Here is another GB example. This time we use the fancy Inv[] notation.
In[1]:= <<NCGB.m
In[2]:= SetNonCommutative[y, Inv[y], Inv[1-y], a, x] In[3]:= SetMonomialOrder[{ y, Inv[y], Inv[1-y], a, x}] In[4]:= resol = {y ** Inv[y] == 1, Inv[y] ** y == 1, (1 - y) ** Inv[1 - y] == 1, Inv[1 - y] ** (1 - y) == 1} |
The following commands makes a Gröbner Basis for resol with respect to the monomial order which has been set.
In[8]:= NCMakeGB[resol,3]
Out[8]= {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]} |