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Diff for /OpenXM/src/asir-contrib/testing/test1-tr.rr between version 1.1 and 1.8

version 1.1, 2005/04/01 08:08:36 version 1.8, 2005/05/11 06:40:10
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   /* $Id$ */
   /* $OpenXM: OpenXM/src/asir-contrib/testing/test1-tr.rr,v 1.7 2005/05/04 05:47:03 takayama Exp $ */
   
   load("tr.rr")$
   
   /*
      qt_ ==> qt.
      tr_ ==> tr.
   */
   
   def test0() {
     A = quotetolist(quote(1+sin(x)+sin(3*@pi)*sin(0)));
     P = quotetolist(quote(sin(pn("x")*@pi)));
     Q = ["qt.sin_int","x"];
     print(A);
     print(P);
     print(Q);
     print("----------------");
     print(tr.match0(A,P));
     A2 = quotetolist(quote(sin(2*@pi)));
     print(tr.match0(A2,P));
     print("----------------");
     print("---- tr.make_binding --------");
     print(tr.make_binding(A2,P));
     print("-----tr.rp -------------");
     R=tr.rp(A,P,Q);
     print("--------------------");
     print(R);
     print("--------------------");
     return quote_input_form_quote_list(R);
   }
   
   def test1()  {
     Rule1=[quote(sin(pn("x")*@pi)),["qt.sin_int","x"]]; /* sin($B@0?t(B*@pi) --> 0 */
     Rule2=[quote(0*pn("y")),       ["qt.zero"]];       /* 0*any --> 0 */
     Rule3=[quote(pn("y")*0),       ["qt.zero"]];       /* any*0 --> 0 */
     Rule4=[quote(pn("y")+0),       ["qt.id","y"]];       /* any+0 --> any */
     Rule5=[quote(0+pn("y")),       ["qt.id","y"]];       /* 0+any --> any */
     Rule6=[quote(sin(0)),          ["qt.zero"]];       /* sin(0) --> 0 */
     R0 = quote(1+sin(sin(2*@pi)*sin(@pi/2))+sin(5*@pi));
     print(print_input_form(R0));
     R=tr.apply_rule1(R0,Rule1[0],Rule1[1]);
     print(print_input_form(R));
     R=tr.apply_rule1(R,Rule2[0],Rule2[1]);
     print(print_input_form(R));
     R=tr.apply_rule1(R,Rule4[0],Rule4[1]);
     print(print_input_form(R));
     R=tr.apply_rule1(R,Rule6[0],Rule6[1]);
     print(print_input_form(R));
     R=tr.apply_rule1(R,Rule4[0],Rule4[1]);
     print(print_input_form(R));
     return R;
   }
   
   
   /* $BITDj@QJ,7W;;$NNc(B
       c x^n $B$NOB$NITDj@QJ,(B (c $B$O(B x $B$K0MB8$;$:(B)
      $B$$$m$$$m(B $BLdBjE@$"$j(B:  $B$?$H$($P(B c $B$,(B $BL5$$$H$-$N=hM}$G$-$:(B.
   */
   
