FreeModule implements free module over a ring with generators indexed by a set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored.

This domain implements linear combinations of elements from the domain S with coefficients in the domain R where S is a set and R is a ring (which may be non-commutative).

Ref: http://en.wikipedia.org/wiki/Free_module

See: [PolySpad]?

A FreeModule over a [Field]? is a VectorSpace? unfortunately this is not currently understood by Axiom:

FreeModule(Fraction Integer,OrderedVariableList [e1,e1]) has VectorSpace(Fraction Integer)

(1)

Ref: http://en.wikipedia.org/wiki/Vector_space#Modules

Add:

        if R has Field then VectorSpace(R)
        ...
        if R has Field then
          if S has Finite then
            dimension():CardinalNumber == coerce size()$S
          else
             dimension():CardinalNumber == Aleph(0)

F2:=FreeModule(Fraction Integer,OrderedVariableList [e1,e1])

(2)

F2 has VectorSpace(Fraction Integer)

(3)

dimension()$F2

   The function dimension is not implemented in FreeModule(Fraction(
      Integer),OrderedVariableList([e1,e1])) .