Mathematics of Computation

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Numerical Calculation of the Multiplicity of a Solution to Algebraic Equations

Author(s): Hidetsune Kobayashi; Hideo Suzuki; Yoshihiko Sakai.
Journal: Math. Comp. 67 (1998), 257-270.
MSC (1991): Primary 14Q99, 65H10; Secondary 14N05, 65H20
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Abstract: A method to calculate numerically the multiplicity of a solution to a system of algebraic equations is presented. The method is an application of Zeuthen's rule which gives the multiplicity of a solution as the multiplicity of a united point of an algebraic correspondence defined naturally by the system. The numerical calculation is applicable to a large scale system of algebraic equations which may have a solution that we cannot calculate the multiplicity by a symbolic computation.

References:

1.: J. S. Semple and L. Roth : Introduction to Algebraic Geometry, Oxford Science Publications, Clarendon Press, Oxford, 1949. MR 11:535d
2.: B. L. van der Waerden : Einführung in die algebraische Geometrie, Springer-Verlag, 1973. MR 49:8984
3.: H. Kobayashi, H. Suzuki and Y. Sakai: Separation of close roots by linear fractional transformation, Proc. of ASCM, 1-10, Scientists INC, 1995.
4.: W. Fulton: Algebraic Curves, The Benjamin/Cummings Publishing Company, 1969. MR 47:1807
5.: A. H. Wright: Finding All Solutions to a System of Polynomial Equations, Mathematics of Computation Vol. 44, No. 169, 1985, 125-133. MR 86i:12001


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