Construction of rankings on partial derivatives
Oleg Golubitsky · ACM communications in computer algebra · 2006
In differential algebra [1], rankings on partial derivatives play the same role as admissible term orders in the theory of Gröbner bases. In fact, an admissible term order is a particular case of a ranking on partial derivatives of a single differential indeterminate. The introduction of a ranking allows to select leading derivatives in differential polynomials, define a pseudo-reduction relation, and consider autoreduced sets; the latter are the a tool for representing differential ideals.