I've been reading up on Bernstein's theorem for an algebraic geometry assignment and I've come across the terms "dense" and "sparse" in relation to the polynomials. However, I have been unable to find a precise definition of what these terms mean in regards to polynomials and was wondering if anyone here might be able to help.
2026-03-26 01:26:36.1774488396
Sparse & Dense Polynomials
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Density vs sparsity for polynomials is an informal distinction: a (multivariate) polynomial is sparse if "most" of the coefficients of its monomials are zero, and dense otherwise.
If you have not found this reference yet, Sturmfels' book on solving polynomial equations has a chapter on Bernstein's theorem, and is in general very instructive.