ?------------------"); - c = Skernel(b[0],v); - c = c[0]; - sm1_pmat([c,b[1],v]); - cc = sm1_res_div(c,b[1],v); - sm1_pmat(sm1_gb(cc,v)); - c = Skernel(b[1],v); - c = c[0]; - cc = sm1_res_div(c,b[2],v); - sm1_pmat(sm1_gb(cc,v)); - return(ans); + ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]]; + Sweyl("x,y,z",ww2); + ans2 = ReParse(ans2); + r= IsExact_h(ans2,[x,y,z]); + Println(r); + return([r,ans2,a]); } +def test11a() { + local a,v,ww2,ans2; +/* constructed by test11. + ans2 = + [[[y*Dy-z*Dz] , [-2*x*Dx-3*z*Dz+h^2] , [2*x*Dy*Dz^2-3*y*Dx^2*h] , [2*x*Dy^2*Dz-3*z*Dx^2*h]] , + [[3*Dx^2*h , 0 , Dy , -Dz] , + [6*x*Dy*Dz^2-9*y*Dx^2*h , -2*x*Dy*Dz^2+3*y*Dx^2*h , -2*x*Dx-3*y*Dy , 0] , + [0 , 2*x*Dy^2*Dz-3*z*Dx^2*h , 0 , 2*x*Dx+3*z*Dz] , + [2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0] , + [0 , 0 , 0 , 0] , + [2*x*Dy*Dz , 0 , z , -y] , + [0 , 0 , 0 , 0] , + [0 , 0 , 0 , 0] , + [0 , 0 , 0 , 0]] , + [[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] , + [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] , + [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] , + [-2*x*Dx-3*y*Dy-3*z*Dz-6*h^2 , -Dy , -Dz , 3*Dx^2*h , 3*Dy^2 , 3*Dy*Dz , -2*x*Dy , 2*x*Dz , 0] , + [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] , + [3*y*z , z , y , -2*x*Dy*Dz , -3*z*Dy , 2*x*Dx , 2*x*z , -2*x*y , 0] , + [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] , + [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] , + [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0]] , + [[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] , + [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] , + [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0]]] +*/ + ans2 = + [[[y*Dy-z*Dz] , [-2*x*Dx-3*z*Dz+h^2] , [2*x*Dy*Dz^2-3*y*Dx^2*h] , [2*x*Dy^2*Dz-3*z*Dx^2*h]] , + [[3*Dx^2*h , 0 , Dy , -Dz] , + [6*x*Dy*Dz^2-9*y*Dx^2*h , -2*x*Dy*Dz^2+3*y*Dx^2*h , -2*x*Dx-3*y*Dy , 0] , + [0 , 2*x*Dy^2*Dz-3*z*Dx^2*h , 0 , 2*x*Dx+3*z*Dz] , + [2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0] , + [2*x*Dy*Dz , 0 , z , -y]], + [[-2*x*Dx-3*y*Dy-3*z*Dz-6*h^2 , -Dy , -Dz , 3*Dx^2*h , 3*Dy*Dz ] , + [3*y*z , z , y , -2*x*Dy*Dz , 2*x*Dx]]]; -/* Comparing two constructions */ -def test9() { - local p,pp,ans,b,c,cc,ww,ww2,ans_all,ans2; - f = "x^3-y^2*z^2"; - p = Sannfs(f,"x,y,z"); + sm1_pmat( ans2[1]*ans2[0] ); + sm1_pmat( ans2[2]*ans2[1] ); ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]]; - sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set "); Sweyl("x,y,z",ww2); - pp = Map(p,"Spoly"); - ans = sm1_resol1([pp,"x,y,z",ww2]); + ans2 = ReParse(ans2); + r= IsExact_h(ans2,[x,y,z]); + Println(r); + return([r,ans2]); +} - f = "x^3-y^2*z^2"; - p = Sannfs(f,"x,y,z"); - sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set "); - ww = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]]; - Sweyl("x,y,z",ww); - pp = Map(p,"Spoly"); - ans_all = Sschreyer(pp); - ans2 = ans_all[0]; +def test12() { + local a,v,ww2,ans2; + a = Sannfs3("x^3-y^2*z^2"); + ans2 = a[0]; + v = [x,y,z]; + ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]]; + Sweyl("x,y,z",ww2); + ans2 = ReParse(ans2); /* DO NOT FORGET! */ + r= IsExact_h(ans2,[x,y,z]); + Println(r); + return([r,ans2]); +} - return([ans,ans2]); +def test13() { + Println("test13 try to construct a minimal free resolution"); + Println("of a GKZ system [[1,2]]. 6/12, 2000."); + ans2 = GKZ([[1,2]],[0]); + /* Be careful!! It resets the grade to module1, not module1v */ + ww2 = [["x1",-1,"x2",-1,"Dx1",1,"Dx2",1]]; + Sweyl("x1,x2",ww2); + ans2 = ReParse(ans2[0]); + Println(ans2); + return(Sminimal(ans2)); +} +def test14() { + Println("test14 try to construct a minimal free resolution"); + Println("of a GKZ system [[1,2,3]]. 