help links subscribe changes refresh edit

	FriCAS Problems
simplify exponents ←	↑

simplifying Expressions

Edit detail for simplifying Expressions revision 3 of 4

	1 2 3 4
Editor: test1 Time: 2017/02/17 17:06:58 GMT+0
Note:

changed:
-In general (unlike some other computer math systems) Axiom automatically
In general (unlike some other computer math systems) FriCAS automatically

changed:
-tell Axiom how to expand square roots. (Since $\sqrt{\ }$ is a multi-valued
tell FriCAS how to expand square roots. (Since $\sqrt{\ }$ is a multi-valued

Simplification of Expressions

Suppose we compute

fricas

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

$\label{eq1}{{\sqrt{2}}\ {\sqrt{\pi}}}\over{\sqrt{2 \ \pi}}$

(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) FriCAS? 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 FriCAS? 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 .)

fricas

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

$\label{eq2}{\sqrt{a \ b}}\mbox{\rm = =}{{\sqrt{a}}\ {\sqrt{b}}}$

(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.

fricas

(%% 1)::Expression Integer

$\label{eq3}{{\sqrt{2}}\ {\sqrt{\pi}}}\over{\sqrt{2 \ \pi}}$

(3)

Type: Expression(Integer)

fricas

expandSqrt %

$\label{eq4}1$

(4)

Type: Expression(Integer)