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Annotation of OpenXM/src/k097/lib/minimal/minimal-test.k, Revision 1.5

1.5     ! takayama    1: /* $OpenXM: OpenXM/src/k097/lib/minimal/minimal-test.k,v 1.4 2000/06/14 07:44:05 takayama Exp $ */
1.1       takayama    2: load["minimal.k"];
                      3: def test5() {
                      4:   local a,b,c,cc,v;
                      5:   a = Sannfs3_laScala2("x^3-y^2*z^2");
                      6:   b = a[0];
                      7:   v = [x,y,z];
                      8:   c = Skernel(b[0],v);
                      9:   c = c[0];
                     10:   sm1_pmat([c,b[1],v]);
                     11:   Println("-----------------------------------");
                     12:   cc = sm1_res_div(c,b[1],v);
                     13:   sm1_pmat(sm1_gb(cc,v));
                     14:   c = Skernel(b[1],v);
                     15:   c = c[0];
                     16:   cc = sm1_res_div(c,b[2],v);
                     17:   sm1_pmat(sm1_gb(cc,v));
                     18:   return(a);
                     19: }
                     20: def test6() {
                     21:   local a,b,c,cc,v;
                     22:   a = Sannfs3("x^3-y^2*z^2");
                     23:   b = a[0];
                     24:   v = [x,y,z];
                     25:   c = Skernel(b[0],v);
                     26:   c = c[0];
                     27:   sm1_pmat([c,b[1],v]);
                     28:   Println("-------ker = im for minimal ?---------------------");
                     29:   cc = sm1_res_div(c,b[1],v);
                     30:   sm1_pmat(sm1_gb(cc,v));
                     31:   c = Skernel(b[1],v);
                     32:   c = c[0];
                     33:   cc = sm1_res_div(c,b[2],v);
                     34:   sm1_pmat(sm1_gb(cc,v));
                     35:   Println("------ ker=im for Schreyer ?------------------");
                     36:   b = a[3];
                     37:   c = Skernel(b[0],v);
                     38:   c = c[0];
                     39:   sm1_pmat([c,b[1],v]);
                     40:   cc = sm1_res_div(c,b[1],v);
                     41:   sm1_pmat(sm1_gb(cc,v));
                     42:   c = Skernel(b[1],v);
                     43:   c = c[0];
                     44:   cc = sm1_res_div(c,b[2],v);
                     45:   sm1_pmat(sm1_gb(cc,v));
                     46:   return(a);
                     47: }
                     48:
                     49: /* May 23, Tue */
                     50: def test7() {
                     51:   local a,b,c,cc,v;
                     52:   a = Sannfs3_laScala2("x^3-y^2*z^2");
                     53:   b = a[0];
                     54:   v = [x,y,z];
                     55:   c = Skernel(b[0],v);
                     56:   c = c[0];
                     57:   sm1_pmat([c,b[1],v]);
                     58:   Println("-------ker = im for minimal ?---------------------");
                     59:   cc = sm1_res_div(c,b[1],v);
                     60:   sm1_pmat(sm1_gb(cc,v));
                     61:   c = Skernel(b[1],v);
                     62:   c = c[0];
                     63:   cc = sm1_res_div(c,b[2],v);
                     64:   sm1_pmat(sm1_gb(cc,v));
                     65:   Println("------ ker=im for Schreyer ?------------------");
                     66:   b = a[3];
                     67:   c = Skernel(b[0],v);
                     68:   c = c[0];
                     69:   sm1_pmat([c,b[1],v]);
                     70:   cc = sm1_res_div(c,b[1],v);
                     71:   sm1_pmat(sm1_gb(cc,v));
                     72:   c = Skernel(b[1],v);
                     73:   c = c[0];
                     74:   cc = sm1_res_div(c,b[2],v);
                     75:   sm1_pmat(sm1_gb(cc,v));
                     76:   return(a);
                     77: }
                     78:
                     79: def sm1_resol1(p) {
                     80:   sm1(" p resol1 /FunctionValue set ");
                     81: }
                     82:
                     83:
                     84: def test8() {
                     85:   local p,pp,ans,b,c,cc,ww,ww2;
                     86:   f = "x^3-y^2*z^2";
