The following command converts a list of relations to a list of rules subordinate to the monomial order specified above.
In[9]:= PolyToRule[%]
Out[9]= {y ** Inv[1 - y] -> -1 + Inv[1 - y], y ** Inv[y] -> 1, > Inv[1 - y] ** y -> -1 + Inv[1 - y], Inv[y] ** y -> 1, > Inv[y] ** Inv[1 - y] -> Inv[1 - y] + Inv[y], > Inv[1 - y] ** Inv[y] -> Inv[1 - y] + Inv[y]} |
The following command converts a list of rules to a list of relations.
In[10]:= PolyToRule[%]
Out[10]= {1 - Inv[1 - y] + y ** Inv[1 - y], -1 + y ** Inv[y], > 1 - Inv[1 - y] + Inv[1 - y] ** y, -1 + Inv[y] ** y, > -Inv[1 - y] - Inv[y] + Inv[y] ** Inv[1 - y], > -Inv[1 - y] - Inv[y] + Inv[1 - y] ** Inv[y]} |
We can apply the rules in §10.3 repeatedly to an expression to put it into “canonical form.” Often the canonical form is simpler than what we started with.
In[11]:= Reduction[{Inv[y]**Inv[1-y] - Inv[y]}, Out[9]]
Out[11]= {Inv[1 - y]} |