I have been struggling with some prolog code for several days and I couldn't find a way out of it. I am trying to write the extended Euclidean algorithm and find values p and s in :
a*p + b*s = gcd(a,b)
equation and here is what I have tried :`
common(X,X,X,_,_,_,_,_,_).
common(0,Y,Y,_,_,_,_,_,_).
common(X,0,X,_,_,_,_,_,_).
common(X,Y,_,1,0,L1,L2,SF,TF):-
append(L1,1,[H]),
append(L2,0,[A]),
SF is H ,
TF is A,
common(X,Y,_,0,1,[H],[A],SF,TF).
common(X,Y,_,0,1,L1,L2,SF,TF):-
append(L1,0,[_,S2]),
append(L2,1,[_,T2]),
Q is truncate(X/Y),
S is 1-Q*0,T is 0-Q*1 ,
common(X,Y,_,S,T,[S2,S],
[T2,T],SF,TF).
common(X,Y,N,S,T,[S1,S2],[T1,T2],SF,TF):-
Q is truncate(X/Y),
K is X-(Y*Q),
si_finder(S1,S2,Q,SF),
ti_finder(T1,T2,Q,TF),
common(Y,K,N,S,T,[S2,S],[T2,T],SF,TF).
si_finder(PP,P,Q,C):- C is PP - Q*P.
ti_finder(P2,P1,QA,C2):- C2 is P2 - QA*P1.
After a little search I found that s and p coefficients start from 1 and 0 and the second values for them are 0 and 1 respectively.Then it continues in a pattern which is what I have done in si_finder and ti_finder predicates.Common predicates are where I tried to control the pattern recursively. However the common predicates keeps on returning false in every call. Can anyone help me implement this algorithm in Prolog.
Thanks in advance.