### 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.