Some group theory commands with MAPLE

This page describes a small file with some elementary group theory commands in MAPLE which may be useful to help in teaching a course in group theory. This package requires MAPLE's group package.

The MAPLEV5 group2.1 package (or the MAPLEV4 group2 package or the MAPLE7 group2.2 package ) contains several routines designed to

1. list all the elements of a permgroup as disjoint cycles (there are also routines to convert to and from list or array permutation notation)
2. find all elements of a given order in a permgroup,
3. find the group table of a permgroup (both as a table of permutations and as a more compact looking table of indexed letters),
4. finds all elements conjugate to a given element in a permgroup,
5. all conjugacy classes of a permgroup,
6. the value (i)p of a permutation as a function

                   p : {1,2,...,n} -> {1,2,...,n}
   

   (or as a function on the columns of a matrix) on an element i where p acts on the right,
7. the "swapping number" (or "length") of a permutation,
8. the sign of the permutation,
9. the permutation matrix associated to a permutation in disjoint cycle notation,
10. the left and right permutation action of a permutation (in disjoint cycle notation) on a vector (in list notation); there are two routines, one for the left action, one for the right action,
11. multiply a list of elements of a permgroup, written in disjoint cycle notation,
12. representation theoretic commands, such as induce, innerprod, and is_reducible,
13. right_coset_reps (and left_coset_reps, which agrees with cosets in the group package).

The MAPLEV5 worksheet gives examples of these procedures.

The html version of this worksheet is also available.

If you have MAPLEV5 and Windows 95 or better then here is how to load the group2 package:

• copy group21_v5.mpl into the /maplev4/share/group subdirectory,
• read this mpl file and use the commands in maple as indicated in the maple worksheet.

Other MAPLE packages which use group theory are ACE, the MAPLE packages group and combinat, and the MAPLEV5 share packages perm and coxeter.

Created 3-28-97 and last updated 6-6-2004.

This page is at the url: http://www.usna.edu/Users/math/wdj/maplestuff/group.html