   /* $B1&JU4X?t(B.  c x^n $B$NITDj@QJ,(B (c $B$O(B x $B$K0MB8$;$:(B)
      Todo: $B1&JU4X?t$rMF0W$K=q$/J}K!(B.
   */
   def r_integral0(C,N) {
     NN = eval_str(quote_input_form_quote_list(quotetolist(N)));
     CC = quote_input_form_quote_list(quotetolist(C));
     if (NN == -1) {
        R = "quote("+CC+"*log(x))";
     }else{
        R = "quote("+CC+"/"+rtostr(NN+1)+"*x^"+rtostr(NN+1)+")";
     }
     print("r_integral0:",0);print(R);
     R = eval_str(R);
     return quotetolist(R);
   }
   /* $B1&JU4X?t(B $B@QJ,$N@~7?@-(B */
   def r_int_linear(F,G) {
     FF = quote_input_form_quote_list(quotetolist(F));
     GG = quote_input_form_quote_list(quotetolist(G));
     R = "quote(integral("+FF+")+integral("+GG+"))";
     print("r_int_linear:",0);print(R);
     R = eval_str(R);
     return quotetolist(R);
   }
   def test3() {
     R0 = quote(1+integral(2*x^(-1)+2*x^2));
     return test3a(R0);
   }
   def test3a(R0)  {
     Rules=[
        /* c*x^n --> (c/(n+1))*x^(n+1) or c*log(x) */
        [quote(integral(pn("c")*x^pn("n"))),["r_integral0","c","n"]],
        [quote(integral(pn("f")+pn("g"))),  ["r_int_linear","f","g"]]
     ];
     print("Input=",0); print(print_input_form(R0));
     N = length(Rules);
     R = R0;
     for (J=0; J<3; J++) {  /* Todo: $B%U%i%0$,$J$$$N$G(B, $B$H$j$"$($:(B 3 $B2s(B */
       for (I=0; I<N; I++) {
         print(print_input_form(R));
         R=tr.apply_rule1(R,Rules[I][0],Rules[I][1]);
       }
     }
     return R;
   }
   
   
   /* $B4X?t$N%^%C%A(B.  N[] $BAjEv(B.  test4(). */
   /*  quote(nn(pn(f),qt.is_function(f))); $B$OITMW(B. qt.map_arg $B$,=hM}(B */
   def test4() {
     Rule=[quote(nn(pn(f))),["qt.map_arg",nn,f]];
     R0 = quote(nn(sin(1/2)*cos(1/3)));
     print(print_input_form(R0));
     R=tr.apply_rule1(R0,Rule[0],Rule[1]);
     return R;
   }
   
   def test5() {
     Rule1=[quote(sin(pn(x)*@pi)),["qt.sin_int",x]]; /* sin($B@0?t(B*@pi) --> 0 */
     Rule2=[quote(0*pn(y)),       ["qt.zero"]];       /* 0*any --> 0 */
     Rule3=[quote(pn(y)*0),       ["qt.zero"]];       /* any*0 --> 0 */
     Rule4=[quote(pn(y)+0),       ["qt.id",y]];       /* any+0 --> any */
     Rule5=[quote(0+pn(y)),       ["qt.id",y]];       /* 0+any --> any */
     Rule6=[quote(sin(0)),          ["qt.zero"]];       /* sin(0) --> 0 */
     R0 = quote(1+sin(sin(2*@pi)*sin(@pi/2))+sin(5*@pi));
     print(print_input_form(R0));
     R=tr.apply_rule1_flag(R0,Rule1[0],Rule1[1]);
     print([R[0],print_input_form(R[1])]);
     R=tr.apply_or_rules(R0,[Rule1,Rule2,Rule3,Rule4,Rule5,Rule6]);
     return R;
   }
   
