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Annotation of OpenXM/src/asir-contrib/packages/sample/exp-dmod, Revision 1.1

1.1     ! takayama    1: /* $OpenXM: OpenXM/src/asir99/lib/contrib/packages/sample/exp-dmod,v 1.1 1999/11/10 12:01:02 takayama Exp $ */
        !             2: /* exp-dmod,  1999/ 9/27 */
        !             3: /* From 1999/Int/exp.asir */
        !             4: /*  Computing exponents of holonomic system along f=0 */
        !             5:
        !             6: /* In order to use #define in k0, use load["exp.asir"] */
        !             7: print("load xm , sm1_start, init0 for initialization. extest2();");
        !             8: def init0() {
        !             9:   extern Xm_noX;
        !            10:   sm1(0,"[(parse) (oxasir.sm1) pushfile] extension");
        !            11:   if (Xm_noX == 1) {
        !            12:     sm1(0," oxNoX ");
        !            13:   }
        !            14:   sm1(0,"[(parse) (intw.sm1) pushfile] extension");
        !            15:   ox_check_errors2(0);
        !            16: }
        !            17:
        !            18: def sm1reset() {
        !            19:   ox_reset(0);
        !            20:   print("Restoring sm1 local variables.")$
        !            21:   sm1(0," db.restore ");
        !            22:   ox_check_errors2(0);
        !            23: }
        !            24: register_handler(sm1reset);
        !            25:
        !            26: def extest2() {
        !            27:   F = x;
        !            28:   A = [t-F, dx+diff(F,x)*dt, dy+diff(F,y)*dt];
        !            29:   EEE = ["dx (2 x dx + 3) - (x dx + y dy + 10) (2 x dx -6)",
        !            30:          "dy (y dy - 8) - (x dx + y dy + 10) (y dy +2)","dt"];
        !            31:   EEE2 = ["dx (x dx-4) - (x dx + y dy + 10) ( x dx -6)",
        !            32:           "dy (y dy - 8) - (x dx + y dy + 10) (y dy +2)","dt"];
        !            33:   B=sm1_wTensor0(0,[A,EEE,
        !            34:                      "t,x,y",[1,2,3]]);
        !            35:   print(["Tensor Product is ", B])$
        !            36:   G = sm1_wbf(0,[B,[t,x,y],[t,-1,dt,1]]);
        !            37:   return(G);
        !            38:
        !            39: }
        !            40:
        !            41: def extest3() {
        !            42:   print("This example seems to be hard!");
        !            43:   F = x*s-y*z;
        !            44:   A = [t-F, dx+diff(F,x)*dt, dy+diff(F,y)*dt,
        !            45:             dz+diff(F,z)*dt, ds+diff(F,s)*dt];
        !            46:   EEE = [x*dx+y*dy+z*dz+s*ds-2/3,
        !            47:               y*dy     +s*ds+1/5,
        !            48:                    z*dz+s*dx-3/2,
        !            49:          dx*ds-dy*dz,
        !            50:          dt];
        !            51:   EEE = sm1_rat_to_p(EEE); EEE = EEE[0];
        !            52:   print(["Numerator: ",EEE]);
        !            53:   B=sm1_wTensor0(0,[A,EEE,
        !            54:                      "t,x,y,z,s",[1,2,3,4,5]]);
        !            55:   print(["Tensor Product is ", B])$
        !            56:   G = sm1_wbf(0,[B,[t,x,y,z,s],[t,-1,dt,1]]);
        !            57:   return(G);
        !            58:
        !            59: }
        !            60:
        !            61: def extest4() {
        !            62:   F = 1-x-y;
        !            63:   A = [t-F, dx+diff(F,x)*dt, dy+diff(F,y)*dt];
        !            64:   EEE = ["dx (2 x dx + 3) - (x dx + y dy + 10) (2 x dx -6)",
        !            65:          "dy (y dy - 8) - (x dx + y dy + 10) (y dy +2)","dt"];
        !            66:   B=sm1_wTensor0(0,[A,EEE,
        !            67:                      "t,x,y",[1,2,3]]);
        !            68:   print(["Tensor Product is ", B])$
        !            69:   G = sm1_wbf(0,[B,[t,x,y],[t,-1,dt,1]]);
        !            70:   return(G);
        !            71:   /* 0 and -27/2 */
        !            72: }
        !            73:
        !            74: def extest4a() {
        !            75:    A = 10; B = -3; Bp = -2; C=5/2;Cp=-7;
        !            76:    print([Cp-A-Bp+C-B,Cp-A-Bp]);
        !            77: }
        !            78: def nody(F) {
        !            79:   if (deg(F,dy) == 0) return(F);
        !            80:   else return(0);
        !            81: }
        !            82:
        !            83: def extest4b() {
        !            84:   EEE = ["dx (2 x dx + 3) - (x dx + y dy + 10) (2 x dx -6)",
        !            85:          "dy (y dy - 8) - (x dx + y dy + 10) (y dy +2)"];
        !            86:   G = sm1_gb(0,[EEE,"x,y",[[dy,1]]]);
        !            87:   G = G[0];
        !            88:   print(["GB is ",G]);
        !            89:   H = map(nody,G);
        !            90:   H = map(subst,H,y,2);
        !            91:   J = sm1_gb(0,[H,"x"]);
        !            92:   print(["GB of ode is ",J]);
        !            93:   K = map(subst,J[0],x,x-1);
        !            94:   G = sm1_wbf(0,[K,[x],[x,-1,dx,1]]);
        !            95:   return(G);
        !            96: }
        !            97:
        !            98: def extest5() {
        !            99:   EEE = ["dx (x dx + 3) - (x dx + y dy + 10) (x dx +y dy -6)",
        !           100:          "dy (y dy - 8) - (x dx + y dy + 10) (x dx + y dy -6)"];
        !           101: /* Compute the singular locus
        !           102:   G = sm1_ch(0,[EEE,[x,y]]);
        !           103:   G = G[0];
        !           104:   print(["characteristic variety is ",G]);
        !           105:   H = sm1_saturation(0,[G,[dx,dy],[x,y,dx,dy]]);
        !           106:   return(gr(H,[dx,dy,x,y],2));
        !           107: */
        !           108:   EEE = sm1_mul(0,1,EEE,[x,y]);
        !           109:   F = -x^2+(2*y+2)*x-y^2+2*y-1;
        !           110:   A = [t-F, dx+diff(F,x)*dt, dy+diff(F,y)*dt];
        !           111:   B=sm1_wTensor0(0,[A,EEE,
        !           112:                      "t,x,y",[3,2,1]]);
        !           113:   print(["Tensor Product is ", B])$
        !           114:   G = sm1_wbf(0,[B,[t,x,y],[t,-1,dt,1]]);
        !           115:   return(G);
        !           116: }
        !           117:
        !           118: end$
        !           119: