# Algebraic factoring and geometry theorem proving

## Abstract

Two methods for polynomial factorization over algebraic extension fields are reviewed. It is explained how geometric theorems may be proved by using irreducible zero decomposition for which algebraic factoring is necessary. A set of selected geometric theorems are taken as examples to illustrate how algebraic factoring can help understand the ambiguity of a theorem and prove it even if its algebraic formulation does not precisely correspond to the geometric statement. Among the polynomials occurring in our examples which need to be algebraically factorized, 12 are presented. Experiments with the two factoring methods for these polynomials are reported in comparison with the Maple's built-in factorizer. Our methods are always faster and any of the 12 polynomials can be factorized within 40 CPU seconds on a SUN SparcServer 690/51. Timings for proving the example theorems are also provided.

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