[GiNaC-devel] evalf() on cube roots

[Richard B. Kreckel]

On 08/02/2015 08:59 PM, Jan Rheinländer wrote:
>> There isn't. GiNaC, like almost all other systems, returns the solution
>> on the principal branch, compatible with exp(log(-1)/3).
> I suppose there is some excellent mathematical reason for this...

Actually, there isn't. Branch cuts are a matter of convention.
Nothing more but also nothing less.

> but for
> me it means that I can't use GiNaC to verify Cardano's formula for a
> cubic function:
> 
>> x = (-1 - sqrt(2))^(1/3) + (-1 + sqrt(2))^(1/3);
> (-1-sqrt(2))^(1/3)+(-1+sqrt(2))^(1/3)
> 
>> evalf(x^3 + 3 * x + 2);
> 3.3544445609126528848+8.9073474964875349776*I
> 
> Surely there must be a way to verify such a formula in GiNaC???

It should be straightforward to replace such rational expressions by the
form you want them to be in before calling evalf(), using techniques
such as these: <http://www.ginac.de/FAQ.html#advanced>

Cheers
  -richy.
-- 
Richard B. Kreckel
<http://in.terlu.de/~kreckel/>