Construct the free abelian group F on n generators, where n is a positive integer. The i-th generator may be referenced by the expression F.i, i = 1, ..., n. Note that a special form of the assignment statement is provided which enables the user to assign names to the generators of F. In this form of assignment, the list of generator names is enclosed within angle brackets and appended to the variable name on the left hand side of the assignment statement.
> F := FreeAbelianGroup(2);creates the free abelian group on two generators. Here the generators may be referenced using the standard names, F.1 and F.2.
The statement
> F<x, y> := FreeAbelianGroup(2);defines F to be the free abelian group on two generators and assigns the names x and y to the generators.
Given an abelian group A with generators e_1, ..., e_r and a sequence Q = [a_1, ..., a_r] of integers, construct the element a_1 e_1 + ... + a_r e_r of A.
Given an abelian group A with exactly one generator x, construct the element n x.
Construct the identity element (empty word) for the abelian group A.
Let A be an abelian group with basis e_1, ..., e_r and suppose x is an element of A, where x = a_1 e_1 + ... + a_r e_r. This function returns the sequence Q of r integers defined by Q[i] = (a_i), for i = 1, ..., r.[Next] [Prev] [Right] [Left] [Up] [Index] [Root]