                     87:   p = Sannfs(f,"x,y,z");
                     88:   ww = [["x",1,"y",1,"z",1,"Dx",1,"Dy",1,"Dz",1,"h",1],
                     89:                  ["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
                     90:   ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
                     91:   sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set ");
                     92:   Sweyl("x,y,z",ww);
                     93:   pp = Map(p,"Spoly");
                     94:   /* return(pp); */
                     95:   /* pp =
                     96:      [y*Dy-z*Dz , -2*x*Dx-3*y*Dy+1 , 2*x*Dy*Dz^2-3*y*Dx^2 ,
                     97:       2*x*Dy^2*Dz-3*z*Dx^2 , 2*x*z*Dz^3-3*y^2*Dx^2+4*x*Dz^2 ]
                     98:   */
                     99:   ans = sm1_resol1([pp,"x,y,z",ww]);
                    100:   /* Schreyer is in ans. */
                    101:
                    102:   v = [x,y,z];
                    103:   b = ans;
                    104:   Println("------ ker=im for Schreyer ?------------------");
                    105:   c = Skernel(b[0],v);
                    106:   c = c[0];
                    107:   sm1_pmat([c,b[1],v]);
                    108:   cc = sm1_res_div(c,b[1],v);
                    109:   sm1_pmat(sm1_gb(cc,v));
                    110:   c = Skernel(b[1],v);
                    111:   c = c[0];
                    112:   cc = sm1_res_div(c,b[2],v);
                    113:   sm1_pmat(sm1_gb(cc,v));
                    114:   return(ans);
                    115: }
                    116: /*
                    117:    a = test8();
                    118:    SisComplex(a):
                    119: */
                    120:
                    121: def test8a() {
                    122:   local p,pp,ans,b,c,cc,ww, ans_all;
                    123:   f = "x^3-y^2*z^2";
                    124:   p = Sannfs(f,"x,y,z");
                    125:   sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set ");
                    126:   ww = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
                    127:   /* Removed "x",1, ... ===> It causes an error. I do not know the reason.*/
                    128:   Sweyl("x,y,z",ww);
                    129:   pp = Map(p,"Spoly");
                    130:   /* return(pp); */
                    131:   /* pp =
                    132:      [y*Dy-z*Dz , -2*x*Dx-3*y*Dy+1 , 2*x*Dy*Dz^2-3*y*Dx^2 ,
                    133:       2*x*Dy^2*Dz-3*z*Dx^2 , 2*x*z*Dz^3-3*y^2*Dx^2+4*x*Dz^2 ]
                    134:   */
                    135:   ans_all = Sschreyer(pp);
                    136:   ans = ans_all[0];
                    137:   /* ans = sm1_resol1([pp,"x,y,z",ww]); */
                    138:   /* Schreyer is in ans. */
                    139:
                    140:   v = [x,y,z];
                    141:   b = ans;
1.3       takayama  142:   Println("------ ker=im for Schreyer ?----- wrong method!!!-----------");
1.1       takayama  143:   c = Skernel(b[0],v);
                    144:   c = c[0];
                    145:   sm1_pmat([c,b[1],v]);
                    146:   cc = sm1_res_div(c,b[1],v);
                    147:   sm1_pmat(sm1_gb(cc,v));
                    148:   c = Skernel(b[1],v);
                    149:   c = c[0];
                    150:   cc = sm1_res_div(c,b[2],v);
                    151:   sm1_pmat(sm1_gb(cc,v));
                    152:   return(ans);
                    153: }
                    154:
                    155: /* Comparing two constructions */
                    156: def test9() {
                    157:   local p,pp,ans,b,c,cc,ww,ww2,ans_all,ans2;
                    158:   f = "x^3-y^2*z^2";
                    159:   p = Sannfs(f,"x,y,z");
                    160:   ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
                    161:   sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set ");
                    162:   Sweyl("x,y,z",ww2);
                    163:   pp = Map(p,"Spoly");
                    164:   ans = sm1_resol1([pp,"x,y,z",ww2]);
                    165:
                    166:   f = "x^3-y^2*z^2";
                    167:   p = Sannfs(f,"x,y,z");
