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Enumerating prime ideals in SAGE

asked 2018-09-19 08:20:46 +0200

mathjain gravatar image

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?

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answered 2018-09-19 18:00:04 +0200

FrédéricC gravatar image

Like that maybe

sage: K.<a>=QuadraticField(5)
sage: K.primes_of_bounded_norm(120)
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Asked: 2018-09-19 08:20:46 +0200

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Last updated: Sep 19 '18