group(deprecated)/elements - Maple Help

group(deprecated)

 elements
 generate the elements of a permutation group

 Calling Sequence elements(pg) elements(gens)

Parameters

 pg - permutation group gens - set of permutations in disjoint cycle notation

Description

 • Important: The group package has been deprecated. Use the superseding command GroupTheory[Elements] instead.
 • The function returns a set of permutations corresponding to the elements of the permutation group represented by pg or gens.
 • When the parameter pg is used, the function returns the elements of pg.
 • When the parameter gens is used, the function returns the elements of the permutation group generated by gens.
 • The command with(group,elements) allows the use of the abbreviated form of this command.

Examples

Important: The group package has been deprecated. Use the superseding command GroupTheory[Elements] instead.

 > $\mathrm{with}\left(\mathrm{group}\right):$
 > $\mathrm{pg}≔\mathrm{permgroup}\left(4,\left\{\left[\left[1,2\right],\left[3,4\right]\right],\left[\left[1,4\right],\left[2,3\right]\right]\right\}\right):$
 > $\mathrm{elements}\left(\mathrm{pg}\right)$
 $\left\{\left[\right]{,}\left[\left[{1}{,}{2}\right]{,}\left[{3}{,}{4}\right]\right]{,}\left[\left[{1}{,}{3}\right]{,}\left[{2}{,}{4}\right]\right]{,}\left[\left[{1}{,}{4}\right]{,}\left[{2}{,}{3}\right]\right]\right\}$ (1)
 > $\mathrm{elements}\left(\left\{\left[\left[1,2\right],\left[3,4\right]\right],\left[\left[1,4\right],\left[2,3\right]\right]\right\}\right)$
 $\left\{\left[\right]{,}\left[\left[{1}{,}{2}\right]{,}\left[{3}{,}{4}\right]\right]{,}\left[\left[{1}{,}{3}\right]{,}\left[{2}{,}{4}\right]\right]{,}\left[\left[{1}{,}{4}\right]{,}\left[{2}{,}{3}\right]\right]\right\}$ (2)