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 |
| Summary: | 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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