Implement compact real forms for matrix Lie algebras

[tscrim]

Because they are interesting and are useful.

[tscrim]

New commits:

​1fb62d7

Implementation of compact real forms for classical matrix Lie algebras.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​23f0930

Added su to Lie algebra examples.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​e72b7c9

Doing some more documentation and small fixes.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​0bea719	Merge branch 'develop' into t/28149/public/lie_algebras/compact_real_form-28149
​429e156	editorial changes

[bsalisbury1]

Hi Travis,

I made some small changes to the documentation. If you are okay with these changes, you may set this to positive review on my behalf.

~Ben

[tscrim]

Thank you!

[vbraun]

On Python 3:

sage -t --long src/sage/algebras/lie_algebras/classical_lie_algebra.py
**********************************************************************
File "src/sage/algebras/lie_algebras/classical_lie_algebra.py", line 1202, in sage.algebras.lie_algebras.classical_lie_algebra.MatrixCompactRealForm.Element._richcmp_
Failed example:
    sorted(L.basis())
Exception raised:
    Traceback (most recent call last):
      File "/var/lib/buildbot/slave/sage3_git/build/local/lib/python3.7/site-packages/sage/doctest/forker.py", line 681, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/var/lib/buildbot/slave/sage3_git/build/local/lib/python3.7/site-packages/sage/doctest/forker.py", line 1105, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.algebras.lie_algebras.classical_lie_algebra.MatrixCompactRealForm.Element._richcmp_[1]>", line 1, in <module>
        sorted(L.basis())
      File "sage/structure/element.pyx", line 1091, in sage.structure.element.Element.__richcmp__ (build/cythonized/sage/structure/element.c:9923)
        return (<Element>self)._richcmp_(other, op)
      File "sage/structure/element.pyx", line 1095, in sage.structure.element.Element._richcmp_ (build/cythonized/sage/structure/element.c:10030)
        cpdef _richcmp_(left, right, int op):
      File "/var/lib/buildbot/slave/sage3_git/build/local/lib/python3.7/site-packages/sage/algebras/lie_algebras/classical_lie_algebra.py", line 1208, in _richcmp_
        return richcmp((self._real, self._imag), (other._real, other._imag), op)
      File "sage/structure/richcmp.pxd", line 6, in sage.structure.richcmp.richcmp (build/cythonized/sage/structure/richcmp.c:3043)
        cpdef inline richcmp(x, y, int op):
      File "sage/structure/richcmp.pxd", line 50, in sage.structure.richcmp.richcmp (build/cythonized/sage/structure/richcmp.c:2939)
        return PyObject_RichCompare(x, y, op)
      File "sage/structure/element.pyx", line 1091, in sage.structure.element.Element.__richcmp__ (build/cythonized/sage/structure/element.c:9923)
        return (<Element>self)._richcmp_(other, op)
      File "sage/matrix/matrix_sparse.pyx", line 373, in sage.matrix.matrix_sparse.Matrix_sparse._richcmp_ (build/cythonized/sage/matrix/matrix_sparse.c:5799)
        return richcmp(self._dict(), right._dict(), op)
      File "sage/structure/richcmp.pxd", line 50, in sage.structure.richcmp.richcmp (build/cythonized/sage/matrix/matrix_sparse.c:14822)
        return PyObject_RichCompare(x, y, op)
    TypeError: '<' not supported between instances of 'dict' and 'dict'
**********************************************************************
1 item had failures:
   1 of   3 in sage.algebras.lie_algebras.classical_lie_algebra.MatrixCompactRealForm.Element._richcmp_
    [210 tests, 1 failure, 47.86 s]

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​bf3c240

More explicit comparisons for sparse matrices (for Python3).

[tscrim]

The root cause is that dict's are incomparable on Python3, which means sparse matrices are incomparable, unlike dense matrices. So I changed how comparisons are done for sparse matrices, which is why I put you in cc Frédéric.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​8afd478

Fixing last doctest.

[tscrim]

(Now) Passes all doctests. Can someone review the last two changes? Should be quick.

[chapoton]

• some pyflakes warnings, see last patchbot (only 2 fixable ones)

• typo "tranposes"

• here the brackets can be removed, I think:

+ names = tuple(['CR%s'%s for s in range(dim)])

Otherwise, looks good. You can set to positive once the above is fixed.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​4adf53b

Final tidbits from Frederic.

[tscrim]

Replying to chapoton:

• some pyflakes warnings, see last patchbot (only 2 fixable ones)

Fixed.

• typo "tranposes"

Fixed.

• here the brackets can be removed, I think:

+ names = tuple(['CR%s'%s for s in range(dim)])

It is actually slightly faster to have the brackets. I think internally Python has some optimization for constructing tuples from lists.

Otherwise, looks good. You can set to positive once the above is fixed.

Thank you. I am allowing myself to set this to a positive review.