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ASME's Mechanical Engine…ing Toolkit 1997 December
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ALGEBRA
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DIFFSV.PRO
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/* -----------------------------------------------------------------
DIFFSV.PRO
(version 1.0)
Copyright 1987 S.Vaghi
Program for the symbolic differentiation of
algebraic functions.
...........................................
Example of how to use the program:
to find the derivative, DY, of the function
y = x^2
with respect to x, one can
a) simply enter
d( x^2, x, DY).
after the Prolog prompt,
or
b) enter
Y = x^2 ,
d( Y, x, DY).
after the prompt,
or
c) enter the complete sequence including
simplification, that is
Y = x^2 ,
d( Y, x, Z),
s( Z, DY).
Method c) is always recommended, in which case the
program is used in combination with SIMPSV.PRO
----------------------------------------------------------------- */
/* definition of operators */
?-op(11, yfx, '^'). /* exponentiation */
?-op( 9, fx, '~'). /* minus sign */
?-op(11, fx, 'ln'). /* natural logarithm */
d(X,X,1).
d(C,X,0) :- atomic(C), C \= X.
d(~U,X,~D) :- d(U,X,D).
d(C+U,X,D) :- atomic(C), C \= X, d(U,X,D), ! .
d(U+C,X,D) :- atomic(C), C \= X, d(U,X,D), ! .
d(U+V,X,D1+D2) :- d(U,X,D1), d(V,X,D2).
d(C-U,X,~D) :- atomic(C), C \= X, d(U,X,D), ! .
d(U-C,X, D) :- atomic(C), C \= X, d(U,X,D), ! .
d(U-V,X,D1-D2) :- d(U,X,D1), d(V,X,D2).
d(C*U,X,C*D) :- atomic(C), C \= X, d(U,X,D), ! .
d(U*C,X,C*D) :- atomic(C), C \= X, d(U,X,D), ! .
d(U*V, X, D2*U+D1*V) :- d(U,X,D1), d(V,X,D2).
d(1/U,X, ~D/(U^2) ) :- d(U,X,D), ! .
d(C/U,X, C*DD) :- atomic(C), C \= X, d(1/U,X,DD), ! .
d(U/C,X, D/C) :- atomic(C), C \= X, d(U,X,D), ! .
d(U/V, X, (V*D1-U*D2)/(V^2) ) :- d(U,X,D1), d(V,X,D2).
d( U^C, X, C*D*U^(C-1) ) :- atomic(C), C \= X, d(U,X,D), ! .
d(U^~C, X, Z) :- d( 1/(U^C), X, Z), ! .
d( U^(A/B),X, (A/B)*D*U^(A/B-1) ) :- atomic(A), atomic(B),
A \= X, B \= X,
d(U,X,D), ! .
d(U^~(A/B),X, Z) :- d(1/U^(A/B) , X, Z), ! .
d(U^V, X, U^V*(V*D1/U+D2*ln(U) )) :- d(U,X,D1), d(V,X,D2).