# linearPart -- returns linear part of a polynomial

## Synopsis

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

## Description

 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

## For the programmer

The object linearPart is .