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Numerical Elimination: Computing Complements of Real Hypersurfaces Using Pseudo-Witness Sets
Paul Breiding, John Cobb, Aviva K. Englander +6
Many hypersurfaces in algebraic geometry, such as discriminants, arise as the projection of another variety. The real complement of such a hypersurface decomposes into connected co…
Toric invariance of vertically parametrized systems
Elisenda Feliu, Oskar Henriksson
We consider the problem of deciding whether the solution sets of a parametrized polynomial system are toric in the sense that they admit a monomial parametrization. We focus on ver…
A tropical method for solving parametrized polynomial systems
Paul Alexander Helminck, Oskar Henriksson, Yue Ren
We give a framework for constructing generically optimal homotopies for parametrized polynomial systems from tropical data. Here, generically optimal means that the number of paths…
Generic consistency and nondegeneracy of vertically parametrized systems
Elisenda Feliu, Oskar Henriksson, Beatriz Pascual-Escudero
We determine the generic consistency, dimension and nondegeneracy of the zero locus over , and of vertically parametrized systems: pa…