# Ideal moduli and residue symbols

Hi, everyone;

I'm fairly new to sage, but I feel like I have some heavy lifting to do. I'm attempting to do a couple of things:

1) I need to see if two complex numbers are equivalent mod an ideal, eg pi == 1 mod 2+2i. It might be a dumb question but my searching thus far has come up short

2) I need to compute residue symbols, and I'm using the Number Field residue symbol method, but I'm having trouble. I have the following: C = ComplexField() I = C.0 r = C.ideal(b).residue_symbol(D,4) with a and b complex numbers. Help!

Could you please define what you mean by "ideal". The complex plane is a field, so every ideal in the usual sense is trivial here.

Okay, after reading a bit more I can clarify. The ambient space is the ring of integers of Q(zeta_m) - mth root of unity. So these ideals are in the ring.