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
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minimal polynomial
Summary
minimal polynomial is an invariant[1]. It draws 64 Wikipedia views per month (invariant category, ranking #14 of 37).[2]
Key Facts
- minimal polynomial's instance of is recorded as invariant[3].
- minimal polynomial's subclass of is recorded as monic polynomial[4].
- minimal polynomial's has part is recorded as minimal polynomial[5].
- minimal polynomial's Freebase ID is recorded as /m/02pnlcl[6].
- minimal polynomial's different from is recorded as minimal polynomial[7].
- minimal polynomial's defining formula is recorded as \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})}[8].
- minimal polynomial's Google Knowledge Graph ID is recorded as /g/1pwgtm21k[9].
- minimal polynomial's MathWorld ID is recorded as AlgebraicNumberMinimalPolynomial[10].
- minimal polynomial's MathWorld ID is recorded as ExtensionFieldMinimalPolynomial[11].
- minimal polynomial's maintained by WikiProject is recorded as WikiProject Mathematics[12].
- minimal polynomial's Microsoft Academic ID is recorded as 112941647[13].
Why It Matters
minimal polynomial draws 64 Wikipedia views per month (invariant category, ranking #14 of 37).[2] It has Wikipedia articles in 18 language editions, a strong signal of global cultural recognition.[14] It is known by 7 alternative names across languages and contexts.[15]