Exploring Abstract Algebra with Mathematica

Al Hibbard - Central College - e-mail homepage

Ken Levasseur - UMass-Lowell - e-mail homepage

Palettes in Exploring Abstract Algebra with Mathematica

The users of the book Exploring Abstract Algebra with Mathematica will find a number of palettes available on the CD. With a proper installation, the palettes are available from the File/Palettes menu of Mathematica (only this first palette--from which all others can be obtained--is placed in this menu), as well as in the Appendix of the documentation in the HelpBrowser.

Pink buttons are for information only

Green buttons perform an action

Gray buttons bring up other palettes

Yellow buttons paste in the given text

AbstractAlgebra palette

From this main palette, all the other palettes can be obtained. As one can see, this palette contains the following buttons:

Needs["AbstractAlgebra`Master`"] - loads the Master package to begin working with the AbstractAlgebra packages
SwitchStructureTo[Group] - specifies that groups are the default structures for future operations
SwitchStructureTo[Ring] - specifies that rings are the default structures for future operations
Help with the palettes - brings up a notebookgiving additional details regarding how to use these palettes
Groupoids - brings up a palette listing many of the common built-in Groupoids
Ringoids and Morphoids - brings up a palette listing many of the common built-in Ringoids and Morphoids
General AA functions - functions that are applicable generally or apply to both Groupoids and Ringoids
Group functions - functions for working with Groupoids
Permutations functions - functions for working with permutations
Morphism functions - functions for working with Morphoids
Ring functions - functions for working with Ringoids
Polynomial functions - functions for working with polynomials over various rings
Matrix functions - functions for working with matrices over various rings
Galois field functions - functions for working with Galois fields
Z[Sqrt[d]] functions - functions for working with Z[Sqrt[d]] rings
palettes for working with groups/rings - brings up a notebook containing a place to enter a group or a ring and oppotunities to explore this group or ring - see below for further details
All AA palettes - brings up a narrow, scrollable notebook containing all of the palettes that are listed above, except for the last one

Groupoids

Ringoids and Morphoids

General AA functions

Group functions

Permutation functions

Morphism functions

Ring functions

Polynomial functions

Matrix functions

Galois field functions

Group (ring) characteristics/properties

After you enter a Groupoid or Ringoid, you are given the following choices:

[Graphics:MULTIPalgr1.gif]

The buttons accomplish the following:

Palette of elements - for Groupoids or Ringoids, provides a button for each element
GroupCalculator - calculate products (and inverses) in any Groupoid
Properties of Groupoid elements - look at information relative to each element in a Groupoid
Properties of a Groupoid - look at status of many possible properties in a Groupoid
Properties of Ringoid elements - look at information relative to each element in a Ringoid
Properties of a Ringoid - look at status of many possible properties in a Ringoid

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