ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 13 Feb 2024 15:11:56 +0100Finding a certain idealhttps://ask.sagemath.org/question/75945/finding-a-certain-ideal/Hey SAGE-Community, <p>
I am new to SAGE and looking for some help for a small university project.
Given 𝒪<sub>K</sub> as the ring of integers to K=ℚ(√5). Given also a totally negative number *d* ∈ 𝒪<sub>K</sub><sup>2</sup>. How can I calculate the largest integral ideal **f** in K whose square divides *d* such that *d* is a square modulo 4 **f**? <p>
I guess that both questions are rather easily done in SAGE but I am missing the necessary experience. Anyways, thanks a lot in advance!Mon, 12 Feb 2024 08:37:27 +0100https://ask.sagemath.org/question/75945/finding-a-certain-ideal/Comment by imbluedabedee for <p>Hey SAGE-Community, </p><p>
I am new to SAGE and looking for some help for a small university project.
Given 𝒪<sub>K</sub> as the ring of integers to K=ℚ(√5). Given also a totally negative number <em>d</em> ∈ 𝒪<sub>K</sub><sup>2</sup>. How can I calculate the largest integral ideal <strong>f</strong> in K whose square divides <em>d</em> such that <em>d</em> is a square modulo 4 <strong>f</strong>? </p><p>
I guess that both questions are rather easily done in SAGE but I am missing the necessary experience. Anyways, thanks a lot in advance!</p>
https://ask.sagemath.org/question/75945/finding-a-certain-ideal/?comment=75979#post-id-75979Hey rburing, thanks for your feedback. This sounds correct, but I am still not sure on how to find the ideal in general.Tue, 13 Feb 2024 15:11:56 +0100https://ask.sagemath.org/question/75945/finding-a-certain-ideal/?comment=75979#post-id-75979Comment by rburing for <p>Hey SAGE-Community, </p><p>
I am new to SAGE and looking for some help for a small university project.
Given 𝒪<sub>K</sub> as the ring of integers to K=ℚ(√5). Given also a totally negative number <em>d</em> ∈ 𝒪<sub>K</sub><sup>2</sup>. How can I calculate the largest integral ideal <strong>f</strong> in K whose square divides <em>d</em> such that <em>d</em> is a square modulo 4 <strong>f</strong>? </p><p>
I guess that both questions are rather easily done in SAGE but I am missing the necessary experience. Anyways, thanks a lot in advance!</p>
https://ask.sagemath.org/question/75945/finding-a-certain-ideal/?comment=75949#post-id-75949Is 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())` gives `True`. It could help someone write an answer.Mon, 12 Feb 2024 11:47:27 +0100https://ask.sagemath.org/question/75945/finding-a-certain-ideal/?comment=75949#post-id-75949