## B Conversion between Generating Sets

We list the three sets of generators and relations among them. We first list below , , , :
We now express the and in terms of , , , :
Further we also list below , , , in terms of :
This proves that since the , generate the required module, the , , , and ,
, also generate the same module.
The Gröbner basis is given in terms of the above generators as follows: , ,
, , and .