Improved Polynomial Remainder Sequences for Ore Polynomials

11/03/2015
by   Maximilian Jaroschek, et al.
0

Polynomial remainder sequences contain the intermediate results of the Euclidean algorithm when applied to (non-)commutative polynomials. The running time of the algorithm is dependent on the size of the coefficients of the remainders. Different ways have been studied to make these as small as possible. The subresultant sequence of two polynomials is a polynomial remainder sequence in which the size of the coefficients is optimal in the generic case, but when taking the input from applications, the coefficients are often larger than necessary. We generalize two improvements of the subresultant sequence to Ore polynomials and derive a new bound for the minimal coefficient size. Our approach also yields a new proof for the results in the commutative case, providing a new point of view on the origin of the extraneous factors of the coefficients.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/27/2019

Nearly Optimal Sparse Polynomial Multiplication

In the sparse polynomial multiplication problem, one is asked to multipl...
research
11/18/2017

A New Algebraic Method to Search Irreducible Polynomials Using Decimal Equivalents of Polynomials over Galois Field GF(p^q)

Irreducible polynomials play an important role till now, in construction...
research
05/12/2023

Dimension results for extremal-generic polynomial systems over complete toric varieties

We study polynomial systems with prescribed monomial supports in the Cox...
research
02/08/2023

A Unified Approach to Unimodality of Gaussian Polynomials

In 2013, Pak and Panova proved the strict unimodality property of q-bino...
research
04/06/2019

Well-Rounded Lattices via Polynomials

Well-rounded lattices have been a topic of recent studies with applicati...
research
12/05/2019

Complexity of a Root Clustering Algorithm

Approximating the roots of a holomorphic function in an input box is a f...
research
04/29/2021

Analyzing the Nuances of Transformers' Polynomial Simplification Abilities

Symbolic Mathematical tasks such as integration often require multiple w...

Please sign up or login with your details

Forgot password? Click here to reset