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Prolog - Simplify Derivative

so I just started working with Prolog this semester and got homework to implement a fairly simple d(function, variable, derivative)one that I liked:

d(X,X,1) :- !.
d(C,X,0) :- atomic(C). %, (C \= X).
d(X**E,X,E*X**(E-1)).
d(U+V,X,A+B) :- d(U,X,A), d(V,X,B).
d(U-V,X,A-B) :- d(U,X,A), d(V,X,B).
d(U*V,X,DU*V+U*DV) :- d(U,X,DU), d(V,X,DV).
d(U/V,X,(DU*V-U*DV)/(V*V)) :- d(U,X,DU), d(V,X,DV).

I know that this is not complete, but it covers all the tasks required in the exercise.

However, ?- d((x*x+2*x+3)/(3*x),x,R). leads to

R = ((1*x+x*1+ (0*x+2*1)+0)* (3*x)- (x*x+2*x+3)* (0*x+3*1))/ (3*x* (3*x)). which doesn't look beautiful at all. is / 2, unfortunately, does not like my x, since it is not a number ...

Is there a simple solution to achieve a cleaner result?

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2 answers

I would prefer this as two separate issues :

First, get the correct definition (you are probably approaching, depending on your specific requirements).

. , ., // ( / ).

" ".

2015-05-14

, , :

expr_simplified(A,B) :-
   (  atomic(A)
   -> A = B
   ;  ( A = X+0 ; A = 0+X ; A = 1*X ; A = X*1 )
   -> expr_simplified(X,B)
   ;  ( A = 0*_ ; A = _*0 )
   -> B = 0
   ;  A = X+X
   -> B = X*2
   ;  A = X*X
   -> B = X**2
   ;  A = X**1
   -> B = X
   ;  A =.. [F|Xs0],                          % defaulty catch-all
      maplist(expr_simplified,Xs0,Xs),
      B =.. [F|Xs]
   ).

, , . expr_simplified/2, :

?- A = ((1*x+x*1+(0*x+2*1)+0)*(3*x)-(x*x+2*x+3)*(0*x+3*1))/(3*x*(3*x)),
   expr_simplified(A,B),
   expr_simplified(B,C),
   expr_simplified(C,D).
A = ((1*x+x*1+(0*x+2*1)+0)*(3*x)-(x*x+2*x+3)*(0*x+3*1))/(3*x*(3*x)),
B = ((x+x+(0+2))*(3*x)-(x**2+2*x+3)*(0+3))/(3*x)**2,
C = ((x*2+2)*(3*x)-(x**2+2*x+3)*3)/(3*x)**2,
D = C.                                        % fixed point reached

, , .

+1

- x , . ,

set_vars(E, Vs, Ev) :-
    E =.. [F,L,R],
    set_vars(L, Vs, Lv),
    set_vars(R, Vs, Rv),
    Ev =.. [F,Lv,Rv].
set_vars(V, Vs, N) :- memberchk(V=N, Vs).
set_vars(V, _, V).


?- d((x*x+2*x+3)/(3*x),x,R), set_vars(R,[x=5],E), T is E.
R = ((1*x+x*1+ (0*x+2*1)+0)* (3*x)- (x*x+2*x+3)* (0*x+3*1))/ (3*x* (3*x)),
E = ((1*5+5*1+ (0*5+2*1)+0)* (3*5)- (5*5+2*5+3)* (0*5+3*1))/ (3*5* (3*5)),
T = 0.29333333333333333

, :

d(X,V,1) :- X == V, !.
...

set_vars/3,

?- d((T*T+2*T+3)/(3*T),T,R), T=8, V is R.
T = 8,
R = ((1*8+8*1+ (0*8+2*1)+0)* (3*8)- (8*8+2*8+3)* (0*8+3*1))/ (3*8* (3*8)),
V = 0.3177083333333333.
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