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SandBoxAbs

Edit detail for SandBoxAbs revision 2 of 3

	1 2 3
Editor: Bill Page Time: 2015/01/30 18:19:18 GMT+0
Note:

changed:
-abs is often defined in terms of the positive square root so comparison with the following is perhaps a surprize.
abs is often defined in terms of the positive square root

changed:
-differentiate(sqrt(x^2),x)
Abs(x)==sqrt(x^2)

added:
so comparison with the following is perhaps a surprize.
\begin{axiom}
differentiate(Abs(x),x)
\end{axiom}

This is how FriCAS? currently differentiates the absolute value function.

fricas

differentiate(abs(x),x)

$\label{eq1}{abs \left({x}\right)}\over x$

(1)

Type: Expression(Integer)

abs is often defined in terms of the positive square root

fricas

Abs(x)==sqrt(x^2)

Type: Void

so comparison with the following is perhaps a surprize.

fricas

differentiate(Abs(x),x)

fricas

Compiling function Abs with type Variable(x) -> Expression(Integer)

$\label{eq2}x \over{\sqrt{{x}^{2}}}$

(2)

Type: Expression(Integer)

Are these expressions really equivalent?