Edit detail for FreeModule revision 4 of 8

A bi-module is a free module over a ring with generators indexed by an ordered 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 an ordered set and R is a ring (which may be non-commutative).

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

)sh FreeModule

 FreeModule(R: Ring,S: OrderedSet)  is a domain constructor
 Abbreviation for FreeModule is FM 
 This constructor is not exposed in this frame.
------------------------------- Operations --------------------------------
 ?*? : (R,S) -> %                      ?*? : (S,R) -> %
 ?*? : (%,R) -> %                      ?*? : (R,%) -> %
 ?*? : (Integer,%) -> %                ?*? : (PositiveInteger,%) -> %
 ?+? : (%,%) -> %                      ?-? : (%,%) -> %
 -? : % -> %                           ?=? : (%,%) -> Boolean
 0 : () -> %                           coefficient : (%,S) -> R
 coefficients : % -> List(R)           coerce : S -> %
 coerce : % -> OutputForm              hash : % -> SingleInteger
 latex : % -> String                   leadingCoefficient : % -> R
 leadingMonomial : % -> S              leadingSupport : % -> S
 map : ((R -> R),%) -> %               monom : (S,R) -> %
 monomial : (R,S) -> %                 monomial? : % -> Boolean
 monomials : % -> List(%)              reductum : % -> %
 retract : % -> S                      sample : () -> %
 support : % -> List(S)                zero? : % -> Boolean
 ?~=? : (%,%) -> Boolean              
 ?*? : (NonNegativeInteger,%) -> %
 construct : List(Record(k: S,c: R)) -> %
 constructOrdered : List(Record(k: S,c: R)) -> %
 leadingTerm : % -> Record(k: S,c: R)
 linearExtend : ((S -> R),%) -> R if R has COMRING
 listOfTerms : % -> List(Record(k: S,c: R))
 numberOfMonomials : % -> NonNegativeInteger
 retractIfCan : % -> Union(S,"failed")
 subtractIfCan : (%,%) -> Union(%,"failed")

See: [PolySpad]?

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

(1)

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