All the examples in the Mathematica documentation specify that the syntax for the
GroebnerBasis command is
however it does return a result when ran just as
(although it does put a red caret in at the end, indicating it is missing an expected second parameter). I assume that, in this case,
GroebnerBasis makes some choice for the variables. My intuition was that it would be
GroebnerBasis[polys] == GroebnerBasis[polys, Variables[polys]], but that does not seem to be the case. What is the behavior of the
GroebnerBasis command without a variable specification?