#7545: Gaussian Integers
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Reporter: wuthrich | Owner:
Type: enhancement | davidloeffler
Priority: minor | Status:
Component: number fields | needs_info
Keywords: gaussian integers, Z[i], | Milestone: sage-
quadratic number ring | wishlist
Authors: | Resolution:
Report Upstream: N/A | Merged in:
Branch: | Reviewers:
Dependencies: | Work issues:
| Commit:
| Stopgaps:
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Comment (by wuthrich):
Maybe I should clarify the original aim of this ticket and the preliminary
code: It was for educational purpose. The code there was in no way
optimized, but it illustrated what I taught at the time. I don't think
that code should go in. Some of the comments above relate to outdated
things. After all this ticket is now 5 years old.
Regardless of that. I believe we should have that the standard {{{I}}} in
sage is an element in the ring of integers of the {{{QuadraticField}}}. It
may be worth to have this particular field and its ring as a class for the
following reason:
* I would really want the printing to change and I am not sure I want to
fight for a change for arbitrary number fields.
* I think the global name {{{GaussianIntegers}}} could be worth having for
educational purposes.
* Maybe there are things from pari's {{{I}}} that one can use to increase
the speed. Presumably pari's {{{I}}} is not just a wrap around
{{{Mod(x,x^2+1)}}} but I don't know about this.
* It is also one of two in the intersection of {{{CyclotomicFields}}} and
{{{QuadraticField}}}.
* It could interact with the symbolic {{{I}}} and other instances of it.
In any case, this should not be more than a wrapper around optimized code
in other places.
What I consider a bug is
{{{
sage: K = QuadraticField(-1)
sage: I in K
False
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/7545#comment:22>
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