On 10/01/2013 12:46 PM, Aleksas Domarkas wrote:
> see
> http://www.math.utexas.edu/pipermail/maxima/2013/034120.html
>
> The cube root of 110+74i would return 5+i.
> How compute this?
>
> (%i1) expand((5+%i)^3);
> (%o1) 74*%i+110
There was an error in my last email because I was confused
about how the flag was set.
Here rectform does *not* choose the principal root.
(%i1) domain:real;
(%o1) real
(%i2) float(rectform( gcfactor( 74* %i + 110)^(1/3)));
(%o2) 3.830127018922193*%i-3.366025403784438
But we can rotate it.
(%i3) expand(float(inpart(roots,2,2)*float(rectform(gcfactor( 74* %i +
110)^(1/3)))));
(%o3) 1.0*%i+4.999999999999999
Here rectform *does* choose the principal root
(%i4) domain:complex;
(%o4) complex
(%i5) float(rectform( gcfactor( 74* %i + 110)^(1/3)));
(%o5) .9999999999999998*%i+5.000000000000001
I also erroneously said that the principal root is
"the root" with positive imaginary part. I should
have said "a root".
>
> Aleksas D
>
>
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