This graduate textbook presents an approach through toric geometry to the problem of
estimating the isolated solutions (counted with appropriate multiplicity) of n polynomial …

Let K be a field and (f 1,…, fs, ϕ) be multivariate polynomials in K [x 1,…, xn](with s< n) each
invariant under the action of S n, the group of permutations of {1,…, n}. We consider the …

One of the biggest open problems in computational algebra is the design of efficient
algorithms for Gröbner basis computations that take into account the sparsity of the input …

Let K be a field of characteristic zero with K¯ its algebraic closure. Given a sequence of
polynomials g=(g 1,…, gs)∈ K [x 1,…, xn] s and a polynomial matrix F=[fi, j]∈ K [x 1,…, xn] …

Grö bner bases is one the most powerful tools in algorithmic nonlinear algebra. Their
computation is an intrinsically hard problem with a complexity at least single exponential in …

Let K be a field of characteristic zero and let K‾ be an algebraic closure of K. Consider a
sequence of polynomials G=(g 1,…, gs) in K [X 1,…, X n] with s< n, a polynomial matrix F=[fi …

We present a polyhedral algorithm to manipulate positive dimensional solution sets. Using
facet normals to Newton polytopes as pretropisms, we focus on the first two terms of a …

Solving polynomial systems is one of the oldest and most important problems in
computational mathematics and has many applications in several domains of science and …

Solving systems of polynomial equations is a central problem in nonlinear and
computational algebra. Since Buchberger's algorithm for computing Gröbner bases in the …

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