This may help:
realp(x) := if imagpart(rhs(x)) = 0 then true else false$
l:solve(x^3-x^2+x+1,x)$
sublist(l,realp);
Some time ago this was already discussed?
Jan
Am 08.12.2013 um 16:18 schrieb Richard Fateman <fateman at berkeley.edu>:
> On 12/8/2013 6:25 AM, Aleksas Domarkas wrote:
>> Ricardo JF on Dec 8 07:26:43 wrote:
>>
>> >hi friends,
>>
>> >why this doesn't give only real roots:
>>
>> >f(x):=x^3-x^2+x+1;
>> >declare(x,real);
>> >solve(f(x));
>>
>> >i just want [x=(sqrt(11)/...)]
>>
>> >thanks.
>>
>> (%i1) load(odes);
>> (%o1) "C:/Users/Aleksas/maxima/odes.mac"
>>
>> Example 1
>> (%i2) eq:x^3-x^2+x+1;
>> (%o2) x^3-x^2+x+1
>> (%i3) solvet(eq,x)$
>> (%i4) sublist(%,lambda([e],freeof(%i,e)));
>> (%o4) [x=(sqrt(11)/3^(3/2)-17/27)^(1/3)-2/(9*(sqrt(11)/3^(3/2)-17/27)^(1/3))+1/3]
>
> What does solvet have to offer here? You can do the exact same thing with solve.
> Also, the fact that an expression involves %i does not mean it is
> necessarily non-real. The imaginary parts may cancel.
>
> The use of trig functions can be useful in reducing the size of the expression,
> but, so far as I can tell, does not address the potential ambiguity
> of subexpressions from polynomial formulas or answer the questions as to which (symbolic, parametric)
> roots are "positive" etc.
>
> Of course in a purely numeric example the situation tends to be completely resolvable if
> floating-point numbers are acceptable (and no overflows etc.)
>
> Note that for the solution of x^2-q=0, you have two roots, x=sqrt(q) and x=-sqrt(q), and you
> don't know which is positive or if they are real.
>
>
>
>
>>
>> Example 2
>> (%i5) eq:x^3-4*x^2+x+1;
>> (%o5) x^3-4*x^2+x+1
>> (%i6) solvet(eq,x)$
>> (%i7) sublist(%,lambda([e],freeof(%i,e)));
>> (%o7) [x=(2*sqrt(13)*cos(atan(3^(3/2)/5)/3)+4)/3,x=(2*sqrt(13)*cos((atan(3^(3/2)/5)-2*%pi)/3)+4)/3,x=(2*sqrt(13)*cos((atan(3^(3/2)/5)+2*%pi)/3)+4)/3]
>> (%i8) float(%), numer;
>> (%o8) [x=3.651093408937175,x=0.72610944503578,x=-0.37720285397296]
>> (%i9) allroots(eq);
>> (%o9) [x=-0.37720285397296,x=0.72610944503578,x=3.651093408937175]
>>
>> function "solvet" see in next Maxima relase
>>
>> best
>> Aleksas
>>
>>
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