This program searches for a path from a given element to the identity using a set of relations. The result is a derivation to the “most-simplified” word, which is possibly the identity.
Relations:
Searching for:
Relations may be inputted in a number of ways. Relations may be separated by newlines or semicolons. A single relation is something which is equal to the identity (such as ij^-1k), though for shorthand they may have an equals sign, as in the case of ij=k; jk=i; ki=j. Exponents for generators are not parenthesized, so x^-22y^1 is valid and correct. The symbol 1 is the identity element.
The “Add inverses” option lets the search use the inverses of the relations as well. Disable it for dealing with monoids rather than groups. Note, however, that since the search starts from the given element, you will need to use the inverses of the monoid generators.
The “Find order” option searches for the identity from all powers of the given element.