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/>