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December 25, 2013 19:49
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prolog rules for differential calculus symbolic computation
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/****************** Differential Calculus ***************/ | |
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, R ):- /* d(U+V)/dX = A+B where */ | |
d( U, X, A ), /* A = d(U)/dX and */ | |
d( V, X, B ), | |
R = A + B. | |
d( U-V, X, R ):- | |
d( U, X, A ), | |
d( V, X, B ), | |
R = A - B. | |
d( C*U, X, R ):- | |
atomic(C), | |
C \= X, | |
d( U, X, A ), | |
R = C * A, | |
!. | |
d( U*V, X, U*B+V*A ):- /* 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^2) ):- /* 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, R ):- /* d(U^C)/dX = C*A*U^(C-1) */ | |
atomic(C), /* where C is a number or */ | |
C\=X, | |
d( U, X, A ), | |
R = C * A * U ^ ( C - 1 ). | |
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 */ | |
d( tan(W), X, (Z*sec(W)^2) ):- /* d(tan(W))/dX = Z*sec(W)^2 */ | |
d( W, X, Z). /* where Z = d(W)/dX */ | |
d( cot(W), X, -(Z*cosec(W)^2) ):- /* d(cot(W))/dX = -Z*cosec(W)^2 */ | |
d( W, X, Z). /* where Z = d(W)/dX */ | |
d( sec(W), X, (Z*sec(W)*tan(W)) ):- /* d(sec(W))/dX = sec(W)*tan(W) */ | |
d( W, X, Z). /* where Z = d(W)/dX */ | |
d( cosec(W), X, -(Z*cosec(W)*cot(W)) ):- /* d(cosec(W))/dX = -cosec(W)*cot(W) */ | |
d( W, X, Z). /* where Z = d(W)/dX */ | |
d( arcsin(W), X, Z/sqrt(1-W^2) ):- /* d(arcsin(W))/dX = Z/sqrt(1-W^2) */ | |
d( W, X, Z). /* where Z = d(W)/dX */ | |
d( arccos(W), X, -(Z/sqrt(1-W^2)) ):- /* d(arccos(W))/dX = -(Z/sqrt(1-W^2) )*/ | |
d( W, X, Z). /* where Z = d(W)/dX */ | |
d( arctan(W), X, Z/(1+W^2) ):- /* d(arctan(W))/dX = Z/(1+W^2) */ | |
d( W, X, Z). /* where Z = d(W)/dX */ | |
d( arccot(W), X, -(Z/(1+W^2)) ):- /* d(arccot(W))/dX = -(Z/(1+W^2)) */ | |
d( W, X, Z). /* where Z = d(W)/dX */ | |
d( arcsec(W), X, (Z/(W*sqrt(W^2-1))) ):- /* d(arcsec(W))/dX = (Z/(W*sqrt(W^2-1))) */ | |
d( W, X, Z). /* where Z = d(W)/dX */ | |
d( arccosec(W), X, -(Z/(W*sqrt(W^2-1))) ):- /* d(arccosec(W))/dX = -(Z/(W*sqrt(W^2-1))) */ | |
d( W, X, Z). /* where Z = d(W)/dX */ | |
/****************** End Differential Calculus ***************/ |
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