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 Topics FrontPage FriCAS Library FriCAS Library Examples NoncommutativePolynomials SandboxFactoringNoncommutativePolynomials FreeMonoid <-- You are here. 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. fricas)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

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