Compute with and visualize permutation groups, finitely presented groups, symbolic groups, and more
Construct cyclic, dihedral, Hamiltonian, linear, semi-linear, and many, many other types of groups, as permutation groups or finitely presented groups; and construct many symbolic types of linear and semi-linear groups
Compute group properties, including the center, centralizer, normal closures, minimal normal subgroup, etc.
Test group properties, such as if a subgroup is normal or a group is directly decomposable
Compute with polynomial ideals in commutative polynomial rings over various fields
Work with matrices in matrix rings
Explore differential rings and Ore rings
Compute towers of field extensions
And more much!
Teaching Group Theory with the GroupTheory Package
Abstract concepts are easier to grasp when you can see them, and Maple provides many helpful visualizations, especially in group theory. These include symmetries of a graph, Cayley graphs, Cayley tables, the lattice of subgroups of a group, and more.
Cayley graph the dihedral group of order 3
Visualization of the subgroup lattice of a group
Cayley table of the Symmetric Group on 3 letters
Cayley Table of a permutation group
Polynomial ideals
Field extensions
Lie Algebras
Galois Fields
Ore Algebras
etc.
Magmas
Overview of the Polynomial Ideals package
Demonstrating concepts and working through examples during lectures
Exploring “what if” scenarios, including on-the-fly responses to questions during class and independent student explorations
Developing lecture notes, assignments, and student resources that can be viewed in Maple, through a web browser, or as PDFs
Working through assignments, including written explanations about reasoning and methods
Investigating, developing, and presenting results for project-based learning activities
Creating custom, interactive applications and algorithms
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