如何构建符号微分OZ莫扎特

Question

我想在OZ Mozart中制作一个符号微分程序，但我被卡住了，不知道如何开始，序言中的规则类似于下面的规则，但我至少需要帮助如何在OZ中制作最具符号的规则，例如，X的导数等于1，这样我就可以制作其余的代码，谢谢！

d( X, X, 1 ):- !.                  /* d(X) w.r.t. X is 1      */
d( C, X, 0 ):- atomic(C).          /* If C is a constant then */
                                   /* d(C)/dX is 0            */
d( U+V, X, A+B ):-                 /* d(U+V)/dX = A+B where   */
   d( U, X, A ),                   /* A = d(U)/dX and         */
   d( V, X, B ).                   /* B = d(V)/dX             */
d( U-V, X, A-B ):-                 /* d(U-V)/dX = A-B where   */
   d( U, X, A ),                   /* A = d(U)/dX and         */
   d( V, X, B ).                   /* B = d(V)/dX             */
d( C*U, X, C*A ):-               /* d(C*U)/dX = C*A where     */
   atomic(C),                    /* C is a number or variable */
   C = X,                       /* not equal to X and        */
   d( U, X, A ), !.              /* A = d(U)/dX               */
d( U*V, X, B*U+A*V ):-           /* d(U*V)/dX = B*U+A*V where */
   d( U, X, A ),                 /* A = d(U)/dX and           */
   d( V, X, B ).                 /* B = d(V)/dX               */
d( U/V, X, (A*V-B*U)/(V*V) ):- /* d(U/V)/dX = (A*V-B*U)/(V*V) */
   d( U, X, A),                /* where A = d(U)/dX and       */
   d( V, X, B).                /*       B = d(V)/dX           */
d( U^C, X, C*A*U^(C-1) ):-       /* d(U^C)/dX = C*A*U^(C-1)   */
   atomic(C),                    /* where C is a number or    */
   C=X,                         /* variable not equal to X   */
   d( U, X, A ).                 /* and d(U)/dX = A           */
d( U^C, X, C*A*U^(C-1) ):-       /* d(U^C)/dX = C*A*U^(C-1)   */
   C = -(C1), atomic(C1),        /* where C is a negated number or  */
   C1=X,                        /* variable not equal to X   */
   d( U, X, A ).                 /* and d(U)/dX = A           */
d( sin(W), X, Z*cos(W) ):-       /* d(sin(W))/dX = Z*cos(W)   */
   d( W, X, Z).                  /* where Z = d(W)/dX         */
d( exp(W), X, Z*exp(W) ):-       /* d(exp(W))/dX = Z*exp(W)   */
   d( W, X, Z).                  /* where Z = d(W)/dX         */
d( log(W), X, Z/W ):-            /* d(log(W))/dX = Z/W        */
   d( W, X, Z).                  /* where Z = d(W)/dX         */
d( cos(W), X, -(Z*sin(W)) ):-    /* d(cos(W))/dX = Z*sin(W)   */
   d( W, X, Z).                  /* where Z = d(W)/dX         */

Answer 1

您必须以Oz中的逻辑编程为起点。开始查看此处了解更多详细信息。你可以像在Prolog中那样在Oz中定义公理。不幸的是，我不是这样的专家，所以我不能帮你更多的忙。