Definition:Degree of Polynomial/Sequence

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Definition

Ring

Let $f = \sequence {a_k} = \tuple {a_0, a_1, a_2, \ldots}$ be a polynomial over a ring $R$.


The degree of $f$ is defined as the largest $n \in \Z$ such that $a_n \ne 0$.


Field

Let $f = \sequence {a_k} = \tuple {a_0, a_1, a_2, \ldots}$ be a polynomial over a field $F$.


The degree of $f$ is defined as the largest $n \in \Z$ such that $a_n \ne 0$.