10.2 MakingGB’s and Inv[], Tp[]

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]}