                    168:   sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set ");
                    169:   ww = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
                    170:   Sweyl("x,y,z",ww);
                    171:   pp = Map(p,"Spoly");
                    172:   ans_all = Sschreyer(pp);
                    173:   ans2 = ans_all[0];
                    174:
                    175:   return([ans,ans2]);
1.2       takayama  176:
                    177: }
                    178:
1.3       takayama  179: /* Check if the complex by Sschreyer() is exact or not in our example? */
1.2       takayama  180: def test10() {
                    181:   local p,pp,ans,b,c,cc,ww,ww2,ans_all,ans2, r;
                    182:   f = "x^3-y^2*z^2";
                    183:   p = Sannfs(f,"x,y,z");
                    184:   ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
                    185:   sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set ");
                    186:   Sweyl("x,y,z",ww2);
                    187:   pp = Map(p,"Spoly");
                    188:   ans = sm1_resol1([pp,"x,y,z",ww2]);
                    189:
                    190:   f = "x^3-y^2*z^2";
                    191:   p = Sannfs(f,"x,y,z");
                    192:   sm1(" p 0 get { [(x) (y) (z) (Dx) (Dy) (Dz)] laplace0 } map /p set ");
                    193:   ww = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
                    194:   Sweyl("x,y,z",ww);
                    195:   pp = Map(p,"Spoly");
                    196:   ans_all = Sschreyer(pp);  /* Schreyer by LaScala-Stillman */
                    197:   ans2 = ans_all[0];
                    198:
1.3       takayama  199:   sm1(" /gb.verbose 1 def ");
                    200:
                    201:   ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
                    202:   Sweyl("x,y,z",ww2);
                    203:   ans2 = ReParse(ans2);
                    204:   r= IsExact_h(ans2,[x,y,z]);
1.2       takayama  205:   Print(r);
                    206:
                    207:   return([r,[ans,ans2]]);
1.1       takayama  208:
                    209: }
1.3       takayama  210:
                    211: def test11() {
                    212:   local  a;
                    213:   a = test_ann3("x^3-y^2*z^2");
                    214:   return(a);
                    215: }
                    216: /* f should be a string. */
1.5     ! takayama  217: /* a=test_ann3("x^3+y^3+z^3");
        !           218: It returns the following resolution in 1.5 hours.  June 14, 2000.
        !           219:  [
        !           220:   [
        !           221:     [    x*Dx+y*Dy+z*Dz-3*h^2 ]
        !           222:     [    -z*Dy^2+y*Dz^2 ]
        !           223:     [    -z*Dx^2+x*Dz^2 ]
        !           224:     [    -y*Dx^2+x*Dy^2 ]
        !           225:   ]
        !           226:   [
        !           227:     [    0 , -x , y , -z ]
        !           228:     [    z*Dx^2-x*Dz^2 , x*Dy , x*Dx+z*Dz-3*h^2 , z*Dy ]
        !           229:     [    y*Dx^2-x*Dy^2 , -x*Dz , y*Dz , x*Dx+y*Dy-3*h^2 ]
        !           230:     [    0 , Dx^2 , -Dy^2 , Dz^2 ]
        !           231:     [    z*Dy^2-y*Dz^2 , x*Dx+y*Dy+z*Dz-2*h^2 , 0 , 0 ]
        !           232:   ]
        !           233:   [
        !           234:     [    -x*Dx+3*h^2 , y , -z , 0 , -x ]
        !           235:     [    Dy^3+Dz^3 , Dy^2 , -Dz^2 , x*Dx+y*Dy+z*Dz , -Dx^2 ]
        !           236:   ]
        !           237:  ]
        !           238: */
1.3       takayama  239: def test_ann3(f) {
                    240:   local a,v,ww2,ans2;
                    241:   a = Sannfs3_laScala2(f);
                    242:   ans2 = a[0];
                    243:   v = [x,y,z];
                    244:   ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
                    245:   Sweyl("x,y,z",ww2);
                    246:   ans2 = ReParse(ans2);
                    247:   r= IsExact_h(ans2,[x,y,z]);
                    248:   Println(r);
                    249:   return([r,ans2]);
                    250: }
                    251: def test11a() {
                    252:   local a,v,ww2,ans2;
                    253: /* constructed by test11.
