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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| Format: | Article |
| Language: | English English |
| Published: |
1986
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| 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 |
| _version_ | 1848839250086199296 |
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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. |
| first_indexed | 2025-11-15T07:08:27Z |
| format | Article |
| id | upm-2449 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T07:08:27Z |
| publishDate | 1986 |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |