On 04/27/2012 01:08 PM, andre maute wrote:
> On 04/27/2012 12:16 PM, Wilhelm Haager wrote:
>> Hi!
>>
>> Solving the equation
>>
>> solve(a*x**3+x*(1-x**2)=0,x);
>>
>> gives imaginary results:
>>
>> [x = -%i/sqrt(a-1),x = %i/sqrt(a-1),x = 0]
>>
>> I would like to have the results in the following form, i.e. real:
>>
>> [x = -1/sqrt(1-a),x = 1/sqrt(1-a),x = 0]
>>
>> assume(a<1) gives the desired result, but I require real solutions in
>> automated calculations
>> where I cannot make any assumptions in advance.
>> Before the equation is solved, I cannot see what I have to assume.
>>
>> Is there a simple way (without subsequent maps and other tricky
>> transformations) to enforce that?
>> (algsys with realonly=true does not work in the desired way).
> Doesn't the casus irreducibilis apply here?
>
> See http://en.wikipedia.org/wiki/Casus_irreducibilis
Oh sorry, for the noise, x=0 is a solution.
Andre