ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 08 Jul 2017 12:52:42 -0500How to compute a cyclic subgroup of a class group?http://ask.sagemath.org/question/38198/how-to-compute-a-cyclic-subgroup-of-a-class-group/ Hello, I am quite new to computing in Sage and I am stuck at this point. Please help me out. I am going to use algebraic number theory notation without explaining them in detail. All computations are in quadratic fields.
What I have :
- $\Delta_p=p^2\Delta_K$ where $p$ is a prime, $\Delta_K=-pq$ and $\Delta_K\equiv 1$ mod $4$
- I computed the class group, $C(\Delta_p)$ in Sage
What I want :
- Set $f=[(p^2,p)]$ in $C(\Delta_p)$ where $(p^2,p)$ is the standard representation of an ideal of norm $p^2$
- Set $F=\langle f \rangle$
My question is :
- How to get that cyclic subgroup $F$?
I have been looking at AbelianGroup and ClassGroup in Sage but I am not quite understanding how to use these to actually get what I want.
Any help in this matter would be greatly appreciated.jakkeonSat, 08 Jul 2017 12:52:42 -0500http://ask.sagemath.org/question/38198/Fundamental Discriminanthttp://ask.sagemath.org/question/32945/fundamental-discriminant/ How can I print a list of around 10000 fundamental discriminant of quadratic number field in sage?LernerFri, 01 Apr 2016 11:43:37 -0500http://ask.sagemath.org/question/32945/Does QuadraticField use any special algorithms for computing the class group of quadratic imaginary number fields?http://ask.sagemath.org/question/26922/does-quadraticfield-use-any-special-algorithms-for-computing-the-class-group-of-quadratic-imaginary-number-fields/ I need to compute the class group of a quadratic imaginary number field that has a fairly large discriminant (over 96 bits.) I was wondering what, if any, algorithms the QuadraticField class uses for computing the class group.
Dan ShumowFri, 22 May 2015 15:23:45 -0500http://ask.sagemath.org/question/26922/Quadratic number fieldshttp://ask.sagemath.org/question/10015/quadratic-number-fields/Hello!
I try to implement an inclusion test, of which I thought it must be quite simple, but until now I cannot figure out how to do it properly.
Problem: Given any element x, test if x is included in some quadratic number field and return true/false.
I tried the following:
x = 2 + sqrt(5)
K = QuadraticField(5)
print(x in K)
Here, the answer is 'no' or 'false' which is obviously wrong, so I assume I'm doing something completely wrong. What do I have to change?pinwheelFri, 12 Apr 2013 05:32:51 -0500http://ask.sagemath.org/question/10015/