ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 03 Jul 2013 00:24:03 -0500Matrix conjugacy classes over Z and ideal classeshttps://ask.sagemath.org/question/8244/matrix-conjugacy-classes-over-z-and-ideal-classes/I had a couple questions; the first involves matrix conjugacy classes over the integers and the second involves integral bases. I'm not sure what the algorithms in Sage are for the following procedures.
1) Is it possible to determine if two integer-valued square matrices (which are conjugate over Q) are also conjugate over Z?
2) In a number field K, given an ideal class I, we can find an integral basis for a representative ideal in I by the command:
sage: I.integral_basis()
Is it possible to work in the reverse direction, that is given a set of elements in K which form an integral basis, is it possible to find the corresponding ideal and ideal class for that integral basis?
Thanks in advance for any advice.CCThu, 28 Jul 2011 14:14:45 -0500https://ask.sagemath.org/question/8244/ideal primality in a polynomial ring with integer coefficientshttps://ask.sagemath.org/question/10313/ideal-primality-in-a-polynomial-ring-with-integer-coefficients/Hello,
how primality of an ideal in a polynomial ring with integer coefficients can be checked?
SageMath (5.7) tells me 'notImplementedError'.
Example:
R = ZZ[x]
I = R.ideal(7)
I.is_prime()
# leads to NotImplementedError
In addition, does someone know a good reference to the related theory?
Thanks,
Jackjack77Wed, 03 Jul 2013 00:24:03 -0500https://ask.sagemath.org/question/10313/