Unique Representation in Polynomial Forms/General Result/Corollary

This page has been identified as a candidate for refactoring of basic complexity. In particular: Add the necessary to the top to define what the objects in question are Until this has been finished, please leave {{Refactor}} in the code. New contributors: Refactoring is a task which is expected to be undertaken by experienced editors only. Because of the underlying complexity of the work needed, it is recommended that you do not embark on a refactoring task until you have become familiar with the structural nature of pages of $\mathsf{Pr} \infty \mathsf{fWiki}$. 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 {{Refactor}} from the code.

This article needs to be linked to other articles. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding these links. 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 {{MissingLinks}} from the code.

Theorem

Dropping the zero terms from the sum we can write the polynomial $f$ as

$f = a_{k_1} \mathbf X^{k_1} + \cdots + a_{k_r} \mathbf X^{k_r}$

for some $a_{k_i}\in R$, $i = 1, \ldots, r$.

Proof

Follows directly from Unique Representation in Polynomial Forms: General Result

$\blacksquare$