[GAP Forum] Re:Extending Orderings, perhaps better posed

[Alexander Hulpke]

Randy Cone asked:


>
> If a free (associative) algebra is created in GAP, say on the  
> generators
> "a","b","c"; is there a way to use the built-in GAP orderings (on  
> associative
> words) on the multiplicative semigroup of words these generators form?
>

Associative words and associative algebra elements really are  
diffferent datatypes and functionality for one does not apply to the  
other.

What you could do is to form the semigroup algebra of the free  
semigroup (or free abelian semigroup), this way there is a connection  
between semigroup and algebra.

The other option would be to write small functions that take a  
monomial and build a ``corresponding'' semigroup element, using these  
``shadows'' for comparison.

Best wishes,

     Alexander Hulpke