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