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Edit detail for FreeModule revision 2 of 8

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Editor: Bill Page
Time: 2011/03/10 16:02:40 GMT-8
Note:

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


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

axiom
)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")