21.4 Second Example

As a second example, after loading the files NCGB.m, SmallBasis.m and RemoveRedundent.m, we can execute the following commands to compute a Gröbner Basis for the set of relations {x2 - a,x3 - b}:

In[3]:= SetKnowns[a,b,x]  
 
In[4]:= NCMakeGB[{x**x-a,x**x**x-b},10]  
Out[4]= {-a + x ** x, -b + a ** x, -b + x ** a, -a ** a + b ** x,  
>    -a ** b + b ** a, -a ** a + x ** b, -b ** b + a ** a ** a}

Now, one might want to find a smaller generating set for the ideal specified above. The following command does that and took 9 seconds using the C++ version of the code.

In[5]:= SmallBasis[%4,{},3]  
Out[5]= {a ** x -> b, x ** x -> a}