Numerical decomposition of the solution sets of polynomial systems into irreducible components (Q2706398)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Numerical decomposition of the solution sets of polynomial systems into irreducible components |
scientific article |
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19 March 2001
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components of solutions
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embedding
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generic points
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homotopy continuation
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irreducible components
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numerical algebraic geometry
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polynomial system
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primary decomposition
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numerical examples
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algorithms
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Numerical decomposition of the solution sets of polynomial systems into irreducible components (English)
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For a given system of \(n\) polynomial equations the authors present an algorithm that computes a lot of the geometric information contained in the primary decomposition of the solution set. The homotopy continuation based algorithms lay out the decomposition of the set of solutions into irreducible components and determine the degree of each component as well as an upper bound of its multiplicity. The theoretical justification of the main subalgorithms is given and their pseudocode representation helps to understand the principal mode of operation. Three nontrivial examples are discussed in detail.
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