group(deprecated)/cosrep - Maple Help

group(deprecated)

 cosrep
 express group element as product of an element in a subgroup multiplied by a right coset representative for that subgroup

 Calling Sequence cosrep(elem, sub)

Parameters

 elem - permutation or a word in the group generators sub - permutation group or a subgrel

Description

 • Important: The group package has been deprecated. Use the superseding command GroupTheory[Factor] instead.
 • If sub is a subgrel, then elem should be a word in the group generators. A two-element list will be returned. The first element is the subgroup element expressed as a word in the subgroup generators, the second is the right coset representative. The coset representative will be an element of the set returned by cosets(sub).
 • If sub is a permgroup, then elem should be a permutation in disjoint cycle notation. A two-element list is returned. The first element is a permutation contained in sub, the second is a right coset representative permutation for sub in the symmetric group of the same degree. The coset representative will be an element of the set returned by cosets(Sn, sub), where Sn is the symmetric group of the same degree as sub.
 • The command with(group,cosrep) allows the use of the abbreviated form of this command.

Examples

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

 > $\mathrm{with}\left(\mathrm{group}\right):$
 > $g≔\mathrm{grelgroup}\left(\left\{a,b,c\right\},\left\{\left[a,b,c,a,\frac{1}{b}\right],\left[b,c,a,b,\frac{1}{c}\right],\left[c,a,b,c,\frac{1}{a}\right]\right\}\right):$
 > $\mathrm{cosrep}\left(\left[c\right],\mathrm{subgrel}\left(\left\{y=\left[a,b,c\right]\right\},g\right)\right)$
 $\left[\left[{y}{,}{y}{,}{y}{,}{y}{,}{y}\right]{,}\left[{a}\right]\right]$ (1)
 > $\mathrm{pg}≔\mathrm{permgroup}\left(7,\left\{\left[\left[1,2,3\right]\right],\left[\left[3,4,5,6,7\right]\right]\right\}\right):$
 > $\mathrm{cosrep}\left(\left[\left[3,4,5,6\right]\right],\mathrm{pg}\right)$
 $\left[\left[\left[{3}{,}{4}{,}{5}{,}{7}{,}{6}\right]\right]{,}\left[\left[{6}{,}{7}\right]\right]\right]$ (2)