Newton Polyhedral Method of Determining padic Orders of Zeros Common to Two Polynomials in Qp[x, y]Mohd Atan, Kamel Ariffin (1986) Newton Polyhedral Method of Determining padic Orders of Zeros Common to Two Polynomials in Qp[x, y]. Pertanika, 9 (3). pp. 375380.
AbstractTo obtain padic 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 padic 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 noncoinddent 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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