Newton Polyhedral Method of Determining p-adic Orders of Zeros Common to Two Polynomials in Qp[x, y]

To obtain p-adic orders of zeros common to two polynomials in Q [x,y], the combination of P . Indicator diagrams assodated with both polynomials are examined. It is proved that the p-adic orders of zeros common to both polynomials give the coordinates of certain intersection points of segments of...

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Main Author: Mohd Atan, Kamel Ariffin
Format: Article
Language:English
English
Published: 1986
Online Access:http://psasir.upm.edu.my/id/eprint/2449/
http://psasir.upm.edu.my/id/eprint/2449/1/Newton_Polyhedral_Method_of_Determining_p-adic_Orders.pdf
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author Mohd Atan, Kamel Ariffin
author_facet Mohd Atan, Kamel Ariffin
author_sort Mohd Atan, Kamel Ariffin
building UPM Institutional Repository
collection Online Access
description To obtain p-adic orders of zeros common to two polynomials in Q [x,y], the combination of P . Indicator diagrams assodated with both polynomials are examined. It is proved that the p-adic orders of zeros common to both polynomials give the coordinates of certain intersection points of segments of the Indicator diagrams assodated with both polynomials. We make a conjecture that if ( A, IJ. ) is a point of intersection of non-coinddent segments in the combination of Indicator diagrams associated with two polynomials in Q [ x,y l then there exists a zero (L Tl) common to both polynomials such that ord ~. = A , ord Tl::: IJ. . A special case of this conjecture is proved.
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institution Universiti Putra Malaysia
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language English
English
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publishDate 1986
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spelling upm-24492013-05-27T07:01:10Z http://psasir.upm.edu.my/id/eprint/2449/ Newton Polyhedral Method of Determining p-adic Orders of Zeros Common to Two Polynomials in Qp[x, y] Mohd Atan, Kamel Ariffin To obtain p-adic orders of zeros common to two polynomials in Q [x,y], the combination of P . Indicator diagrams assodated with both polynomials are examined. It is proved that the p-adic orders of zeros common to both polynomials give the coordinates of certain intersection points of segments of the Indicator diagrams assodated with both polynomials. We make a conjecture that if ( A, IJ. ) is a point of intersection of non-coinddent segments in the combination of Indicator diagrams associated with two polynomials in Q [ x,y l then there exists a zero (L Tl) common to both polynomials such that ord ~. = A , ord Tl::: IJ. . A special case of this conjecture is proved. 1986 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/2449/1/Newton_Polyhedral_Method_of_Determining_p-adic_Orders.pdf Mohd Atan, Kamel Ariffin (1986) Newton Polyhedral Method of Determining p-adic Orders of Zeros Common to Two Polynomials in Qp[x, y]. Pertanika, 9 (3). pp. 375-380. English
spellingShingle Mohd Atan, Kamel Ariffin
Newton Polyhedral Method of Determining p-adic Orders of Zeros Common to Two Polynomials in Qp[x, y]
title Newton Polyhedral Method of Determining p-adic Orders of Zeros Common to Two Polynomials in Qp[x, y]
title_full Newton Polyhedral Method of Determining p-adic Orders of Zeros Common to Two Polynomials in Qp[x, y]
title_fullStr Newton Polyhedral Method of Determining p-adic Orders of Zeros Common to Two Polynomials in Qp[x, y]
title_full_unstemmed Newton Polyhedral Method of Determining p-adic Orders of Zeros Common to Two Polynomials in Qp[x, y]
title_short Newton Polyhedral Method of Determining p-adic Orders of Zeros Common to Two Polynomials in Qp[x, y]
title_sort newton polyhedral method of determining p-adic orders of zeros common to two polynomials in qp[x, y]
url http://psasir.upm.edu.my/id/eprint/2449/
http://psasir.upm.edu.my/id/eprint/2449/1/Newton_Polyhedral_Method_of_Determining_p-adic_Orders.pdf