Advice: Fractional powers of negative numbers
Maple's mathematics is largely based on complex numbers rather than real numbers. In particular, it uses the "principal branch" of fractional powers: the principal branch of
has argument between
, and the argument of
So for example:
The surd function provides "elementary" 'th roots, i.e. if is a negative number and is odd, then surd(x,n) is the real (negative) 'th root of .
In order to have a somewhat nicer syntax, as well as covering rational exponents with numerators other than 1, I have defined an infix-form operator &^ . This is part of the Maple Advisor Database, and must be read in before being used:
> (-1)&^(2/5), (-1) &^ (3/5);
For positive , is the same as . For negative , if is a fraction we have the following cases:
and both odd:
> x &^ (3/5);
> x &^ (4/5);
odd, even: is complex.
> x &^ (3/8);
When is not known to be real, and is a fraction, is written as a surd. When p is given in decimal form, it is converted to a fraction.
> x:= 'x': x &^ (3/8);
> x &^ 0.375;
> plot(x &^ (2/3), x = -1 .. 1);
> plot(x &^ (3/5), x = -1 .. 1);
See also: ^ , &^, surd
Maple Advisor Database R. Israel, 1998