Buchberger’s Algorithm
Thursday, January 20th, 2005
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An algorithm for determining a Gröbner basis for a collection of polynomials.
Archive for January, 2005
Gröbner Basis
Tuesday, January 18th, 2005
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A Gröbner basis for a system of polynomials preserves the common roots whilst being simpler relative to an ordering.
Canonical Representation of polynomials
Saturday, January 15th, 2005
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Discussion of canonical forms for polynomials- single variable dense and sparse representations; orderings for multivariate polynomials.
Analytic proof of the Baire category theorem
Friday, January 7th, 2005
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Formulation and proof of the Baire category theorem in analytic terms (E2 already has a game-theoretic proof!)
The Baire category theorem and cardinality
Friday, January 7th, 2005
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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.
