Definition:Addition of Polynomials/Polynomial Forms

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$\ds f = \sum_{k \mathop \in Z} a_k \mathbf X^k$
$\ds g = \sum_{k \mathop \in Z} b_k \mathbf X^k$

be polynomials in the indeterminates $\set {X_j: j \in J}$ over $R$.

The operation polynomial addition is defined as:

$\ds f + g := \sum_{k \mathop \in Z} \paren {a_k + b_k} \mathbf X^k$

The expression $f + g$ is known as the sum of $f$ and $g$.

Also see