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Thursday, October 7, 2010

From AbstractAlgebra for Mathematica to GAP.

A few notes about the Mathematica video's I created on YouTube.

AbstractAlgebra is a Mathematica add-on package. It is open source, has been written entirely in the Mathematica programming language by two mathematics professors Hibbard and Levasseur. The download url is

The functions I used like FormGroupoid, GenerateGroupoidByRelations and FormMorphoid are defined in a Mathematica package called Master in the AbstractAlgebra directory. The group I created as G1=FormGroupoid[Range[0,11],Mod[#1+#2,12]&] is by default available as Z[12] ( when SwitchStructureTo[Group] has been used ), in fact all groups I used are available as defaults. I wanted to demonstrate that you can define any group you want, in any case much more than the familiar 'textbook example groups'.

The AbstractAlgebra package is meant as a tool to visualize the often abstract concepts in Group Theory and other topics in Abstract Algebra. There is a book available from which you can learn Abstract Algebra with Labs and Exercises in Mathematica with the Abstract Algebra package. Other algebraic structures which can be created are Rings, Polynomials, Polynomials over Rings, Galois Fields, Permutations, Permutation Cycles and more.

The package AbstractAlgebra is NOT a tool for Computational Group Theory. Group Theory is alive as it is being actively researched. A state-of-the-art tool for Computational Group Theory is GAP. ( I might give some GAP demo's soon. )

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