The expected number of real roots of a multihomogeneous system of polynomial equations (Q2784129)
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scientific article; zbMATH DE number 1731123
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The expected number of real roots of a multihomogeneous system of polynomial equations |
scientific article; zbMATH DE number 1731123 |
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The expected number of real roots of a multihomogeneous system of polynomial equations (English)
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8 January 2003
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polynomial equations
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number of roots
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multihomogeneous system
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Roots of a multihomogeneous system of polynomial equations with real coefficients are discussed in this interesting paper. It is shown that the mean number of real roots is at least as large as the square root of the maximal number of the regular complex roots. This generalizes the results of \textit{M. Shub} and \textit{S. Smale} [Progr. Math. 109, 267-285 (1993; Zbl 0851.65031)] and of \textit{J. M. Rojas} [American Mathematical Society. Lect. Appl. Math. 32, 689-699 (1996; Zbl 0857.65055)].
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