TABLE OF CONTENTS In this section we describe two operators that manipulate general polynomial expressions. Both of the operators are based on the two distributive transformations:
The collection of coefficients of like terms in a polynomial occurs frequently in algebraic manipulation. During automatic simplification this operation is applied only to monomials with coefficient parts that are rational numbers. The collection of (rational and non-rational) coefficients is obtained with the Collect_terms operator. The goal of this operator is given in the next definition.
Definition 6.42. An algebraic expression u is in collected form in a set S of generalized variables if it satisfies one of the following properties:
u is a GME in S.
u is a sum of GMEs in S with distinct variable parts.
The definition is similar to Definition 6.16 for general polynomial expressions (page 225), except now property (2) requires that the variable parts be distinct.
The expression
is in collected form in S={x, y}, where the two distinct variable parts are xy and x. On the other hand, the expanded form of Expression (6.32)
is not in collected form (in S) because there are two monomials with variable part xy and two with variable part x.
The collected form depends, of course, on which expressions are taken as the generalized variables. For example, if S={ a, b}, the collected form of Expression (6.33) is (2 xy
