Category:Definitions/Complex Polynomial Functions
This category contains definitions related to Complex Polynomial Functions.
Related results can be found in Category:Complex Polynomial Functions.
Let $S \subset \C$ be a subset of the complex numbers.
Definition 1
A complex polynomial function on $S$ is a function $f : S \to \C$ for which there exist:
- a natural number $n \in \N$
- complex numbers $a_0, \ldots, a_n \in \C$
such that for all $z \in S$:
- $\map f z = \ds \sum_{k \mathop = 0}^n a_k z^k$
where $\ds \sum$ denotes indexed summation.
Definition 2
Let $\C \sqbrk X$ be the polynomial ring in one variable over $\C$.
Let $\C^S$ be the ring of mappings from $S$ to $\C$.
Let $\iota \in \C^S$ denote the inclusion $S \hookrightarrow \C$.
A complex polynomial function on $S$ is a function $f: S \to \C$ which is in the image of the evaluation homomorphism $\C \sqbrk X \to \C^S$ at $\iota$.
Pages in category "Definitions/Complex Polynomial Functions"
The following 4 pages are in this category, out of 4 total.