Operations - Maple Help

GroupTheory

 Operations
 obtain a module of group operations

 Calling Sequence Operations(g)

Parameters

 g - group data structure

Description

 • The procedure Operations returns a module exporting procedures that implement the group operations for the elements of g. The module is in the same format that Group accepts for specifying the operations on a custom group:

 symbol description . Two-argument procedure to compute group operation / One-argument procedure to invert element 1 Unit element of the group = Two-argument procedure to test equality < Two-argument procedure to determine ordering print One-argument procedure to display elements

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $\mathrm{gens1}≔\left[\mathrm{Perm}\left(\left[\left[1,2\right],\left[3,4,5\right]\right]\right),\mathrm{Perm}\left(\left[\left[1,2,3\right],\left[4,5\right]\right]\right)\right]$
 ${\mathrm{gens1}}{≔}\left[\left({1}{,}{2}\right)\left({3}{,}{4}{,}{5}\right){,}\left({1}{,}{2}{,}{3}\right)\left({4}{,}{5}\right)\right]$ (1)
 > $\mathrm{g1}≔\mathrm{PermutationGroup}\left(\mathrm{gens1}\right)$
 ${\mathrm{g1}}{≔}⟨\left({1}{,}{2}\right)\left({3}{,}{4}{,}{5}\right){,}\left({1}{,}{2}{,}{3}\right)\left({4}{,}{5}\right)⟩$ (2)
 > $\mathrm{ops1}≔\mathrm{Operations}\left(\mathrm{g1}\right)$
 ${\mathrm{ops1}}{≔}{\mathbf{module}}\left({}\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{local}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{ModuleApply}}{,}{\mathrm{ModuleLoad}}{;}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{export}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathrm{.}}{,}{\mathrm{/}}{,}{\mathrm{=}}{,}{\mathrm{<}}{,}{\mathrm{print}}{,}{1}{;}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\mathbf{end module}}$ (3)
 > $\mathrm{ops1}:-\mathrm{.}\left(\mathrm{gens1}\left[1\right],\mathrm{gens1}\left[2\right]\right)$
 $\left({1}{,}{3}{,}{5}\right)$ (4)
 > $\mathrm{ops1}:-\mathrm{/}\left(\mathrm{gens1}\left[1\right]\right)$
 $\left({1}{,}{2}\right)\left({3}{,}{5}{,}{4}\right)$ (5)
 > $\mathrm{ops1}:-\mathrm{.}\left(\mathrm{gens1}\left[1\right],\mathrm{ops1}:-\mathrm{/}\left(\mathrm{gens1}\left[1\right]\right)\right)$
 $\left(\right)$ (6)
 > $\mathrm{ops1}:-\mathrm{=}\left(\mathrm{ops1}:-\mathrm{1},\right)$
 $\left(\right){=}\left(\right)$ (7)
 > $\mathrm{evalb}\left(\right)$
 ${\mathrm{true}}$ (8)

Compatibility

 • The GroupTheory[Operations] command was introduced in Maple 17.