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## [Axiom-developer] [simplifying Expressions] (new)

 From: kratt6 Subject: [Axiom-developer] [simplifying Expressions] (new) Date: Tue, 08 Nov 2005 07:38:20 -0600

Changes
http://page.axiom-developer.org/zope/mathaction/SimplifyingExpressions/diff
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Simplification of Expressions

Suppose we compute

\begin{axiom}
integrate(exp(-x**2/2)/sqrt(2*%pi),x=%minusInfinity..%plusInfinity)
\end{axiom}

*And now I wonder why common factors are not cancelled and why not the
result "1" is produced.*

In general (unlike some other computer math systems) Axiom automatically
performs only a very small number of basic simplifications. This is not
one of them, so we need to provide some help. In particular we need to
tell Axiom how to expand square roots. (Since $\sqrt{\ }$ is a multi-valued
function this rule is true only in a restricted sense for a particular
choice of branches. Consider $a=-1, b=-1$.)

\begin{axiom}
expandSqrt := rule sqrt(a*b)==sqrt(a)*sqrt(b)
\end{axiom}

Next, notice that the output of the integration operation has a complicated
type structure. This would interfere with the simplification, so we first
simplify the type before we apply the rule.

\begin{axiom}
(%% 1)::Expression Integer
expandSqrt %
\end{axiom}
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