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# Free algebra quotient elements

AUTHORS:
  - William Stein (2011-11-19): improved doctest coverage to 100%
  - David Kohel (2005-09): initial version

class `sage.algebras.free_algebra_quotient_element.``FreeAlgebraQuotientElement`(A, x)

  Bases: `sage.structure.element.AlgebraElement`

  Create the element x of the FreeAlgebraQuotient A.

  EXAMPLES:

      sage: H, (i,j,k) = sage.algebras.free_algebra_quotient.hamilton_quatalg(ZZ)
      sage: sage.algebras.free_algebra_quotient.FreeAlgebraQuotientElement(H, i)
      i
      sage: a = sage.algebras.free_algebra_quotient.FreeAlgebraQuotientElement(H, 1); a
      1
      sage: a in H
      True

  TESTS:

      sage: TestSuite(i).run()

  `vector`()

    Return underlying vector representation of this element.

    EXAMPLES:

        sage: H, (i,j,k) = sage.algebras.free_algebra_quotient.hamilton_quatalg(QQ)
        sage: ((2/3)*i - j).vector()
        (0, 2/3, -1, 0)

`sage.algebras.free_algebra_quotient_element.``is_FreeAlgebraQuotientElement`(x)

  EXAMPLES:

      sage: H, (i,j,k) = sage.algebras.free_algebra_quotient.hamilton_quatalg(QQ)
      sage: sage.algebras.free_algebra_quotient_element.is_FreeAlgebraQuotientElement(i)
      True

  Of course this is testing the data type:

      sage: sage.algebras.free_algebra_quotient_element.is_FreeAlgebraQuotientElement(1)
      False
      sage: sage.algebras.free_algebra_quotient_element.is_FreeAlgebraQuotientElement(H(1))
      True

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