The field of polynomial systems occupies a central role in computational mathematics, where the intricate interplay between algebra, geometry, and computational complexity is evident. Research in this ...

Integrable systems and orthogonal polynomials form a vibrant research frontier that bridges pure and applied mathematics. Integrable systems are distinguished by their rich symmetry properties and the ...

We give conditions under which the number of solutions of a system of polynomial equations over a finite field 𝔽q of characteristic p is divisible by p. Our setup involves the substitution ti ↦ f(ti) ...

Both algebraic and arithmetic geometry are concerned with the study of solution sets of systems of polynomial equations. Algebraic geometry deals primarily with solutions lying in an algebraically ...

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of recent work by the ...

Vol. 58, No. 4, Part 2 of 2. Special Issue on Computational Economics (July-August 2010), pp. 1037-1050 (14 pages) Multiplicity of equilibria is a prevalent problem in many economic models. Often ...

New research details an intriguing new way to solve "unsolvable" algebra problems that go beyond the fourth degree – something that has generally been deemed impossible using traditional methods for ...

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and ...