#11111: More support for finite dimensional modules and algebras with basis
-------------------------------------+-------------------------------------
       Reporter:  nthiery            |        Owner:  nthiery
           Type:  enhancement        |       Status:  new
       Priority:  major              |    Milestone:  sage-6.4
      Component:  categories         |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Florent Hivert,    |    Reviewers:
  Franco Saliola, Nicolas M. ThiƩry  |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  195d14e5a309834179015f4066d27dd5b7ca5b20
  
public/11111-more_support_for_finite_dimensional_modules_and_algebras_with_basis|
     Stopgaps:
   Dependencies:  #10963, #8678      |
-------------------------------------+-------------------------------------

Comment (by aschilling):

 There are currently failing tests:
 {{{
 sage -t algebras.py
 **********************************************************************
 File "algebras.py", line 236, in
 sage.categories.algebras.Algebras.Subobjects.ElementMethods._mul_
 Failed example:
     Z = SymmetricGroup(5).algebra(QQ).center()
 Exception raised:
     Traceback (most recent call last):
       File "/Applications/sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 480, in _run
         self.compile_and_execute(example, compiler, test.globs)
       File "/Applications/sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 843, in compile_and_execute
         exec compiled in globs
       File "<doctest
 sage.categories.algebras.Algebras.Subobjects.ElementMethods._mul_[0]>",
 line 1, in <module>
         Z = SymmetricGroup(Integer(5)).algebra(QQ).center()
       File "cachefunc.pyx", line 2143, in
 sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__
 (build/cythonized/sage/misc/cachefunc.c:12263)
       File "/Applications/sage/local/lib/python2.7/site-
 packages/sage/categories/finite_dimensional_algebras_with_basis.py", line
 340, in center
         center = self.submodule(self.center_basis(),
       File "/Applications/sage/local/lib/python2.7/site-
 packages/sage/categories/groups.py", line 682, in center_basis
         self.basis().keys().conjugacy_classes()]
       File "parent.pyx", line 864, in
 sage.structure.parent.Parent.__getattr__
 (build/cythonized/sage/structure/parent.c:7377)
       File "misc.pyx", line 251, in
 sage.structure.misc.getattr_from_other_class
 (build/cythonized/sage/structure/misc.c:1687)
     AttributeError: 'StandardPermutations_n_with_category' object has no
 attribute 'conjugacy_classes'
 **********************************************************************
 File "algebras.py", line 237, in
 sage.categories.algebras.Algebras.Subobjects.ElementMethods._mul_
 Failed example:
     B = Z.basis()
 Exception raised:
     Traceback (most recent call last):
       File "/Applications/sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 480, in _run
         self.compile_and_execute(example, compiler, test.globs)
       File "/Applications/sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 843, in compile_and_execute
         exec compiled in globs
       File "<doctest
 sage.categories.algebras.Algebras.Subobjects.ElementMethods._mul_[1]>",
 line 1, in <module>
         B = Z.basis()
     NameError: name 'Z' is not defined
 **********************************************************************
 File "algebras.py", line 238, in
 sage.categories.algebras.Algebras.Subobjects.ElementMethods._mul_
 Failed example:
     B[3] * B[2]
 Exception raised:
     Traceback (most recent call last):
       File "/Applications/sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 480, in _run
         self.compile_and_execute(example, compiler, test.globs)
       File "/Applications/sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 843, in compile_and_execute
         exec compiled in globs
       File "<doctest
 sage.categories.algebras.Algebras.Subobjects.ElementMethods._mul_[2]>",
 line 1, in <module>
         B[Integer(3)] * B[Integer(2)]
     NameError: name 'B' is not defined
 **********************************************************************
 1 item had failures:
    3 of   4 in
 sage.categories.algebras.Algebras.Subobjects.ElementMethods._mul_
     [25 tests, 3 failures, 0.66 s]
 sage -t category_with_axiom.py
 **********************************************************************
 File "category_with_axiom.py", line 1642, in
 sage.categories.category_with_axiom
 Failed example:
     FiniteGroups().Algebras(QQ)
 Expected:
     Join of Category of finite dimensional hopf algebras with basis over
 Rational Field
         and Category of group algebras over Rational Field
         and Category of finite set algebras over Rational Field
 Got:
     Category of finite group algebras over Rational Field
 **********************************************************************
 1 item had failures:
    1 of 166 in sage.categories.category_with_axiom
     [322 tests, 1 failure, 0.49 s]
 sage -t fields.py
 **********************************************************************
 File "fields.py", line 128, in
 sage.categories.fields.Fields._contains_helper
 Failed example:
     Q.category()
 Expected:
     Join of Category of commutative algebras over Rational Field and
 Category of subquotients of monoids and Category of quotients of
 semigroups
 Got:
     Category of commutative quotients of algebras over Rational Field
 **********************************************************************
 1 item had failures:
    1 of   8 in sage.categories.fields.Fields._contains_helper
     [75 tests, 1 failure, 1.66 s]
 sage -t groups.py
 **********************************************************************
 File "groups.py", line 673, in
 sage.categories.groups.Groups.Algebras.ParentMethods.center_basis
 Failed example:
     SymmetricGroup(3).algebra(QQ).center_basis()
 Exception raised:
     Traceback (most recent call last):
       File "/Applications/sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 480, in _run
         self.compile_and_execute(example, compiler, test.globs)
       File "/Applications/sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 843, in compile_and_execute
         exec compiled in globs
       File "<doctest
 sage.categories.groups.Groups.Algebras.ParentMethods.center_basis[0]>",
 line 1, in <module>
         SymmetricGroup(Integer(3)).algebra(QQ).center_basis()
       File "/Applications/sage/local/lib/python2.7/site-
 packages/sage/categories/groups.py", line 682, in center_basis
         self.basis().keys().conjugacy_classes()]
       File "parent.pyx", line 864, in
 sage.structure.parent.Parent.__getattr__
 (build/cythonized/sage/structure/parent.c:7377)
       File "misc.pyx", line 251, in
 sage.structure.misc.getattr_from_other_class
 (build/cythonized/sage/structure/misc.c:1687)
     AttributeError: 'StandardPermutations_n_with_category' object has no
 attribute 'conjugacy_classes'
 **********************************************************************
 File "groups.py", line 809, in
 sage.categories.groups.Groups.Algebras.ElementMethods.central_form
 Failed example:
     A.central_form()
 Expected:
     B[(1,2,3)]
 Got:
     B[[2, 3, 1]]
 **********************************************************************
 File "groups.py", line 813, in
 sage.categories.groups.Groups.Algebras.ElementMethods.central_form
 Failed example:
     B.central_form()
 Expected:
     4*B[()] + 3*B[(1,2)] + 2*B[(1,2)(3,4)] + 2*B[(1,2,3)] + B[(1,2,3,4)]
 Got:
     4*B[[1, 2, 3, 4]] + 3*B[[2, 1, 3, 4]] + 2*B[[2, 1, 4, 3]] + 2*B[[2, 3,
 1, 4]] + B[[2, 3, 4, 1]]
 **********************************************************************
 2 items had failures:
    2 of   9 in
 sage.categories.groups.Groups.Algebras.ElementMethods.central_form
    1 of   2 in
 sage.categories.groups.Groups.Algebras.ParentMethods.center_basis
     [124 tests, 3 failures, 2.94 s]
 sage -t modules_with_basis.py
 **********************************************************************
 File "modules_with_basis.py", line 509, in
 sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods.submodule
 Failed example:
     basis
 Expected:
     [B[()], B[(2,3)] + B[(1,2)] + B[(1,3)], B[(1,2,3)] + B[(1,3,2)]]
 Got:
     [[1, 2, 3], [1, 3, 2] + [2, 1, 3] + [3, 2, 1], [2, 3, 1] + [3, 1, 2]]
 **********************************************************************
 File "modules_with_basis.py", line 520, in
 sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods.submodule
 Failed example:
     c[1].lift()
 Expected:
     B[(2,3)] + B[(1,2)] + B[(1,3)]
 Got:
     [1, 3, 2] + [2, 1, 3] + [3, 2, 1]
 **********************************************************************
 File "modules_with_basis.py", line 530, in
 sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods.submodule
 Failed example:
     center = S3A.center()
 Exception raised:
     Traceback (most recent call last):
       File "/Applications/sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 480, in _run
         self.compile_and_execute(example, compiler, test.globs)
       File "/Applications/sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 843, in compile_and_execute
         exec compiled in globs
       File "<doctest
 
sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods.submodule[22]>",
 line 1, in <module>
         center = S3A.center()
       File "cachefunc.pyx", line 2143, in
 sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__
 (build/cythonized/sage/misc/cachefunc.c:12263)
       File "/Applications/sage/local/lib/python2.7/site-
 packages/sage/categories/finite_dimensional_algebras_with_basis.py", line
 340, in center
         center = self.submodule(self.center_basis(),
       File "/Applications/sage/local/lib/python2.7/site-
 packages/sage/categories/groups.py", line 682, in center_basis
         self.basis().keys().conjugacy_classes()]
       File "parent.pyx", line 864, in
 sage.structure.parent.Parent.__getattr__
 (build/cythonized/sage/structure/parent.c:7377)
       File "misc.pyx", line 251, in
 sage.structure.misc.getattr_from_other_class
 (build/cythonized/sage/structure/misc.c:1687)
     AttributeError: 'StandardPermutations_n_with_category' object has no
 attribute 'conjugacy_classes'
 **********************************************************************
 1 item had failures:
    3 of  26 in
 sage.categories.modules_with_basis.ModulesWithBasis.ParentMethods.submodule
     [550 tests, 3 failures, 1.92 s]
 sage -t sets_cat.py
 **********************************************************************
 File "sets_cat.py", line 1402, in
 sage.categories.sets_cat.Sets.ParentMethods.algebra
 Failed example:
     SymmetricGroup(5).algebra(QQ) in SemisimpleAlgebras(QQ)
 Expected:
     True
 Got:
     False
 **********************************************************************
 1 item had failures:
    1 of  27 in sage.categories.sets_cat.Sets.ParentMethods.algebra
     [340 tests, 1 failure, 2.63 s]
 ----------------------------------------------------------------------
 sage -t algebras.py  # 3 doctests failed
 sage -t category_with_axiom.py  # 1 doctest failed
 sage -t fields.py  # 1 doctest failed
 sage -t groups.py  # 3 doctests failed
 sage -t modules_with_basis.py  # 3 doctests failed
 sage -t objects.py  # Source line number found
 sage -t sets_cat.py  # 1 doctest failed
 ----------------------------------------------------------------------
 Total time for all tests: 139.2 seconds
     cpu time: 86.4 seconds
     cumulative wall time: 126.4 seconds
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/11111#comment:26>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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