# Definition:Addition of Polynomials/Polynomial Forms

< Definition:Addition of Polynomials(Redirected from Definition:Addition of Polynomial Forms)

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## 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 $R$.

This article, or a section of it, needs explaining.In particular: What is $Z$ in the above? Presumably the integers, in which case they need to be denoted $\Z$ and limited in domain to non-negative? However, because $Z$ is used elsewhere in the exposition of polynomials to mean something else (I will need to hunt around to find out exactly what), I can not take this assumption for granted.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Explain}}` from the code. |

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.