linearPart -- returns linear part of a polynomial

Synopsis

Usage:

l = linearPart(f)
Inputs:
- f, a ring element, f is a polynomial
Outputs:
- l, a ring element, l is the sum of the terms of f whose monomial is a variable

i1 : R = ZZ/32003[a,b,c];

i2 : f = a^2 + 3*b + 5*a*b*c + 2*a +b^2;

i3 : linearPart f

o3 = 2a + 3b

o3 : R

If we have a polynomial ring over another polynomial ring, the command only looks at the exponents on the new set of variables.

i4 : S = ZZ/32003[a,b,c][x,y,z];

i5 : g = a*b*x + 3*y + a + b^2

                   2
o5 = a*b*x + 3y + b  + a

o5 : S

i6 : linearPart g

o6 = a*b*x + 3y

o6 : S

Note that in the previous example, linearPart g does not include a but does include a*b*x