[GAP Forum] cyclotomic number
Alexander Konovalov
alexk at mcs.st-and.ac.uk
Tue Jun 11 20:31:56 BST 2013
On 5 Jun 2013, at 16:08, Flisphy wrote:
> Dear gap developers,
>
> Could I convert cyclotomic number into complex number using gap?
>
> yours,
>
> Peng Long
Dear Peng Long,
cyclotomic numbers *are* complex numbers - I guess what you may have in
mind is getting a floating-point approximation of the real and imaginary
parts of a cyclotomic number. This can be achieved using the GAP package
Float by Laurent Bartholdi: see
http://laurentbartholdi.github.io/float/chap0.html
For example,
gap> LoadPackage("float");
Loading FLOAT 0.5.10 ...
true
gap> SetFloats(MPC);
gap> Float(E(6));
.5e0+.866025e0ⅈ
gap> x:=E(3)+E(5)^2;
-E(15)-E(15)^2-E(15)^8-2*E(15)^11-E(15)^14
gap> y:=Float(x);
-.130902e1+.145381e1ⅈ
gap> Norm(y);
.382709e1
gap> RealPart(y);
-.130902e1
gap> ImaginaryPart(y);
.145381e1
gap> ComplexConjugate(y);
-.130902e1-.145381e1ⅈ
See the documentation for the Float package for installation requirements
and further details. In particular, I am not aware of Float being usable
under Windows.
Hope this helps,
Alexander
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