Introduction
Roughly speaking, Alge.bfLa.lc Complexity lhtcih.ij is the investigation of
the following question :
Let X.,...,X be indeterminates over a field fe, and let
1 n
F.,...,F 6 fe(X,,...,X ) be rational functions.
1 m 1 n
Regarding the elements of fe U {X.,...,X } as given, what
are the "optimal computatlom Ojj IF. ,...,F } " ?
Obviously our first task is to make precise some notions, in particular:
(i) we have to define "computation", and
(ii) in order to call a computation optimal, we have to make clear
the relation in which it is a "best one".
We shall compare computations relative to the number of certain
arithmetic operations they contain. But before we give exact
definitions (cf. Chapter I), we are going to present some typical
Examples :