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grelgroup

represent a group by generators and relations

 Calling Sequence grelgroup(gens, rels)

Parameters

 gens - set of names taken to be the generators of the group rels - set of relations among the generators which define the group

Description

 • The function grelgroup is used as a procedure and an unevaluated procedure call. As a procedure, grelgroup checks its arguments and then either exits with an error or returns the unevaluated grelgroup call.
 • The first argument is a set of Maple names which stand for the generators of the group. The second argument is a set of words'' in the generators. A word'' is a list of generators and/or inverses of generators representing a product.  The inverse of a generator $g$ is represented by $\frac{1}{g}$. An empty list represents the identity element.  The words w1, w2, ..., wn in rels are such that the relations $\mathrm{w1}=\mathrm{w2}=\mathrm{...}=\mathrm{wn}=1$ define the group.

Examples

 > $\mathrm{grelgroup}\left(\left\{a,b\right\},\left\{\left[a,a,a\right],\left[b,b\right],\left[a,b,\frac{1}{a},\frac{1}{b}\right]\right\}\right)$
 ${\mathrm{grelgroup}}{}\left(\left\{{a}{,}{b}\right\}{,}\left\{\left[{b}{,}{b}\right]{,}\left[{a}{,}{a}{,}{a}\right]{,}\left[{a}{,}{b}{,}\frac{{1}}{{a}}{,}\frac{{1}}{{b}}\right]\right\}\right)$ (1)

the following will give an error:

 > $\mathrm{grelgroup}\left(\left\{a,b\right\},\left\{\left[a,\frac{1}{c},a\right],\left[b,a\right]\right\}\right)$