I want to describe an algorithm, which is not changing a given input but it is producing a new element:
\documentclass[a4paper, 11pt]{scrbook}
\usepackage{algorithm}
\usepackage{algorithmic}
...
\begin{algorithmic}
\REQUIRE $\mathcal{P} \subset F[X_1 \dots X_{k-1 }][X_k]$
\ENSURE % something about the return value
\RETURN $\operatorname{Elim}_{X_k}(\mathcal{P})$
\end{algorithmic}
Ensure is not quite the thing I'm looking for because I want to make a statemanent about the output which does not have its own name.
Another thing is that I want to name the algorithm and lateron call it. I know that the algorithm does not to anthing different than call the function Elim but I want to underline the difference between the existence of a mathematical function and the algorithm (e.g. I don't want to discuss the computional complexity of a mathematical function).
Any ideas?

\documentclassand the appropriate packages so that those trying to help don't have to recreate it. – Peter Grill Nov 27 '11 at 18:04