 permgroup - Maple Programming Help

# Online Help

###### All Products    Maple    MapleSim

Home : Support : Online Help : System : Libraries and Packages : Deprecated Packages and Commands : Deprecated commands : permgroup(deprecated)

permgroup

represent a permutation group

 Calling Sequence permgroup(deg, gens)

Parameters

 deg - degree of the permutation group gens - set of generators for the permutation group

Description

 • Important: The permgroup command has been deprecated. Use the superseding command GroupTheory[Group] instead.
 • The function permgroup is used as a procedure and an unevaluated procedure call. As a procedure, permgroup checks its arguments and then either exits with an error or returns the unevaluated permgroup call.
 • The first argument is the degree of the group, and should be an integer. The second argument is a set of group generators. Each generator is represented in disjoint cycle notation. The generators may be named or unnamed. A named generator is an equation; the left operand is the generator's name, the right operand is the permutation in disjoint cycle notation.
 • A permutation in disjoint cycle notation is a list of lists. Each sub-list represents a cycle; the permutation is the product of these cycles. The cycle $[{a}_{1},{a}_{2},...,{a}_{n}]$ represents the permutation which maps ${a}_{1}$ to ${a}_{2}$, ${a}_{2}$ to ${a}_{3}$, ..., ${a}_{n-1}$ to ${a}_{n}$, and ${a}_{n}$ to ${a}_{1}$. The identity element is represented by the empty list $\left[\right]$.
 • The permgroup function follows the convention that permutations act on the right''. In other words, if $\mathrm{p1}$ and $\mathrm{p2}$ are permutations, then the product of $\mathrm{p1}$ and $\mathrm{p2}$, $\mathrm{p1}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&*\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathrm{p2}$ is defined such that $\left(\mathrm{p1}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&*\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathrm{p2}\right)\left(i\right)=\mathrm{p2}\left(\mathrm{p1}\left(i\right)\right)$ for $i=1..\mathrm{deg}$.

Examples

Important: The permgroup command has been deprecated. Use the superseding command GroupTheory[Group] instead.

 > permgroup(5, {a=[[1,2], [4,5]], b=[[5,4,3,2,1]]});
 ${\mathrm{permgroup}}{}\left({5}{,}\left\{{a}{=}\left[\left[{1}{,}{2}\right]{,}\left[{4}{,}{5}\right]\right]{,}{b}{=}\left[\left[{5}{,}{4}{,}{3}{,}{2}{,}{1}\right]\right]\right\}\right)$ (1)
 > permgroup(6, {[[1,2]], [[1,2,3,4,5,6]]});
 ${\mathrm{permgroup}}{}\left({6}{,}\left\{\left[\left[{1}{,}{2}\right]\right]{,}\left[\left[{1}{,}{2}{,}{3}{,}{4}{,}{5}{,}{6}\right]\right]\right\}\right)$ (2)

the following is not legal:

 > permgroup(5, {x=[[3,4]], y=[[7,2]]});

 See Also