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.Sun, 16 May 2021 15:26:29 +0200Enumerating prime ideals in SAGEhttps://ask.sagemath.org/question/43698/enumerating-prime-ideals-in-sage/Given a number Field K and its ring of integers $O_K$, I want to enumerate prime ideals and calculate some quantities in $O_K$ modulo the prime ideals. This computation depends on the size of the ideal.
What I did earlier was taking a prime number, creating its ideal, factorizing it and using the factors as prime ideals. But this way I think I am doing very large computations because the norm would be very high.
I want to enumerate prime ideals below a certain norm in SAGE. What can I do?
Wed, 19 Sep 2018 08:20:46 +0200https://ask.sagemath.org/question/43698/enumerating-prime-ideals-in-sage/Comment by slelievre for <p>Given a number Field K and its ring of integers $O_K$, I want to enumerate prime ideals and calculate some quantities in $O_K$ modulo the prime ideals. This computation depends on the size of the ideal.</p>
<p>What I did earlier was taking a prime number, creating its ideal, factorizing it and using the factors as prime ideals. But this way I think I am doing very large computations because the norm would be very high.</p>
<p>I want to enumerate prime ideals below a certain norm in SAGE. What can I do?</p>
https://ask.sagemath.org/question/43698/enumerating-prime-ideals-in-sage/?comment=57138#post-id-57138Related:
- [Math Stack Exchange question 3709597: List prime ideals with norm up to 3 in a quadratic number field](https://math.stackexchange.com/questions/3709597)
- [Ask Sage question 51803: Prime ideals up to some norm in a quadratic number field](https://ask.sagemath.org/question/51803)Sun, 16 May 2021 15:26:29 +0200https://ask.sagemath.org/question/43698/enumerating-prime-ideals-in-sage/?comment=57138#post-id-57138Answer by FrédéricC for <p>Given a number Field K and its ring of integers $O_K$, I want to enumerate prime ideals and calculate some quantities in $O_K$ modulo the prime ideals. This computation depends on the size of the ideal.</p>
<p>What I did earlier was taking a prime number, creating its ideal, factorizing it and using the factors as prime ideals. But this way I think I am doing very large computations because the norm would be very high.</p>
<p>I want to enumerate prime ideals below a certain norm in SAGE. What can I do?</p>
https://ask.sagemath.org/question/43698/enumerating-prime-ideals-in-sage/?answer=43703#post-id-43703Like that maybe
sage: K.<a>=QuadraticField(5)
sage: K.primes_of_bounded_norm(120)
Wed, 19 Sep 2018 18:00:04 +0200https://ask.sagemath.org/question/43698/enumerating-prime-ideals-in-sage/?answer=43703#post-id-43703