allroots patch



Andrej Vodopivec wrote:
> Here is a system of polynomials (posted on sage-support forum) which
> maxima can't solve:
>
> (%i1) [x^3 + 3*x^2*y + 3*x*y^2 = 45487, y^3 =
> 549755813888];
> (%o1) [3*x*y^2+3*x^2*y+x^3=45487,y^3=549755813888]
> (%i2) solve(%);
> allroots: no roots found.
>
>   
... for what it is worth, the commercial Macsyma produces this:

[[y = 8192, x = root_of(x^3 + 24576 * x^2 + 201326592 * x - 45487, x)], 
[y = 4096 * sqrt(3) * %i - 4096,
x = root_of(x^3 + (12288 * sqrt(3) * %i - 12288) * x^2 + ( - 100663296 * 
sqrt(3) * %i - 100663296) * x - 45487, x)],
[y =  - 4096 * sqrt(3) * %i - 4096, x
 = root_of(x^3 + ( - 12288 * sqrt(3) * %i - 12288) * x^2 + (100663296 * 
sqrt(3) * %i - 100663296) * x - 45487, x)]]