54 lines
2.1 KiB
Diff
54 lines
2.1 KiB
Diff
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From 6330cee1a69229b2f5d8ac4a09a73d8152f5e14d Mon Sep 17 00:00:00 2001
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From: =?UTF-8?q?Gonzalo=20Tornar=C3=ADa?= <tornaria@cmat.edu.uy>
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Date: Mon, 28 Feb 2022 23:15:16 -0300
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Subject: trac 33360: avoid factoring in is_prime()
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In the added TEST, the ideal norm is product of two primes but factoring
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this product takes about half an hour, so factoring the ideal is slow.
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To fix the issue, we only factor the ideal if the norm is a prime power.
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---
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src/sage/rings/number_field/number_field_ideal.py | 22 ++++++++++++++++++++++
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1 file changed, 22 insertions(+)
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diff --git a/src/sage/rings/number_field/number_field_ideal.py b/src/sage/rings/number_field/number_field_ideal.py
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index f785f22..10d1f88 100644
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--- a/src/sage/rings/number_field/number_field_ideal.py
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+++ b/src/sage/rings/number_field/number_field_ideal.py
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@@ -995,10 +995,32 @@ class NumberFieldIdeal(Ideal_generic):
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False
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sage: K.ideal(17).is_prime() # ramified
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False
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+
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+ TESTS::
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+
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+ Check that we do not factor the norm of the ideal, this used
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+ to take half an hour, see :trac:`33360`
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+
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+ sage: K.<a,b,c> = NumberField([x^2-2,x^2-3,x^2-5])
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+ sage: t = (((-2611940*c + 1925290/7653)*b - 1537130/7653*c
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+ ....: + 10130950)*a + (1343014/7653*c - 8349770)*b
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+ ....: + 6477058*c - 2801449990/4002519)
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+ sage: t.is_prime()
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+ False
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+
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"""
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try:
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return self._pari_prime is not None
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except AttributeError:
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+ K = self.number_field().pari_nf()
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+ I = self.pari_hnf()
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+ # This would be better, but it is broken in pari 2.13.3.
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+ # self._pari_prime = K.idealismaximal(I) or None
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+ # Instead we factor I, but only if the norm is a prime power
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+ n = K.idealnorm(I)
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+ if n.denominator() > 1 or not n.isprimepower():
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+ self._pari_prime = None
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+ return False
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F = self.factor() # factorization with caching
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if len(F) != 1 or F[0][1] != 1:
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self._pari_prime = None
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--
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cgit v1.0-1-gd88e
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