Exploring Abstract Algebra with Mathematica

Palettes with AbstractAlgebra

Starting with version 3.0, Mathematica included palettes as part of its user interface. The AbstractAlgebra package also includes a collection of palettes. When properly installed, the main palette, AbstractAlgebra, can be found under the Palettes submenu in the File menu of Mathematica. All the other palettes are obtained from this one. (Note that one configuration of GroupCalculator acts as a palette, found as the second to last item on the main palette.)

This section displays and describes each of the palettes that are available. This information is also available in the documentation in the Help Browser. Although initially the palettes were only available with the EAAM book, they are now included in the basic AbstractAlgebra package.

The colors of the buttons in the palettes convey information, as indicated below.

• Pink buttons are for information only
• Green buttons perform an action
• Gray buttons generally paste in the command or bring up other palettes
• Yellow buttons paste in the given text

You can either scroll through the displays and descriptions or you may select a particular palette from the following list.

AbstractAlgebra, 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

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 notebook giving 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

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Groupoids

For a description of the functions/commands listed here, either consult the AbstractAlgebra documentation in the Help Browser, type a ? followed by the function name in Mathematica after having read in the packages, or read the usage statements at this web site.

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Ringoids and Morphoids

For a description of the functions/commands listed here, either consult the AbstractAlgebra documentation in the Help Browser, type a ? followed by the function name in Mathematica after having read in the packages, or read the usage statements at this web site.

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General AA functions

For a description of the functions/commands listed here, either consult the AbstractAlgebra documentation in the Help Browser, type a ? followed by the function name in Mathematica after having read in the packages, or read the usage statements at this web site.

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Group functions

For a description of the functions/commands listed here, either consult the AbstractAlgebra documentation in the Help Browser, type a ? followed by the function name in Mathematica after having read in the packages, or read the usage statements at this web site.

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Permutation functions

For a description of the functions/commands listed here, either consult the AbstractAlgebra documentation in the Help Browser, type a ? followed by the function name in Mathematica after having read in the packages, or read the usage statements at this web site.

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Morphism functions

For a description of the functions/commands listed here, either consult the AbstractAlgebra documentation in the Help Browser, type a ? followed by the function name in Mathematica after having read in the packages, or read the usage statements at this web site.

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Ring functions

For a description of the functions/commands listed here, either consult the AbstractAlgebra documentation in the Help Browser, type a ? followed by the function name in Mathematica after having read in the packages, or read the usage statements at this web site.

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Polynomial functions

For a description of the functions/commands listed here, either consult the AbstractAlgebra documentation in the Help Browser, type a ? followed by the function name in Mathematica after having read in the packages, or read the usage statements at this web site.

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Matrix functions

For a description of the functions/commands listed here, either consult the AbstractAlgebra documentation in the Help Browser, type a ? followed by the function name in Mathematica after having read in the packages, or read the usage statements at this web site.

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Galois field functions

For a description of the functions/commands listed here, either consult the AbstractAlgebra documentation in the Help Browser, type a ? followed by the function name in Mathematica after having read in the packages, or read the usage statements at this web site.

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Group (ring) characteristics/properties

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

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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Prepared by Al Hibbard. Most recent update: 6/16/2006. This page has been viewed 269 times since June 16, 2006. The entire EAAM web site has had 669,502 hits since July 23, 2002.