### Begin Citation ### Do not delete this line ### %R 2000-07 %U /web/faculty/regan/papers/DeRe00.ps %A Denis, Charles %A Regan, Kenneth %T On Arithmetical Formulas Whose Jacobians are Groebner Bases %D July 13, 2000 %I Department of Computer Science and Engineering, SUNY Buffalo %K polynomial, ideal, Groebner basis, Jacobian, computational complexity %X We exhibit classes of polynomials whose sets of k-th partial derivatives form Groebner bases for all k, with respect to all term orders. The classes are defined by syntactic constraints on arithmetical formulas defining the polynomials. Read-once formulas without constants have this property for all k, while those with constants have a weaker ``Groebner-bounding'' property introduced here. For k = 1 the same properties hold even with arbitrary powering of subterms of the formulas.