The convex polytopes and homogeneous coordinate rings of bivariate polynomials / Shamsatun Nahar Ahmad, Nor’Aini Aris and Azlina Jumadi

The convex polytopes and homogeneous coordinate rings of bivariate polynomials / Shamsatun Nahar Ahmad, Nor’Aini Aris and Azlina Jumadi

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated wi...

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Main Authors: Ahmad, Shamsatun Nahar, Aris, Nor’Aini, Jumadi, Azlina
Format: Article
Language:English
Published: Penerbit UiTM (UiTM Press) 2019
Subjects:
Algebra
Online Access:http://ir.uitm.edu.my/id/eprint/28260/
http://ir.uitm.edu.my/id/eprint/28260/
http://ir.uitm.edu.my/id/eprint/28260/1/28260.pdf
id uitm-28260
recordtype eprints
spelling uitm-282602020-02-11T09:59:48Z http://ir.uitm.edu.my/id/eprint/28260/ The convex polytopes and homogeneous coordinate rings of bivariate polynomials / Shamsatun Nahar Ahmad, Nor’Aini Aris and Azlina Jumadi Ahmad, Shamsatun Nahar Aris, Nor’Aini Jumadi, Azlina Algebra Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven. Penerbit UiTM (UiTM Press) 2019 Article PeerReviewed text en http://ir.uitm.edu.my/id/eprint/28260/1/28260.pdf Ahmad, Shamsatun Nahar and Aris, Nor’Aini and Jumadi, Azlina (2019) The convex polytopes and homogeneous coordinate rings of bivariate polynomials / Shamsatun Nahar Ahmad, Nor’Aini Aris and Azlina Jumadi. Scientific Research Journal, 16 (2). pp. 1-16. ISSN 1675-7009 https://doi.org/10.24191/srj.v16i2.5507
repository_type Digital Repository
institution_category Local University
institution Universiti Teknologi MARA
building UiTM Institutional Repository
collection Online Access
language English
topic Algebra
spellingShingle Algebra
Ahmad, Shamsatun Nahar
Aris, Nor’Aini
Jumadi, Azlina
The convex polytopes and homogeneous coordinate rings of bivariate polynomials / Shamsatun Nahar Ahmad, Nor’Aini Aris and Azlina Jumadi
description Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.
format Article
author Ahmad, Shamsatun Nahar
Aris, Nor’Aini
Jumadi, Azlina
author_facet Ahmad, Shamsatun Nahar
Aris, Nor’Aini
Jumadi, Azlina
author_sort Ahmad, Shamsatun Nahar
title The convex polytopes and homogeneous coordinate rings of bivariate polynomials / Shamsatun Nahar Ahmad, Nor’Aini Aris and Azlina Jumadi
title_short The convex polytopes and homogeneous coordinate rings of bivariate polynomials / Shamsatun Nahar Ahmad, Nor’Aini Aris and Azlina Jumadi
title_full The convex polytopes and homogeneous coordinate rings of bivariate polynomials / Shamsatun Nahar Ahmad, Nor’Aini Aris and Azlina Jumadi
title_fullStr The convex polytopes and homogeneous coordinate rings of bivariate polynomials / Shamsatun Nahar Ahmad, Nor’Aini Aris and Azlina Jumadi
title_full_unstemmed The convex polytopes and homogeneous coordinate rings of bivariate polynomials / Shamsatun Nahar Ahmad, Nor’Aini Aris and Azlina Jumadi
title_sort convex polytopes and homogeneous coordinate rings of bivariate polynomials / shamsatun nahar ahmad, nor’aini aris and azlina jumadi
publisher Penerbit UiTM (UiTM Press)
publishDate 2019
url http://ir.uitm.edu.my/id/eprint/28260/
http://ir.uitm.edu.my/id/eprint/28260/
http://ir.uitm.edu.my/id/eprint/28260/1/28260.pdf
first_indexed 2023-09-18T23:19:54Z
last_indexed 2023-09-18T23:19:54Z
_version_ 1777419361355563008

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