codomain could not be determined

asked 2018-06-25 14:12:25 -0600

ml9nn gravatar image

I created an InfiniteDimensionalFreeAlgebra using CombinatorialFreeModule. It looks something like this:

class InfiniteDimensionalFreeAlgebra(CombinatorialFreeModule):
    r""" The algebra generated by ``a[0], a[1], a[2], ...`` over the integers. """
    def __init__(self,
            base_ring=IntegerRing(),
            prefix='a',
            index_set=NonNegativeIntegerSemiring()):
        self._base_ring = base_ring
        self._basis_monoid = FreeMonoid(index_set=index_set, commutative=True, prefix=prefix)
        # category
        category = Algebras(self._base_ring.category()).WithBasis().Commutative()
        category = category.or_subcategory(category)
        # init
        CombinatorialFreeModule.__init__(
            self,
            self._base_ring,
            self._basis_monoid,
            category=category,
            prefix='',
            bracket=False)

Now I want to view it as a ring and take symmetric polynomials over the ring. For example, in 2 variables, the following is one such symmetric polynomial:

2a[7] * x[1] + 2a[7] * x[2] + x[1]x[2] + 5

In my code, I attempt to initialize some Schur symmetric functions over this ring with something like:

a = InfiniteDimensionalFreeAlgebra()
sym = SymmetricFunctions(a)
s = sym.s()
one = s.one()
one_poly = one.expand(2)

at which point I run into the error codomain could not be determined when it attempts to apply some sort of morphism to the Schur function one. The full stacktrace is

Traceback (most recent call last):
  File "./test_all.py", line 1162, in <module>
    h = double_homogeneous(1, 1)
  File "/Users/Matthew/programming/sage/morse-code/k_combinat_for_sage/all.py", line 664, in double_homogeneous
    one_poly = one.expand(n)
  File "/Users/Matthew/programming/sage/official-git-repo/local/lib/python2.7/site-packages/sage/combinat/sf/schur.py", line 537, in expand
    return self._expand(condition, n, alphabet)
  File "/Users/Matthew/programming/sage/official-git-repo/local/lib/python2.7/site-packages/sage/combinat/sf/sfa.py", line 4986, in _expand
    return parent._apply_module_morphism(self, f)
  File "/Users/Matthew/programming/sage/official-git-repo/local/lib/python2.7/site-packages/sage/categories/modules_with_basis.py", line 1096, in _apply_module_morphism
    raise ValueError('codomain could not be determined')
ValueError: codomain could not be determined

and the full code can be found at k_combinat_for_sage.

Thank you, your help is greatly appreciated.

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