Buchberger’s Algorithm
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An algorithm for determining a Gröbner basis for a collection of polynomials.
Archive for January 2005
Gröbner Basis
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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
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Discussion of canonical forms for polynomials- single variable dense and sparse representations; orderings for multivariate polynomials.
The Baire category theorem and cardinality
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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.
