- sage: set_random_seed()
- sage: J = random_eja()
- sage: v = J.vector_space().random_element()
- sage: J(v).vector() == v
- True
-
- """
- # Goal: if we're given a matrix, and if it lives in our
- # parent algebra's "natural ambient space," convert it
- # into an algebra element.
- #
- # The catch is, we make a recursive call after converting
- # the given matrix into a vector that lives in the algebra.
- # This we need to try the parent class initializer first,
- # to avoid recursing forever if we're given something that
- # already fits into the algebra, but also happens to live
- # in the parent's "natural ambient space" (this happens with
- # vectors in R^n).
- try:
- FiniteDimensionalAlgebraElement.__init__(self, A, elt)
- except ValueError:
- natural_basis = A.natural_basis()
- if elt in natural_basis[0].matrix_space():
- # Thanks for nothing! Matrix spaces aren't vector
- # spaces in Sage, so we have to figure out its
- # natural-basis coordinates ourselves.
- V = VectorSpace(elt.base_ring(), elt.nrows()**2)
- W = V.span( _mat2vec(s) for s in natural_basis )
- coords = W.coordinates(_mat2vec(elt))
- FiniteDimensionalAlgebraElement.__init__(self, A, coords)