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 Topics FrontPage AboutAxiom AxiomDocumentation Axiom Algebra OrderedDirectProduct <-- You are here. SandBox SandBoxGroebnerBasis OrderedDirectProduct <-- You are here. fricas)show OrderedDirectProduct OrderedDirectProduct(dim: NonNegativeInteger,S: OrderedAbelianMonoidSup,f: ((Vector(S),Vector(S)) -> Boolean)) is a domain constructor Abbreviation for OrderedDirectProduct is ODP This constructor is not exposed in this frame. ------------------------------- Operations -------------------------------- 1 : () -> % if S has MONOID coerce : % -> Vector(S) copy : % -> % directProduct : Vector(S) -> % ?.? : (%,Integer) -> S elt : (%,Integer,S) -> S empty : () -> % empty? : % -> Boolean entries : % -> List(S) eq? : (%,%) -> Boolean index? : (Integer,%) -> Boolean indices : % -> List(Integer) map : ((S -> S),%) -> % qelt : (%,Integer) -> S sample : () -> % #? : % -> NonNegativeInteger if $has ATFINAG ?*? : (PositiveInteger,%) -> % if S has ABELSG ?*? : (S,%) -> % if S has MONOID ?*? : (NonNegativeInteger,%) -> % if S has ABELMON and S has FIELD or S has ABELMON and S has RING or S has CABMON ?*? : (Integer,%) -> % if S has ABELGRP and S has FIELD or S has RING ?*? : (%,S) -> % if S has MONOID ?*? : (%,%) -> % if S has MONOID ?+? : (%,%) -> % if S has ABELSG -? : % -> % if S has ABELGRP and S has FIELD or S has RING ?-? : (%,%) -> % if S has ABELGRP and S has FIELD or S has RING ?/? : (%,S) -> % if S has FIELD ? Boolean if S has OAMONS or S has ORDRING ?<=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING ?=? : (%,%) -> Boolean if$ has ATFINAG and S has BASTYPE or S has SETCAT ?>? : (%,%) -> Boolean if S has OAMONS or S has ORDRING ?>=? : (%,%) -> Boolean if S has OAMONS or S has ORDRING D : (%,(S -> S)) -> % if S has RING D : (%,(S -> S),NonNegativeInteger) -> % if S has RING D : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL) and S has RING D : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL) and S has RING D : (%,List(Symbol)) -> % if S has PDRING(SYMBOL) and S has RING D : (%,Symbol) -> % if S has PDRING(SYMBOL) and S has RING D : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING D : % -> % if S has DIFRING and S has RING 0 : () -> % if S has ABELMON and S has FIELD or S has ABELMON and S has RING or S has CABMON ?^? : (%,PositiveInteger) -> % if S has MONOID ?^? : (%,NonNegativeInteger) -> % if S has MONOID abs : % -> % if S has ORDRING annihilate? : (%,%) -> Boolean if S has RING any? : ((S -> Boolean),%) -> Boolean if $has ATFINAG characteristic : () -> NonNegativeInteger if S has RING coerce : S -> % if S has SETCAT coerce : Fraction(Integer) -> % if S has RETRACT(FRAC(INT)) and S has SETCAT coerce : Integer -> % if S has RETRACT(INT) and S has SETCAT or S has RING coerce : % -> OutputForm if S has KOERCE(OUTFORM) convert : % -> InputForm if S has FINITE count : (S,%) -> NonNegativeInteger if$ has ATFINAG and S has BASTYPE count : ((S -> Boolean),%) -> NonNegativeInteger if $has ATFINAG differentiate : (%,(S -> S)) -> % if S has RING differentiate : (%,(S -> S),NonNegativeInteger) -> % if S has RING differentiate : (%,List(Symbol),List(NonNegativeInteger)) -> % if S has PDRING(SYMBOL) and S has RING differentiate : (%,Symbol,NonNegativeInteger) -> % if S has PDRING(SYMBOL) and S has RING differentiate : (%,List(Symbol)) -> % if S has PDRING(SYMBOL) and S has RING differentiate : (%,Symbol) -> % if S has PDRING(SYMBOL) and S has RING differentiate : (%,NonNegativeInteger) -> % if S has DIFRING and S has RING differentiate : % -> % if S has DIFRING and S has RING dimension : () -> CardinalNumber if S has FIELD dot : (%,%) -> S if S has RING entry? : (S,%) -> Boolean if$ has ATFINAG and S has SETCAT enumerate : () -> List(%) if S has FINITE eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT every? : ((S -> Boolean),%) -> Boolean if $has ATFINAG fill! : (%,S) -> % if$ has ATSHMUT first : % -> S if Integer has ORDSET hash : % -> SingleInteger if S has SETCAT hashUpdate! : (HashState,%) -> HashState if S has SETCAT index : PositiveInteger -> % if S has FINITE latex : % -> String if S has SETCAT less? : (%,NonNegativeInteger) -> Boolean lookup : % -> PositiveInteger if S has FINITE map! : ((S -> S),%) -> % if $has ATSHMUT max : (%,%) -> % if S has OAMONS or S has ORDRING maxIndex : % -> Integer if Integer has ORDSET member? : (S,%) -> Boolean if$ has ATFINAG and S has BASTYPE members : % -> List(S) if $has ATFINAG min : (%,%) -> % if S has OAMONS or S has ORDRING minIndex : % -> Integer if Integer has ORDSET more? : (%,NonNegativeInteger) -> Boolean negative? : % -> Boolean if S has ORDRING one? : % -> Boolean if S has MONOID opposite? : (%,%) -> Boolean if S has ABELMON and S has FIELD or S has ABELMON and S has RING or S has CABMON parts : % -> List(S) if$ has ATFINAG positive? : % -> Boolean if S has ORDRING qsetelt! : (%,Integer,S) -> S if $has ATSHMUT random : () -> % if S has FINITE recip : % -> Union(%,"failed") if S has MONOID reducedSystem : Matrix(%) -> Matrix(S) if S has RING reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(S),vec: Vector(S)) if S has RING reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if S has LINEXP(INT) and S has RING reducedSystem : Matrix(%) -> Matrix(Integer) if S has LINEXP(INT) and S has RING retract : % -> S if S has SETCAT retract : % -> Fraction(Integer) if S has RETRACT(FRAC(INT)) and S has SETCAT retract : % -> Integer if S has RETRACT(INT) and S has SETCAT retractIfCan : % -> Union(S,"failed") if S has SETCAT retractIfCan : % -> Union(Fraction(Integer),"failed") if S has RETRACT(FRAC(INT)) and S has SETCAT retractIfCan : % -> Union(Integer,"failed") if S has RETRACT(INT) and S has SETCAT setelt : (%,Integer,S) -> S if$ has ATSHMUT sign : % -> Integer if S has ORDRING size : () -> NonNegativeInteger if S has FINITE size? : (%,NonNegativeInteger) -> Boolean smaller? : (%,%) -> Boolean if S has OAMONS or S has ORDRING subtractIfCan : (%,%) -> Union(%,"failed") if S has ABELGRP and S has FIELD or S has ABELGRP and S has RING or S has CABMON sup : (%,%) -> % if S has OAMONS swap! : (%,Integer,Integer) -> Void if $has ATSHMUT unitVector : PositiveInteger -> % if S has RING zero? : % -> Boolean if S has ABELMON and S has FIELD or S has ABELMON and S has RING or S has CABMON ?~=? : (%,%) -> Boolean if$ has ATFINAG and S has BASTYPE or S has SETCAT

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