   
   /* $BHyJ,4D$N7W;;(B */
   /* x $B$K0MB8$7$F$k$+(B?  u, u_0, u_1, u_2, ... $B$O(B x $B$K0MB8$7$F$k(B.*/
   def to_quote(L) {
     return eval_str("quote("+listtoquote_str(L)+")");
   }
   def dep6(Q) {
     if (type(Q) == 4) {
       Q = to_quote(Q);
     }
     if (qt.is_dependent(Q,x)) return 1;
     if (qt.is_dependent(Q,u)) return 1;
     /* $B$H$j$"$($:(B 10 $B<!$^$G$N(B f. --> $B$J$s$H$+$;$h(B. */
     for (I=0; I<10; I++) {
       if (qt.is_dependent(Q,idxtov(u,I))) return 1;
     }
     return 0;
   }
   def diff_lin(F,G) {
     if (type(F) == 4) F=to_quote(F);
     if (type(G) == 4) G=to_quote(G);
     return qt.replace(quote(diff(f)+diff(g)),[[f,F],[g,G]]);
   }
   def diff_mul(F,G) {
     F1 = dep6(F); G1 = dep6(G);
     if (type(F) == 4) F=to_quote(F);
     if (type(G) == 4) G=to_quote(G);
     if (F1 && G1)
       return qt.replace(quote(diff(f)*g+f*diff(g)),[[f,F],[g,G]]);
     if ((F1 == 1) &&  (G1 == 0))
       return qt.replace(quote(diff(f)*g),[[f,F],[g,G]]);
     if ((F1 == 0) &&  (G1 == 1))
       return qt.replace(quote(f*diff(g)),[[f,F],[g,G]]);
     if ((F1 == 0) && (G1 == 0))
       return qt.zero();
   }
   def diff_x_n(N) {
     N = eval_quote(N);
     N1=N-1;
     if (N1 == 0)  return qt.one();
     if (N1 == 1)  return quote(2*x);
     if (N1 > 1) return eval_str("quote("+rtostr(N)+"*x^"+rtostr(N1)+")");
   }
   /* F $B$,(B u $B$H$+(B u_0, u_1, ... $B$J$i(B 1 $B$rLa$9(B. */
   /* debug $BMQ$NF~NO(B.
     tr.check_pn(quote(u_1),quote(pn(x,is_u_variable(x))));
   */
   def is_u_variable(F) {
     /* $B=R8l$NA0$N(B check point $B$b(B debugger $B$KM_$7$$(B. */
     /* print("is_u_variable: ",0); print(print_input_form(F)); */
     if (type(F) == 17) F=quotetolist(F);
     if (rtostr(F[0]) == "internal") {
       V = eval_str(rtostr(F[1]));
       if (vtoidx(V)[0] == "u") return 1;
     }
     return 0;
   }
   /*  u_i^n $B$NHyJ,$r$9$k(B.  n*u_{i+1}*u_i^{n-1}
      Todo: $B$b$C$H4J7i$K(B quote $B$r=q$1$J$$$+(B?
   */
   def diff_u_n(F,N) {
     F = eval_quote(F);
     I = vtoidx(F);
     if (length(I) == 1) I = 0; else I=I[1];
     N = eval_quote(N);
     N1=N-1;
     NextU = "u_"+rtostr(I+1);
     if (I == 0) U = "u"; else U = "u_"+rtostr(I);
   
     NN = objtoquote(N);
     NN1 = objtoquote(N1);
     NextU = objtoquote(eval_str(NextU));
     U = objtoquote(eval_str(U));
   
     if (N1 == 0)  return NextU;
     if (N1 == 1)  return qt.replace(quote(2*up*uu),[[up,NextU],[uu,U]]);
     if (N1 > 1) return qt.replace(quote(n*up*uu^m),[[up,NextU],[uu,U],
        [n,NN],[m,NN1]]);
   }
   
   def test6b() {
     T1=[quote(diff(x)),["qt.one"]];
     T2=[quote(diff(x^pn(n))),[diff_x_n,n]];  /* is_poly? $B$,M_$7$$(B. */
     R1=[quote(diff(pn(f)+pn(g))),[diff_lin,f,g]];
     R2=[quote(diff(pn(f)*pn(g))),[diff_mul,f,g]];
   
     A = quote(diff(2*4*x^3+x));
     print(print_input_form(A));
     R=tr.apply_or_rules(A,[R1,R2,T1,T2]);
     return R;
   }
   
   /* Use Debug2=1; $B$O(B debug $B$K$H$F$bM-1W(B. */
   def test6() {
     T1=[quote(diff(x)),["qt.one"]];
     T2=[quote(diff(x^pn(n))),[diff_x_n,n]];  /* is_poly? $B$,M_$7$$(B. */
     T3=[quote(diff(pn(f,is_u_variable(f))^pn(n))),[diff_u_n,f,n]];
     R1=[quote(diff(pn(f)+pn(g))),[diff_lin,f,g]];
     R2=[quote(diff(pn(f)*pn(g))),[diff_mul,f,g]];
   
     /* A = quote(diff(2*x^3+x));*/
     A = quote(diff(2*u^3+x));
     print(print_input_form(A));
     R=tr.apply_or_rules(A,[R1,R2,T1,T2,T3]);
     return R;
   }
   end$
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