Editing Weierstrass preparation theorem (section)

{{Use American English|date = March 2019}}
{{Short description|Local theory of several complex variables}}
In [[mathematics]], the '''Weierstrass preparation theorem''' is a tool for dealing with [[analytic function]]s of [[Function of several complex variables|several complex variables]], at a given point ''P''. It states that such a function is, [[up to]] multiplication by a function not zero at ''P'', a [[polynomial]] in one fixed variable ''z'', which is [[monic polynomial|monic]], and whose [[coefficient]]s of lower degree terms are analytic functions in the remaining variables and zero at ''P''.

There are also a number of variants of the theorem, that extend the idea of factorization in some [[ring (mathematics)|ring]] ''R'' as ''u''·''w'', where ''u'' is a [[Unit (ring theory)|unit]] and ''w'' is some sort of distinguished '''Weierstrass polynomial'''. [[Carl Siegel]] has disputed the attribution of the theorem to [[Weierstrass]], saying that it occurred under the current name in some of late nineteenth century ''Traités d'analyse'' without justification.