Picking up this old thread...
I would like to submit a patch that allows choosing the convention for
negative cube roots between the solution on the principal branch and the
real-valued solution.
That is, in the cln library, file complex/transcendental/cl_C_expt_C.cc
I would like to handle the following case separately:
y rational and y ratio m/n
x rational and x < 0
n odd
What about introducing a flag called (e.g.)
cln::cl_odd_roots_of_rationals_real (similar to
cln::cl_inhibit_floating_point_underflow)?
If the flag is false (default), the above case evaluates to exp(log(x) *
y) as before
If the flag is true, it evaluates to (-1)^m * (-x)^(m/n)
Would such a patch be acceptable?
Greetings,
Jan Rheinländer
Am 02.08.2015 um 21:55 schrieb 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.