Definition:Addition of Polynomials/Polynomial Forms

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

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

 * Polynomials Closed under Addition: $f + g$ is a polynomial.