Interesting Examples from AbstractAlgebra
This section shows interesting examples of Groupoids, Ringoids, Morphoids, or uses of AbstractAlgebra. As you work with the packages, please forward your findings. Use the Feedback menu above.
- Use GenerateGroupoid to create groups based on families of functions (under composition). Here are three instances. Try these out and see what you get. Each of these can be also viewed (with output) in a Mathematica notebook.
- G1=GenerateGroupoid[{1/x,1/(1-x)},Simplify[#1/.{x->#2}]&]
- G2=GenerateGroupoid[{I x,1/x},Simplify[#1/.{x->#2}]&]
- Caution: Don't automatically assume you will get a group. Consider:
G3=GenerateGroupoid[Map[Simplify,{1/x,(x+1)/(1-x)}],Simplify[#1/.{x->#2}]&]
- Group version of Pascal's Triangle
Prepared by Al Hibbard. Most recent update: 6/16/2006. This page has been viewed 334 times since June 16, 2006. The entire EAAM web site has had 669,407 hits since July 23, 2002.
