Question: Factorization in a linear combination of a given base.

Hi! This is probably simple, but
I would like to know if there's an specific algorithm to do this:

let B = {x[i], i=1..n} in such a way that:

f( B ) = Sum(a[i]*b[i], i=1..N); a_i in R; b_i in B; N>n.

so Linearcomb: f->V(R).

Linearcomb( f ) =

 (Sum(a[j],j in J))*x[1]+(Sum(a[k],k in K))*x[2] + ... +(Sum(a[z],z in Z))*x[n].

with V(R) a vector space; R the Real numbers, and B the base. Neither the "factorize", nor the "simplify" are proving useful to this. Is there something i'm missng?

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