Definition:Polynomial Addition/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 $R$.

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.

Sources

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