Dear Wolfgang, I am not sure if you perhaps already got a private reply to your email. If not, maybe the following will help you.
Am 14.03.2012 um 09:05 schrieb Wolfgang Lindner: > dear group, > > I know how to calculate with Rationals, ZmodnZ, Integers etc. > But I could not find infos in the help-index of GAP > how to do calculations in the complex field C > (I know about gaussionInteger). Short answer: Use "Cyclotomics" or one of its subfields. Make sure to read the GAP manual on them and on abelian number fields: <http://www.gap-system.org/Manuals/doc/htm/ref/CHAP018.htm> <http://www.gap-system.org/Manuals/doc/htm/ref/CHAP058.htm> The following might also be of interest: <http://www.gap-system.org/Manuals/doc/htm/ref/CHAP056.htm> <http://www.gap-system.org/Manuals/doc/htm/ref/CHAP065.htm> Long answer: It is essentially impossible to compute with the "full set" of complex numbers (or real numbers) on a computer; in particular, not every real (and hence not every complex) number is computable (see e.g. <http://en.wikipedia.org/wiki/Computable_number>). But for the vast majority of cases (at least in my personal experience), one doesn't really need the full set of real or complex numbers; rather, one only needs to deal with a few select numbers, such as "square root of 2" or "pi". GAP allows you to work with the former: One can construct abelian extension fields of the rational numbers in GAP, which all are subfields of the "field of cyclotomic numbers". So the following works: gap> Sqrt(-1); E(4) gap> Sqrt(2); E(8)-E(8)^3 However, this does not allow you to work with pi directly, as that lives in a transcendental extension. There are some tricks to deal with that to a certain extent. Note that pi and similar transcendentals seem not to be really necessary to do group theory, which is probably why they are not supported as such. > I would like to work in C[X] etc. gap> R:=PolynomialRing(Cyclotomics, "x"); Cyclotomics[x] gap> x:=R.1; x gap> f:=x^2-x+1; x^2-x+1 Cheers, Max _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
