NDLI: A New Algorithm for General Factorizations of Multivariate Polynomial Matrices

Please wait, while we are loading the content...

Calculating the Power Residue Symbol and Ibeta: Applications of Computing the Group Structure of the Principal Units of a p-adic Number Field Completion

Polynomial Time Interactive Proofs for Linear Algebra with Exponential Matrix Dimensions and Scalars Given by Polynomial Time Circuits

Certificates for Triangular Equivalence and Rank Profiles

On Signature-Based Gröbner Bases Over Euclidean Rings

Matrix Representations by Means of Interpolation

Nemo/Hecke: Computer Algebra and Number Theory Packages for the Julia Programming Language

Parametrizations for Families of ECM-Friendly Curves

An Algebraic-Geometric Method for Computing Zolotarev Polynomials

Computing the Nearest Rank-Deficient Matrix Polynomial

Dimension-Dependent Upper Bounds for Gröbner Bases

A Constructive Approach to Arithmetics in Ore Localizations

Algorithms for Structured Linear Systems Solving and Their Implementation

Formula Simplification for Real Quantifier Elimination Using Geometric Invariance

Automated Generation of Non-Linear Loop Invariants Utilizing Hypergeometric Sequences

Efficiently Computing Real Roots of Sparse Polynomials

Early Termination in Parametric Linear System Solving and Rational Function Vector Recovery with Error Correction

Bounds for Substituting Algebraic Functions into D-finite Functions

Popov Form Computation for Matrices of Ore Polynomials

The Truncated Fourier Transform for Mixed Radices

Riemann Tensor Polynomial Canonicalization by Graph Algebra Extension

A New Algorithm for General Factorizations of Multivariate Polynomial Matrices

Algorithmic Verification of Linearizability for Ordinary Differential Equations

M4GB: An Efficient Gröbner-Basis Algorithm

Sparse Rational Univariate Representation

Resultants and Discriminants for Bivariate Tensor-Product Polynomials

Reconstruction Algorithms for Sums of Affine Powers

Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant K

Fast Algorithm for Border Bases of Artinian Gorenstein Algebras

Parametric Greatest Common Divisors using Comprehensive Gröbner Systems

Fast Computation of the Roots of Polynomials Over the Ring of Power Series

Computing Canonical Bases of Modules of Univariate Relations

Exploring the Dynamic Buchberger Algorithm

Growth in Varieties of Multioperator Algebras and Groebner Bases in Operads

Improved Bounds on Absolute Positiveness of Multivariate Polynomials

Characteristic Polynomials of p-adic Matrices

Two Fast Parallel GCD Algorithms of Many Integers

Factorization of Polynomials over $Z/(p^{n})$

CAD Adjacency Computation Using Validated Numerics

Functional Decomposition Using Principal Subfields

A Tropical F5 Algorithm

The Frobenius FFT

Composition Modulo Powers of Polynomials

A New Algorithm for General Factorizations of Multivariate Polynomial Matrices

Content Provider	ACM Digital Library
Author	Ma, Xiaodong Wang, Dingkang Lu, Dong
Abstract	We investigate how to factorize a multivariate polynomial matrix into the product of two matrices. There are two major parts. The first is a factorization theorem, which asserts that a multivariate polynomial matrix whose lower order minors satisfy certain conditions admits a matrix factorization. Our theory is a generalization to the previous results given by Lin et.al [16] and Liu et.al [17]. The second is the implementation for factorizing polynomial matrices. According to the proof of factorization theorem, we construct a main algorithm which extends the range of polynomial matrices that can be factorized. In this algorithm, two critical steps are involved in how to compute a zero left prime matrix and a unimodular matrix. Firstly, based on the famous Quillen-Suslin theorem, a new sub-algorithm is presented to obtain a zero left prime matrix by calculating the bases of the syzygies of two low-order polynomial matrices. Experiments show that it is more efficient than the algorithm constructed by Wang and Kwong [31]. Secondly, some auxiliary information provided by the above new sub-algorithm is used to construct a unimodular matrix. As a consequence, the main algorithm extends the application range of the constructive algorithm in [17]. We implement all the algorithms proposed above on the computer algebra system Singular and give a nontrivial example to show the process of the main algorithm.
Starting Page	277
Ending Page	284
Page Count	8
File Format	PDF
ISBN	9781450350648
DOI	10.1145/3087604.3087607
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2017-07-23
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Multivariate polynomial matrices Reduced minors Unimodular matrix Zero left prime matrix Matrix factorization
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

On multivariate polynomial matrix factorization problems

Further results on n-d polynomial matrix factorizations (2000).

Factorizations fornD polynomial matrices

On General Factorizations for n-D Polynomial Matrices

Some properties of laurent polynomial matrices (2012).

On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices

On Factor Left Prime Factorization Problems for Multivariate Polynomial Matrices

On Factor Prime Factorizations for $n$-D Polynomial Matrices

On minor prime factorizations for n-D polynomial matrices

A New Algorithm for General Factorizations of Multivariate Polynomial Matrices

Similar Documents

On multivariate polynomial matrix factorization problems

Further results on n-d polynomial matrix factorizations (2000).

Factorizations fornD polynomial matrices

On General Factorizations for n-D Polynomial Matrices

Some properties of laurent polynomial matrices (2012).

On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices

On Factor Left Prime Factorization Problems for Multivariate Polynomial Matrices

On Factor Prime Factorizations for $n$-D Polynomial Matrices

On minor prime factorizations for n-D polynomial matrices

A New Algorithm for General Factorizations of Multivariate Polynomial Matrices