The free monoid on a set S is the monoid of finite products of the form reduce(*, [si ^ ni]) where the si's are in S, and the ni's are nonnegative integers. The multiplication is not commutative. When S is an OrderedSet, then FreeMonoid(S) has order: for two elements x and y the relation x < y holds if either length(x) < length(y) holds or if these lengths are equal and if x is smaller than y w.r.t. the lexicographical ordering induced by S.

)sh FreeMonoid

 FreeMonoid(S: SetCategory) is a domain constructor
 Abbreviation for FreeMonoid is FMONOID 
 This constructor is not exposed in this frame.
------------------------------- Operations --------------------------------

 ?*? : (%, S) -> %                     ?*? : (S, %) -> %
 ?*? : (%, %) -> %                     ?=? : (%, %) -> Boolean
 1 : () -> %                           ?^? : (%, PositiveInteger) -> %
 coerce : S -> %                       coerce : % -> OutputForm
 first : % -> S                        hash : % -> SingleInteger
 hclf : (%, %) -> %                    hcrf : (%, %) -> %
 latex : % -> String                   length : % -> NonNegativeInteger
 mapGen : ((S -> S), %) -> %           mirror : % -> %
 nthFactor : (%, Integer) -> S         one? : % -> Boolean
 recip : % -> Union(%,"failed")        rest : % -> %
 retract : % -> S                      sample : () -> %
 size : % -> NonNegativeInteger        ?~=? : (%, %) -> Boolean
 ?<? : (%, %) -> Boolean if S has ORDSET
 ?<=? : (%, %) -> Boolean if S has ORDSET
 ?>? : (%, %) -> Boolean if S has ORDSET
 ?>=? : (%, %) -> Boolean if S has ORDSET
 ?^? : (S, NonNegativeInteger) -> %
 ?^? : (%, NonNegativeInteger) -> %
 divide : (%, %) -> Union(Record(lm: %,rm: %),"failed")
 factors : % -> List(Record(gen: S,exp: NonNegativeInteger))
 hashUpdate! : (HashState, %) -> HashState
 leftPower : (%, NonNegativeInteger) -> %
 leftPower : (%, PositiveInteger) -> %
 leftRecip : % -> Union(%,"failed")
 lexico : (%, %) -> Boolean if S has ORDSET
 lquo : (%, S) -> Union(%,"failed")
 lquo : (%, %) -> Union(%,"failed")
 mapExpon : ((NonNegativeInteger -> NonNegativeInteger), %) -> %
 max : (%, %) -> % if S has ORDSET
 min : (%, %) -> % if S has ORDSET
 nthExpon : (%, Integer) -> NonNegativeInteger
 overlap : (%, %) -> Record(lm: %,mm: %,rm: %)
 retractIfCan : % -> Union(S,"failed")
 rightPower : (%, NonNegativeInteger) -> %
 rightPower : (%, PositiveInteger) -> %
 rightRecip : % -> Union(%,"failed")
 rquo : (%, S) -> Union(%,"failed")
 rquo : (%, %) -> Union(%,"failed")
 smaller? : (%, %) -> Boolean if S has COMPAR
 varList : % -> List(S) if S has BASTYPE