The typical dimension of a system of first-order differential equations (Q6597859)
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scientific article; zbMATH DE number 7906279
| Language | Label | Description | Also known as |
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| English | The typical dimension of a system of first-order differential equations |
scientific article; zbMATH DE number 7906279 |
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The typical dimension of a system of first-order differential equations (English)
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4 September 2024
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Let \(F\subset L\) be partial differential fields. For the estimation of the differential transcendence degree \(L\) over \(F\), Kolchin (see [\textit{E. R. Kolchin}, Differential algebra and algebraic groups. New York etc.: Academic Press (1973; Zbl 0264.12102)]) introduced the concept of a differential dimension polynomial. In the paper, the author proves ``that if a system of first-order partial differential equations in one variable has a nonzero Kolchin dimension polynomial, then its leading coefficient is equal to 1.''
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differential polynomials
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differential ideal
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characteristic set
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Rosenfeld-Gröbner's algorithm
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