Finding a certain ideal
Hey SAGE-Community,
I am new to SAGE and looking for some help for a small university project. Given 𝒪K as the ring of integers to K=ℚ(√5). Given also a totally negative number d ∈ 𝒪K2. How can I calculate the largest integral ideal f in K whose square divides d such that d is a square modulo 4 f?
I guess that both questions are rather easily done in SAGE but I am missing the necessary experience. Anyways, thanks a lot in advance!
Is this an example of what you want?
K.<a> = NumberField(x^2 - 5); OK = K.ring_of_integers(); d = -4; f = OK.fractional_ideal(2); I = 4*f; I.reduce(d) in set(I.reduce(c^2) for c in I.residues())
givesTrue
. It could help someone write an answer.Hey rburing, thanks for your feedback. This sounds correct, but I am still not sure on how to find the ideal in general.