Formalization of a Newton Series Representation of Polynomials

Cyril Cohen 1 Boris Djalal 1
1 MARELLE - Mathematical, Reasoning and Software
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We formalize an algorithm to change the representation of a polynomial to a Newton power series. This provides a way to compute efficiently polynomials whose roots are the sums or products of roots of other polynomials, and hence provides a base component of efficient computation for algebraic numbers. In order to achieve this, we formalize a notion of truncated power series and develop an abstract theory of poles of fractions.
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Submitted on : Thursday, December 10, 2015 - 8:39:38 AM
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Cyril Cohen, Boris Djalal. Formalization of a Newton Series Representation of Polynomials. Certified Programs and Proofs, Jan 2016, St. Petersburg, Florida, United States. ⟨hal-01240469⟩

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