                    254:   ans2 =
                    255:        [[[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]] ,
                    256:         [[3*Dx^2*h , 0 , Dy , -Dz] ,
                    257:          [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] ,
                    258:          [0 , 2*x*Dy^2*Dz-3*z*Dx^2*h , 0 , 2*x*Dx+3*z*Dz] ,
                    259:          [2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0] ,
                    260:          [0 , 0 , 0 , 0] ,
                    261:          [2*x*Dy*Dz , 0 , z , -y] ,
                    262:          [0 , 0 , 0 , 0] ,
                    263:          [0 , 0 , 0 , 0] ,
                    264:          [0 , 0 , 0 , 0]] ,
                    265:   [[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
                    266:    [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
                    267:    [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
                    268:    [-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] ,
                    269:    [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
                    270:    [3*y*z , z , y , -2*x*Dy*Dz , -3*z*Dy , 2*x*Dx , 2*x*z , -2*x*y , 0] ,
                    271:    [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
                    272:    [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
                    273:    [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0]] ,
                    274:    [[0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
                    275:     [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0] ,
                    276:     [0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0]]]
                    277: */
                    278:   ans2 =
                    279:        [[[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]] ,
                    280:         [[3*Dx^2*h , 0 , Dy , -Dz] ,
                    281:          [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] ,
                    282:          [0 , 2*x*Dy^2*Dz-3*z*Dx^2*h , 0 , 2*x*Dx+3*z*Dz] ,
                    283:          [2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0] ,
                    284:          [2*x*Dy*Dz , 0 , z , -y]],
                    285:   [[-2*x*Dx-3*y*Dy-3*z*Dz-6*h^2 , -Dy , -Dz , 3*Dx^2*h , 3*Dy*Dz ] ,
                    286:    [3*y*z , z , y , -2*x*Dy*Dz , 2*x*Dx]]];
                    287:
                    288:   sm1_pmat( ans2[1]*ans2[0] );
                    289:   sm1_pmat( ans2[2]*ans2[1] );
                    290:   ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
                    291:   Sweyl("x,y,z",ww2);
                    292:   ans2 = ReParse(ans2);
                    293:   r= IsExact_h(ans2,[x,y,z]);
                    294:   Println(r);
                    295:   return([r,ans2]);
                    296: }
                    297:
                    298: def test12() {
                    299:   local a,v,ww2,ans2;
                    300:   a = Sannfs3("x^3-y^2*z^2");
                    301:   ans2 = a[0];
                    302:   v = [x,y,z];
                    303:   ww2 = [["x",-1,"y",-1,"z",-1,"Dx",1,"Dy",1,"Dz",1]];
1.4       takayama  304:   Sweyl("x,y,z",ww2);
                    305:   ans2 = ReParse(ans2); /* DO NOT FORGET! */
1.3       takayama  306:   r= IsExact_h(ans2,[x,y,z]);
                    307:   Println(r);
                    308:   Println("It may stop by non-exact statement. The code of Sminimal_v (non-LaScala-Stillman contains bugs.");
                    309:   return([r,ans2]);
                    310: }
1.4       takayama  311:
                    312: def test13() {
                    313:   Println("test13 try to construct a minimal free resolution");
                    314:   Println("of a GKZ system [[1,2]]. 6/12, 2000.");
1.5     ! takayama  315:   ans2 = GKZ([[1,2]],[0]);
        !           316:    /* Be careful!! It resets the grade to module1, not module1v */
1.4       takayama  317:   ww2 = [["x1",-1,"x2",-1,"Dx1",1,"Dx2",1]];
