Symbolic Computation : Solving Equations in Algebra, Geometry, and Engineering.

Intro -- Contents -- Preface -- Equations of parametric curves and surfaces via syzygies -- An explicit description for the triangular decomposition of a zero-dimensional ideal through trace computation -- Numerical irreducible decomposition using projections from points on the components -- Counting stable solutions of sparse polynomial systems in chemistry -- Central configurations in the Newtonian N-body problem of celestial mechanics -- A power function approach to Kouchnirenko's conjecture -- Finiteness for arithmetic fewnomial systems -- Constructing double-exponential number of vectors of multiplicities of solutions of polynomial systems -- Computing sparse projection operators -- Gröbner bases of abelian matrix groups -- Lexicographic Gröbner bases of 3-dimensional transportation problems -- Simplicial complexes and syzygies of lattice ideals -- Algorithmic determination of the rational cohomology of complex varieties via differential forms -- 1. Introduction -- 2. Review of the affine case -- 3. Chern classes in projective space -- 4. Open sets in projective space -- 5. An example -- 6. Closed and locally closed subsets -- 7. Toric varieties -- References -- Differential algebras on semigroup algebras -- Noncommutative Gröbner bases and Hochschild cohomology.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.