Electronic Thesis and Dissertation Repository

Thesis Format

Monograph

Degree

Master of Science

Program

Computer Science

Supervisor

Moreno Maza, Marc

Abstract

We discuss the design and implementation of lazy multivariate power series, univariate polynomials over power series, and their associated arithmetic within the Basic Polynomial Algebra Subprograms (BPAS) Library. This implementation is employed by lazy variations of Weierstrass preparation and the factorization of univariate polynomials over power series following Hensel's lemma. Our implementation is lazy in that power series terms are only computed when explicitly requested. The precision of a power series is dynamically extended upon request, without requiring any re-computation of existing terms. This design extends into an ``ancestry'' of power series whereby power series created from the result of arithmetic or Weierstrass preparation automatically hold on to enough information to dynamically update themselves to higher precision using information from their ``parents''.

Summary for Lay Audience

We discuss the design and implementation of lazy multivariate power series, univariate polynomials over power series, and their associated arithmetic within the Basic Polynomial Algebra Subprograms (BPAS) Library. This implementation is employed by lazy variations of Weierstrass preparation and the factorization of univariate polynomials over power series following Hensel's lemma. Our implementation is lazy in that power series terms are only computed when explicitly requested. The precision of a power series is dynamically extended upon request, without requiring any re-computation of existing terms. This design extends into an ``ancestry'' of power series whereby power series created from the result of arithmetic or Weierstrass preparation automatically hold on to enough information to dynamically update themselves to higher precision using information from their ``parents''.

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