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group(deprecated)

 pres
 find a presentation for a subgroup of a group

 Calling Sequence pres( sg )

Parameters

 sbgrl - subgroup of a group given by generators and relations (i.e. a subgrel

Description

 • Important: The group package has been deprecated. Use the superseding package GroupTheory instead.
 • This procedure attempts to find a set of relations among the given subgroup's generators sufficient to define the subgroup. The result is returned as a grelgroup.
 • The algorithm uses Todd-Coxeter coset enumeration, which is an inherently non-terminating process for infinite groups. Therefore, the algorithm will halt with an exception if too many cosets are generated during an attempt to enumerate cosets of a subgroup. The point at which the coset enumeration terminates is controlled by the environment variable _EnvMaxCosetsToddCoxeter, which has the default value $128000$.

Examples

Important: The group package has been deprecated. Use the superseding package GroupTheory instead.

 > $\mathrm{with}\left(\mathrm{group}\right):$
 > $g≔\mathrm{grelgroup}\left(\left\{a,b,c,d\right\},\left\{\left[a,b,c,\frac{1}{d}\right],\left[b,c,d,\frac{1}{a}\right],\left[c,d,a,\frac{1}{b}\right],\left[d,a,b,\frac{1}{c}\right]\right\}\right):$
 > $\mathrm{sg}≔\mathrm{subgrel}\left(\left\{x=\left[a,b\right],y=\left[a,c\right]\right\},g\right):$
 > $\mathrm{pres}\left(\mathrm{sg}\right)$
 ${\mathrm{grelgroup}}{}\left(\left\{{x}{,}{y}\right\}{,}\left\{\left[\frac{{1}}{{x}}{,}{y}{,}{y}{,}\frac{{1}}{{x}}{,}\frac{{1}}{{y}}{,}{x}{,}{x}{,}\frac{{1}}{{y}}\right]{,}\left[\frac{{1}}{{x}}{,}{y}{,}\frac{{1}}{{x}}{,}\frac{{1}}{{y}}{,}{x}{,}{y}{,}{x}{,}\frac{{1}}{{y}}\right]{,}\left[{y}{,}\frac{{1}}{{x}}{,}\frac{{1}}{{x}}{,}\frac{{1}}{{x}}{,}{y}{,}{x}{,}\frac{{1}}{{y}}{,}{x}{,}\frac{{1}}{{y}}{,}{x}\right]\right\}\right)$ (1)
 > $s≔\mathrm{subgrel}\left(\left\{x=\left[a,b,\frac{1}{a}\right]\right\},\mathrm{grelgroup}\left(\left\{a,b\right\},\left\{\left[b,b\right],\left[a,a,a\right]\right\}\right)\right):$
 > $\mathrm{pres}\left(s\right)$