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

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

Abstract

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.

Metadata

Item Type: Article
Creators:
CreatorsID Num. / Email
Ahmad, Shamsatun Naharshams551@uitm.edu.my
Aris, Nor’AiniUNSPECIFIED
Jumadi, AzlinaUNSPECIFIED
Subjects: Q Science > QA Mathematics > Algebra
Divisions: Universiti Teknologi MARA, Shah Alam > Research Management Centre (RMC)
Journal or Publication Title: Scientific Research Journal
Journal: UiTM Journal > Scientific Research Journal
ISSN: 1675-7009
Volume: 16
Number: 2
Page Range: pp. 1-16
Item ID: 28260
Uncontrolled Keywords: Algebraic geometry, Bèzout resultant matrix, Combinatorial, Facet variable, Homogeneous coordinates
URI: http://ir.uitm.edu.my/id/eprint/28260

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