21 Dec
2015
21 Dec
'15
6:22 p.m.
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? 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