* James Propp <jamespropp@gmail.com> [Dec 22. 2015 08:18]:
On Monday, December 21, 2015, Neil Sloane <njasloane@gmail.com> wrote:
JJ,
Concerning the ring of Eisenstein integers: There is no room for argument! They are the complex numbers of the form a + b omega, where omega = e^(2 Pi i / 3) = -1/2 + i sqrt(3)/2 and a and b are ordinary integers.
That is one way to describe them. Joerg's description is equally valid. It's a matter of esthetics and convenience. Joerg, can you say why you prefer your way of describing the ring?
I did all my drawings (lots!), calculations, and programming with the basis { 1, \omega_6 }, so it is a bit of a practical thing. It will be painless for my write-up to switch to the third primitive root, so I will do that (unless I'll find compelling reason not to).
You should not use a sixth root of unity.
Why shouldn't he?
(Yes, -w is in the ring, but so what)
Maybe because for some applications it's nice to have a norm-form in which all coefficients are positive? (I'm just guessing.)
Best regards
Neil
Jim Propp
Thanks for the answers! If anyone wants to murder some of the remaining terminology, kindly speak up. Best regards, jj
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun