On Arithmetical Formulas Whose Jacobians are Groebner Bases
Denis Charles, Kenneth W. Regan · 2000
We exhibit classes of polynomials whose sets of first partial derivatives form Grobner bases, with respect to all term orders. The classes are defined by syntactic constraints on arithmetical formulas defining the polynomials. Read-once formulas without constants also have this property, while those with constants have a weaker “Grobner-bounding” property introduced here. The same properties hold even with arbitrary powering of subterms of the formulas.