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

(1) -> )sh FreeModule

 FreeModule(R: Join(SemiRng,AbelianMonoid),S: SetCategory) is a domain constructor
 Abbreviation for FreeModule is FM 
 This constructor is not exposed in this frame.
------------------------------- Operations --------------------------------

 ?*? : (S, R) -> %                     ?*? : (R, S) -> %
 ?*? : (%, R) -> %                     ?*? : (R, %) -> %
 ?*? : (PositiveInteger, %) -> %       ?+? : (%, %) -> %
 -? : % -> % if R has ABELGRP          ?=? : (%, %) -> Boolean
 coefficient : (%, S) -> R             coefficients : % -> List(R)
 coerce : % -> OutputForm              latex : % -> String
 map : ((R -> R), %) -> %              monomial : (R, S) -> %
 monomial? : % -> Boolean              monomials : % -> List(%)
 support : % -> List(S)                ?~=? : (%, %) -> Boolean
 ?*? : (Integer, %) -> % if R has ABELGRP
 ?*? : (NonNegativeInteger, %) -> % if R has ABELMON or R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 ?-? : (%, %) -> % if R has ABELGRP
 ?<? : (%, %) -> Boolean if R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 ?<=? : (%, %) -> Boolean if R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 ?>? : (%, %) -> Boolean if R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 ?>=? : (%, %) -> Boolean if R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 0 : () -> % if R has ABELMON or R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 coerce : S -> % if R has SRING
 construct : List(Record(k: S,c: R)) -> %
 constructOrdered : List(Record(k: S,c: R)) -> % if S has COMPAR
 hash : % -> SingleInteger if R has HASHABL and S has HASHABL
 hashUpdate! : (HashState, %) -> HashState if R has HASHABL and S has HASHABL
 inf : (%, %) -> % if R has OAMONS and S has ORDSET
 leadingCoefficient : % -> R if S has COMPAR
 leadingMonomial : % -> % if S has COMPAR
 leadingSupport : % -> S if S has COMPAR
 leadingTerm : % -> Record(k: S,c: R) if S has COMPAR
 linearExtend : ((S -> R), %) -> R if R has COMRING
 listOfTerms : % -> List(Record(k: S,c: R))
 max : (%, %) -> % if R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 min : (%, %) -> % if R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 numberOfMonomials : % -> NonNegativeInteger
 opposite? : (%, %) -> Boolean if R has ABELMON or R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 reductum : % -> % if S has COMPAR
 retract : % -> S if R has SRING
 retractIfCan : % -> Union(S,"failed") if R has SRING
 sample : () -> % if R has ABELMON or R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 smaller? : (%, %) -> Boolean if R has COMPAR and S has COMPAR or R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET
 subtractIfCan : (%, %) -> Union(%,"failed") if R has ABELGRP or R has CABMON or R has OAMONS and S has ORDSET
 sup : (%, %) -> % if R has OAMONS and S has ORDSET
 zero? : % -> Boolean if R has ABELMON or R has OAMON and S has ORDSET or R has OAMONS and S has ORDSET

See: [PolySpad]?

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

   There are no library operations named VectorSpace 
      Use HyperDoc Browse or issue
                            )what op VectorSpace
      to learn if there is any operation containing " VectorSpace " in 
      its name.

   Cannot find a definition or applicable library operation named 
      VectorSpace with argument type(s) 
                                    Type

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

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