#15384: Improvements to root systems
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.3
Component: combinatorics | Resolution:
Keywords: root systems, | Merged in:
days54 | Reviewers: Dan Bump
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 18fd0946874e2e54a75cdcd761311dea3f2810a4
public/combinat/root_systems/improvements-15384| Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Comment (by bump):
The scalar product that was implemented is fundamental in Kac' book and
for that alone this is an important patch.
I got one doctest failure in weight_space.py:
{{{
sage -t weight_space.py
**********************************************************************
File "weight_space.py", line 131, in
sage.combinat.root_system.weight_space.WeightSpace
Failed example:
for ct in
CartanType.samples(crystallographic=True)+[CartanType(["A",2],["C",5,1])]:
TestSuite(ct.root_system().weight_lattice()).run()
TestSuite(ct.root_system().weight_space()).run()
Expected nothing
Got:
Failure in _test_not_implemented_methods:
Traceback (most recent call last):
[snip]
AssertionError: Not implemented method: _symmetric_form_matrix
}}}
In the {{{cartan_type.py}}} you could delete the sentence on line 108
since you do implement Coxeter numbers!
For the positive roots, imaginary roots, etc. The user might like to know
how to get a list of them. I guess you can do this.
{{{
sage: PR=RootSystem(['A',3,1]).root_lattice().positive_real_roots()
sage: [PR.unrank(i) for i in [0..4]]
[alpha[1], alpha[2], alpha[3], alpha[1] + alpha[2], alpha[2] + alpha[3]]
}}}
Is there a more obvious way? And should something like this be in the
doctest?
In the method basic_imaginary_roots the docstring still refers to simple
imaginary roots (twice).
It would be good if there were pointers to Kac' book in some places. For
example, in symmetric_form, the doc could have a pointer to Chapter 6. The
Coxeter number method could have a pointer to Bourbaki, Lie Groups and Lie
Algebras V.6.1.
--
Ticket URL: <http://trac.sagemath.org/ticket/15384#comment:19>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
