No, like anyone who isn’t watching out for traps caused by bad notation. It’s much easier to copy down numbers than it is to alter them appropriately. If you see “e^(pi i/3)”, what stands out is the 3 in the denominator. Except oops, pi actually only means half a circle, so this is a sixth root of unity, not a third one. Part of why I like to just write zeta_n instead of e^(2pi i/n). Sure, this can be avoided with a bit of thought, but thought shouldn’t be required here; notation that forces you to think about something so trivial, is not good notation.
I’ve certainly used it for that—but I pattern it with dropping the subscript n, when it is clear when there is only one particular root of unity we’re basing off of. I’ve never ever seen zeta used.
What? Like who, 6th graders?
I find that unfair. I have made the mistake Sniffnoy describes many times, all of them after I was in 6th grade.
Easy solution. Pi is half a circle. Pie is the whole one. Then there is a smooth transition from grade 3 to university.
I’ve been looking for a good thing to call 2*Pi—this might cut it.
Nice one! ;)
No, like anyone who isn’t watching out for traps caused by bad notation. It’s much easier to copy down numbers than it is to alter them appropriately. If you see “e^(pi i/3)”, what stands out is the 3 in the denominator. Except oops, pi actually only means half a circle, so this is a sixth root of unity, not a third one. Part of why I like to just write zeta_n instead of e^(2pi i/n). Sure, this can be avoided with a bit of thought, but thought shouldn’t be required here; notation that forces you to think about something so trivial, is not good notation.
omega_n is the notation I most often run across.
Hm, I’ve generally just seen omega for zeta_3.
I’ve certainly used it for that—but I pattern it with dropping the subscript n, when it is clear when there is only one particular root of unity we’re basing off of. I’ve never ever seen zeta used.