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# Edit detail for FreeModule revision 8 of 8

 1 2 3 4 5 6 7 8 Editor: test1 Time: 2018/04/13 15:52:36 GMT+0 Note:

changed:
-A bi-module is a free module
-over a ring with generators indexed by an ordered set.
FreeModule implements free module
over a ring with generators indexed by a set.

changed:
-in the domain **R** where **S** is an ordered set
in the domain **R** where **S** is a set


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).

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)
 (1)
Type: Boolean

        if R has Field then VectorSpace(R)
dimension():CardinalNumber == coerce size()$S else dimension():CardinalNumber == Aleph(0)  fricas F2:=FreeModule(Fraction Integer,OrderedVariableList [e1,e1])  (2) Type: Type fricas F2 has VectorSpace(Fraction Integer)  (3) Type: Boolean fricas dimension()$F2
Integer),OrderedVariableList([e1,e1])) .