MuPad reduce roots

I find MuPad does not reduce roots for example

simplify( (z^3)^(1/3) )

to simply z as expected, instead leaving it as (z^3)^(1/3).

Is there a way to get MuPad to reduce roots like the above example?

Answer 1

[Paulo Silva]

MuPad and Maple don't simplify it like you expect unless you do this:

%matlab syntax
z=sym('z','positive')
simplify((z^3)^(1/3))

ans=

z

In MuPad use this syntax

assume(z, Type::Positive)
simplify((z^3)^(1/3))

In Maple use this syntax

assume(0 < z)
simplify((z^3)^(1/3))

The reason can be found by testing:

z=-1
(-1^3)^(1/3)
ans =
  0.500000000000000 + 0.866025403784439i

z=1
(1^3)^(1/3)
ans =
     1

Roots of negative values give results with imaginary parts while roots of positive values always return real numbers, in the case provided for all z>0 (and z=0) the simplified expression is z and for all z<0 the simplified expression remains (z^3)^(1/3)

The symbolic engine by default doesn't limit the symbolic variables (type, range of values, etc) so if it simplified the expression to just z that would be incorrect!

[Billy]

Yeah, I figured it was trying to keep the answer strictly correct without making bad assumptions.

The syntax you used doesn't work in MuPad - what is the MuPad syntax?

[Paulo Silva]

assume(z, Type::Positive)

simplify((z^3)^(1/3))