Many of this is just a single or immediate step beyond the documentation. I wish can be advanced further.
https://gist.github.com/Observatorio-de-Matematica/6ee41a31409268be7804ed4f2e39c68b
https://gist.github.com/Observatorio-de-Matematica/72ebb0a98029e96f336ed2c8b575de68
https://gist.github.com/Observatorio-de-Matematica/11bbd98efd2e1b11c32553f0ff9fb766
Old Macsyma
http://kfe.fjfi.cvut.cz/~liska/ca/node123.html#SECTION00532400000000000000
Pascual Jara from Universidad de Granada made some use of this package.
https://gist.github.com/Observatorio-de-Matematica/f5fcef35a50b47347d9fabbd04026555
https://gist.github.com/Observatorio-de-Matematica/d5ed02e7f9e8ccc8d6a73e002d6103ec
https://gist.github.com/Observatorio-de-Matematica/71664c74cd31f3aca22367fb5997d4a9
https://gist.github.com/Observatorio-de-Matematica/92e32329235e0dc3d93b69a77c80b288
Ray D. Sameshima
https://github.com/raydsameshima/Groebner
Vladimir Rutsky
https://github.com/rutsky/semester07/blob/master/Computer_algebra/toric_ideal.wxm