Definition:Degree of Polynomial/Field

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Definition

Let $\struct {F, +, \times}$ be a field whose zero is $0_F$.

Let $\struct {K, +, \times}$ be a subfield of $F$.

Let $x \in F$.

Let $\ds f = \sum_{j \mathop = 0}^n \paren {a_j x^j} = a_0 + a_1 x + \cdots + a_n x^n$ be a polynomial over $K$ in $x$ such that $a_n \ne 0$.

Then the degree of $f$ is $n$.

The degree of $f$ can be denoted $\map \deg f$ or $\partial f$.

Also known as

The degree of a polynomial $f$ is also sometimes called the order of $f$.

Some sources denote $\map \deg f$ by $\partial f$ or $\map \partial f$.

Sources

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• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Polynomial Equations