Counting solutions of polynomial systems via iterated fibrations (Q1016493)
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scientific article; zbMATH DE number 5551219
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Counting solutions of polynomial systems via iterated fibrations |
scientific article; zbMATH DE number 5551219 |
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Counting solutions of polynomial systems via iterated fibrations (English)
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6 May 2009
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The counting polynomial for a system of polynomial equations and inequalities in affine or projective space is defined via a decomposition of the solution set into subsets that can be defined by triangular-like systems, in the sense of \textit{J. M. Thomas} [Differential systems. AMS Coll. Publ. 21 (1937; JFM 63.0438.03)]. Its properties are similar to those of the Hilbert polynomial: its degree is the dimension of the solution set, and if the number of solution is finite, then the polynomial is the number of solutions.
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polynomial equations
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polynomial inequations
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solutions of polynomial systems
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Thomas algorithm
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counting polynomial
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simple systems
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triangular decomposition
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0.9187606
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0.9175321
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0.89837897
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0.8852372
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0.87947416
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0.8790448
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