Mathematics in Computer Science
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Symbolic Computation for Rankin-Cohen Differential Algebras: A Case Study
Mathematics in Computer Science - Tập 11 - Trang 401-415 - 2017
Don Zagier defined a “Rankin-Cohen algebra”, motivated by the study of
differential operators that send modular forms to modular forms. We devised an
algorithm that computes the result of the differentiation given by the modular
forms that correspond to higher-order Wronskians over Klein’s quartic curve,
which are modular forms of arbitrarily high degree canonically attached to the
curve; this too...
Localizations of a Ring at Localizable Sets, their Groups of Units and Saturations
Mathematics in Computer Science - Tập 16 Số 1 - Trang 1-15 - 2022
We continue to develop the most general theory of one-sided fractions started in
Bavula (Localizable sets and the localization of a ring at a localizable set.
arXiv:2112.13447 ). The aim of the paper is to introduce 10 types of saturations
of a set in a ring and using them to study localizations of a ring at
localizable sets, their groups of units and various maximal localizable sets
satisfying so...
Structured Low Rank Approximation of a Bezout Matrix
Mathematics in Computer Science - Tập 1 - Trang 427-437 - 2007
The task of determining the approximate greatest common divisor (GCD) of more
than two univariate polynomials with inexact coefficients can be formulated as
computing for a given Bezout matrix a new Bezout matrix of lower rank whose
entries are near the corresponding entries of that input matrix. We present an
algorithm based on a version of structured nonlinear total least squares (SNTLS)
method ...
Last Symbol Distribution in Pattern Avoiding Catalan Words
Mathematics in Computer Science - Tập 18 - Trang 1-16 - 2024
We study the distribution of the last symbol statistics on the sets of Catalan
words avoiding a pattern of length at most three. For each pattern p, we provide
a bivariate rational generating function where the coefficient
$$\varvec{c}_p(n,k)$$ of $$x^ny^k$$ in its series expansion is the number of
length n Catalan words avoiding p and ending with the symbol k. We deduce
recurrence relations or cl...
Block Graphs in Practice
Mathematics in Computer Science - Tập 11 Số 2 - Trang 191-196 - 2017
Motivated by the rapidly increasing size of genomic databases, code repositories
and versioned texts, several compression schemes have been proposed that work
well on highly-repetitive strings and also support fast random access: e.g.,
LZ-End, RLZ, GDC, augmented SLPs, and block graphs. Block graphs have good
worst-case bounds but it has been an open question whether they are practical.
We describ...
A New Method for Real Root Isolation of Univariate Polynomials
Mathematics in Computer Science - Tập 1 - Trang 305-320 - 2007
A new algorithm for real root isolation of univariate polynomials is proposed,
which is mainly based on exact interval arithmetic and bisection method.
Although exact interval arithmetic is usually supposed to be inefficient, our
algorithm is surprisingly fast because the termination condition of our
algorithm is different from those of existing algorithms which are mostly based
on Descartes’ rule...
Supra-Hereditary Properties of Hypergraphs
Mathematics in Computer Science - Tập 5 Số 1 - Trang 3-6 - 2011
Optimal Eighth Order Iterative Methods
Mathematics in Computer Science - Tập 5 - Trang 237-243 - 2011
We develop an eighth order family of methods, consisting of three steps and
three parameters, for solving nonlinear equations. Per iteration the methods
require four evaluations (three function evaluations and one evaluation of the
first derivative). Convergence analysis shows that the family is eighth-order
convergent which is also substantiated through the numerical work. Computational
results a...
Degree Upper Bounds for Involutive Bases
Mathematics in Computer Science - Tập 15 - Trang 233-254 - 2020
The aim of this paper is to investigate upper bounds for the maximum degree of
the elements of any minimal Janet basis of an ideal generated by a set of
homogeneous polynomials. The presented bounds depend on the number of variables
and the maximum degree of the generating set of the ideal. For this purpose, by
giving a deeper analysis of the method due to Dubé (SIAM J Comput 19:750–773,
1990), we...
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