6/12, 2000."); + ans2 = GKZ([[1,2,3]],[0]); + /* It stops by the strategy error. + July 26, 2000. It works fine after fixing a bug in resol.c */ + ww2 = [["x1",-1,"x2",-1,"x3",-1,"Dx1",1,"Dx2",1,"Dx3",1]]; + Sweyl("x1,x2,x3",ww2); + ans2 = ReParse(ans2[0]); + return(Sminimal(ans2)); } +def test14a() { + Println("test14a try to construct a minimal free resolution"); + Println("of a GKZ system [[1,2,3]]. 6/12, 2000."); + Println("Without automatic homogenization."); + ww2 = [["x1",-1,"x2",-1,"x3",-1,"Dx1",1,"Dx2",1,"Dx3",1]]; + Sweyl("x1,x2,x3",ww2); + ans2 = [x1*Dx1+2*x2*Dx2+3*x3*Dx3 , Dx1^2-Dx2*h , -Dx1*Dx2+Dx3*h , + Dx2^2-Dx1*Dx3 ]; + ans2 = ReParse(ans2); + return(Sminimal(ans2,["homogenized"])); +} -/* Check if the complex is exact or not? */ -def test10() { - local p,pp,ans,b,c,cc,ww,ww2,ans_all,ans2, r; - f = "x^3-y^2*z^2"; - p = Sannfs(f,"x,y,z"); - ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]]; - sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set "); - Sweyl("x,y,z",ww2); - pp = Map(p,"Spoly"); - ans = sm1_resol1([pp,"x,y,z",ww2]); +def test15() { + Println("test15 try to construct a minimal free resolution"); + Println("of a GKZ system [[1,2,3]] by the order filt. 6/12, 2000."); + ww2 = [["Dx1",1,"Dx2",1,"Dx3",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]); + Sweyl("x1,x2,x3"); + ans3 = ReParse(a[0]); + r= IsExact_h(ans3,[x1,x2,x3]); + Println(r); + return(a); +} - f = "x^3-y^2*z^2"; - p = Sannfs(f,"x,y,z"); - sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set "); - ww = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]]; - Sweyl("x,y,z",ww); - pp = Map(p,"Spoly"); - ans_all = Sschreyer(pp); /* Schreyer by LaScala-Stillman */ - ans2 = ans_all[0]; - - r= SisExact_h(ans2,[x,y,z]); - Print(r); - - return([r,[ans,ans2]]); +def test15b() { + Println("test15b try to construct a minimal free resolution"); + Println("of toric [[1,2,3]] by the order filt. 6/12, 2000."); + ww2 = [["Dx1",1,"Dx2",1,"Dx3",1]]; + Sweyl("x1,x2,x3",ww2); + ans2 = [Dx1^2-Dx2*h , -Dx1*Dx2+Dx3*h , Dx2^2-Dx1*Dx3 ]; + ans2 = ReParse(ans2); + return(Sminimal(ans2,["homogenized"])); +} +def test15c() { + Println("test15c try to construct a minimal free resolution "); + 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]); + Sweyl("x1,x2,x3"); + ans3 = ReParse(a[0]); + r= IsExact_h(ans3,[x1,x2,x3]); + Println(r); + return(a); } +def test16() { + Println("test16 try to construct a minimal free resolution"); + Println("of a GKZ system [[1,2,3,5]] by the order filt. 6/12, 2000."); + ww2 = [["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1]]; + Sweyl("x1,x2,x3,x4",ww2); + ans2 = GKZ([[1,2,3,5]],[0]); + ans2 = ReParse(ans2[0]); + return(Sminimal(ans2)); +} + +def test16b() { + Println("test16b try to construct a minimal free resolution"); + Println("of a toric [[1,2,3,5]] by the order filt. 6/12, 2000."); + ww2 = [["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1]]; + Sweyl("x1,x2,x3,x4",ww2); + ans2 = GKZ([[1,2,3,5]],[0]); + ans3 = Rest(ans2[0]); + ans3 = ReParse(ans3); + Println("Toric variety:"); + Println(ans3); + return(Sminimal(ans3)); +} + + +def test17() { + 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); + c=Sinit_w(b,w); + Println("Resolution (b)----"); + sm1_pmat(b); + Println("Initial (c)----"); + 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); + c=Sinit_w(b,w); + Println("Resolution (b)----"); + sm1_pmat(b); + Println("Initial (c)----"); + sm1_pmat(c); + Println(IsExact_h(c,"x,y,z")); + g = Sinvolutive(b[0],w); + Println("Involutive basis ---"); + sm1_pmat(g); + Println("Is same ideal?"); + Println(IsSameIdeal_h(g,c[0],"x,y")); +} + +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")); + +} + +