coefficient -- coefficient of a monomial

Synopsis

Usage:
coefficient(m,f)
Inputs:
- m, a ring element, a monomial
- f, a ring element, in the same ring R as m
Outputs:
- a ring element, the coefficient of the monomial m in f as an element of the coefficient ring of R

i1 : R = GF(25,Variable=>a)[x,y,z];

i2 : f = ((a+1)*x+a*y+a^2*z)^2

        2                    2                      2
o2 = a*x  - 2x*y + (- a - 1)y  - 2a*x*z + 2y*z + a*z

o2 : R

i3 : coefficient(y^2,f)

o3 = - a - 1

o3 : GF 25

The returned value is an element of the coefficient ring, even in the case when that ring is another polynomial ring.

i4 : S = R[r,s,t];

i5 : coefficient(r,a*x*(r+a*s))

o5 = a*x

o5 : R