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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:

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

\label{eq1} \mbox{\rm false} (1)
Type: Boolean

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)

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

\label{eq2}\hbox{\axiomType{FreeModule}\ } (\hbox{\axiomType{Fraction}\ } (\hbox{\axiomType{Integer}\ }) , \hbox{\axiomType{OrderedVariableList}\ } ([ e 1, e 1 ]))(2)
Type: Type
fricas
F2 has VectorSpace(Fraction Integer)

\label{eq3} \mbox{\rm false} (3)
Type: Boolean
fricas
dimension()$F2
The function dimension is not implemented in FreeModule(Fraction( Integer),OrderedVariableList([e1,e1])) .




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