Question

I am trying to multiply two vectors in Prolog but, if those vectors contain imaginary numbers, I can’t get it to work. My code so far:

vector_product([X|Xs],[Y|Ys],OP) :-
    inner(Xs,Ys,OP1),
    OP is X*Y+OP1.
vector_product([],[],0).

Answer 1

See if this could help you…

Formulae from Wikipedia:

% (a+bi) + (c+di) = (a+c) + (b+d)i
c_sum((A,B), (C,D), (E,F)) :- E is A+C, F is B+D.

% (a+bi) (c+di) = (ac-bd) + (bc+ad)i
c_mul((A,B), (C,D), (E,F)) :- E is A*C - B*D, F is B*C + A*D.

Numbers are represented as (Real, Imaginary).

vector_product([X|Xs], [Y|Ys], OP) :-
    vector_product(Xs, Ys, OP1),
    c_mul(X, Y, M),
    c_sum(M, OP1, OP).
vector_product([], [], (0,0)).