minimal polynomial (Q1698)
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given an element α of a field extension E/F, the unique monic polynomial p∈F[x] of minimal degree such that p(α) = 0
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | minimal polynomial |
given an element α of a field extension E/F, the unique monic polynomial p∈F[x] of minimal degree such that p(α) = 0 |
Statements
![{\displaystyle \min_{a \le b \iff \deg a \le \deg b}\{p\in K[x] \colon p(\alpha) = 0,\; p(x)=x^{\deg p}+\mathcal O(x^{\deg p-1})\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4b674cc349e9cc29684c4eb9fc354d6a35809e61)
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Identifiers
ExtensionFieldMinimalPolynomial
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112941647
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/g/1pwgtm21k
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