# partialsum(y,k,0,n) is partial sum of y index k from 0 to n ;

partialsum(y_,k_,a_,b_):= sum(y,k,a,b);
partialsum(y_,k_,b_):= sum(y,k,0,b);
partialsum(y_,k_):= sum(y,k,0,n);

partialsum(a_+b_,k_):= partialsum(a,k)+partialsum(b,k);

partialsum(y_):=sum(y,k,0,n);