Edit detail for simplifying Expressions revision 1 of 1

changed:
-
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}

Simplification of Expressions

Suppose we compute

axiom

integrate(exp(-x**2/2)/sqrt(2*%pi),x=%minusInfinity..%plusInfinity)

(1)

Type: Union(f1: OrderedCompletion? Expression Integer,...)

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 is a multi-valued function this rule is true only in a restricted sense for a particular choice of branches. Consider .)

axiom

expandSqrt := rule sqrt(a*b)==sqrt(a)*sqrt(b)

(2)

Type: RewriteRule?(Integer,Integer,Expression Integer)

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.

axiom

(%% 1)::Expression Integer

(3)

Type: Expression Integer

axiom

expandSqrt %

(4)

Type: Expression Integer