The study of differential algebraic geometry and model theory occupies a pivotal position at the interface of algebra, geometry, and logic. Differential algebraic geometry investigates solution sets ...

Transactions of the American Mathematical Society, Vol. 365, No. 9 (SEPTEMBER 2013), pp. 4575-4632 (58 pages) In this paper, an intersection theory for generic differential polynomials is presented.

Take graded Grassmann algebras and equip them with a differential of degree +1 squaring to 0. The result, quasi-free differential graded algebras, happens to be equivalent to ∞ \infty-Lie algebras ...

Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central ...

In 1970, Robert Risch published [Ri70], which sketched in four pages how to bound the torsion of a divisor on an algebraic curve, and thus provided the "missing link" in a comprehensive algorithm that ...

Abstract: Many systems can be represented using polynomial differential equations, particularly in process control, biotechnology, and systems biology [1], [2]. For example, models of chemical and ...

The conference "Numerical Algebra, Matrix Theory, Differential-Algebraic Equations, and Control Theory" brought together about 160 experts in the mathematical research fields mentioned in its title.

ABSTRACT: When a differential field K having n commuting derivations is given together with two finitely generated differential extensions L and M of K, an important problem in differential algebra is ...

ABSTRACT: The purpose of this short but difficult paper is to revisit the mathematical foundations of both General Relativity (GR) and Gauge Theory (GT) in the light of a modern approach to nonlinear ...

In this paper we introduce a working generalization of the theory of Gröbner bases for algebras of partial difference polynomials with constant coefficients. One obtains symbolic (formal) computation ...

Important note: the package is being updated: a new subpackge, DalgSeq, is under construction. It will contains all commands for difference-algebraic sequences ...