                    318:   Sweyl("x1,x2",ww2);
                    319:   ans2 = ReParse(ans2[0]);
1.5     ! takayama  320:   Println(ans2);
1.4       takayama  321:   return(Sminimal(ans2));
                    322: }
                    323:
                    324: def test14() {
                    325:   Println("test14 try to construct a minimal free resolution");
                    326:   Println("of a GKZ system [[1,2,3]]. 6/12, 2000.");
1.5     ! takayama  327:   ans2 = GKZ([[1,2,3]],[0]);  /* It stops by the strategy error. */
1.4       takayama  328:   ww2 = [["x1",-1,"x2",-1,"x3",-1,"Dx1",1,"Dx2",1,"Dx3",1]];
                    329:   Sweyl("x1,x2,x3",ww2);
                    330:   ans2 = ReParse(ans2[0]);
                    331:   return(Sminimal(ans2));
                    332: }
                    333: def test14a() {
                    334:   Println("test14a try to construct a minimal free resolution");
                    335:   Println("of a GKZ system [[1,2,3]]. 6/12, 2000.");
                    336:   Println("Without automatic homogenization.");
                    337:   ww2 = [["x1",-1,"x2",-1,"x3",-1,"Dx1",1,"Dx2",1,"Dx3",1]];
                    338:   Sweyl("x1,x2,x3",ww2);
                    339:   ans2 = [x1*Dx1+2*x2*Dx2+3*x3*Dx3 , Dx1^2-Dx2*h , -Dx1*Dx2+Dx3*h ,
                    340:           Dx2^2-Dx1*Dx3 ];
                    341:   ans2 = ReParse(ans2);
                    342:   return(Sminimal(ans2,"homogenized"));
                    343: }
                    344:
                    345: def test15() {
                    346:   Println("test15 try to construct a minimal free resolution");
                    347:   Println("of a GKZ system [[1,2,3]] by the order filt. 6/12, 2000.");
                    348:   ww2 = [["Dx1",1,"Dx2",1,"Dx3",1]];
                    349:   Sweyl("x1,x2,x3",ww2);
                    350:   ans2 = GKZ([[1,2,3]],[0]);
                    351:   ans2 = ReParse(ans2[0]);
                    352:   return(Sminimal(ans2));
                    353: }
                    354:
                    355: def test15b() {
                    356:   Println("test15b try to construct a minimal free resolution");
                    357:   Println("of toric [[1,2,3]] by the order filt. 6/12, 2000.");
                    358:   ww2 = [["Dx1",1,"Dx2",1,"Dx3",1]];
                    359:   Sweyl("x1,x2,x3",ww2);
                    360:   ans2 = [Dx1^2-Dx2*h , -Dx1*Dx2+Dx3*h , Dx2^2-Dx1*Dx3 ];
                    361:   ans2 = ReParse(ans2);
                    362:   return(Sminimal(ans2,"homogenized"));
                    363: }
                    364:
                    365: def test16() {
                    366:   Println("test16 try to construct a minimal free resolution");
                    367:   Println("of a GKZ system [[1,2,3,5]] by the order filt. 6/12, 2000.");
                    368:   ww2 = [["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1]];
                    369:   Sweyl("x1,x2,x3,x4",ww2);
                    370:   ans2 = GKZ([[1,2,3,5]],[0]);
                    371:   ans2 = ReParse(ans2[0]);
                    372:   return(Sminimal(ans2));
                    373: }
                    374:
                    375: def test16b() {
                    376:   Println("test16b try to construct a minimal free resolution");
                    377:   Println("of a toric [[1,2,3,5]] by the order filt. 6/12, 2000.");
                    378:   ww2 = [["Dx1",1,"Dx2",1,"Dx3",1,"Dx4",1]];
                    379:   Sweyl("x1,x2,x3,x4",ww2);
                    380:   ans2 = GKZ([[1,2,3,5]],[0]);
                    381:   ans3 = Rest(ans2[0]);
                    382:   ans3 = ReParse(ans3);
                    383:   Println("Toric variety:");
                    384:   Println(ans3);
                    385:   return(Sminimal(ans3));
                    386: }
                    387:
                    388:
                    389:
1.3       takayama  390:

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