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An algorithm for determining a Gröbner basis for a collection of polynomials.
Posted in Algebra, CM30070 | No Comments »
A Gröbner basis for a system of polynomials preserves the common roots whilst being simpler relative to an ordering.
Discussion of canonical forms for polynomials- single variable dense and sparse representations; orderings for multivariate polynomials.
Formulation and proof of the Baire category theorem in analytic terms (E2 already has a game-theoretic proof!)
Posted in Analysis, MA40043 | No Comments »
Application of the Baire category theorem to something more interesting than functional analysis- cardinality. Demonstrates the uncountability of the reals, and the incompleteness of the rationals.
Graeme TaylorPhD Student,Number TheoryAbout this blog