OrderedCompletion(R)
complet.spad line 1
[edit on github]
Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989
- + : (%, %) -> % if R has AbelianMonoid
- - : % -> % if R has AbelianGroup
- < : (%, %) -> Boolean if R has OrderedSet
- from PartialOrder
- <= : (%, %) -> Boolean if R has OrderedSet
- from PartialOrder
- = : (%, %) -> Boolean
- from BasicType
- > : (%, %) -> Boolean if R has OrderedSet
- from PartialOrder
- >= : (%, %) -> Boolean if R has OrderedSet
- from PartialOrder
- coerce : R -> %
- from CoercibleFrom(R)
- coerce : Fraction(Integer) -> % if R has RetractableTo(Fraction(Integer))
- from CoercibleFrom(Fraction(Integer))
- coerce : Integer -> % if R has RetractableTo(Integer)
- from CoercibleFrom(Integer)
- coerce : % -> OutputForm
- from CoercibleTo(OutputForm)
- convert : % -> InputForm if R has ConvertibleTo(InputForm)
- from ConvertibleTo(InputForm)
- finite? : % -> Boolean
finite?(x) tests if x is finite.
- infinite? : % -> Boolean
infinite?(x) tests if x is +infinity or -infinity,
- latex : % -> String
- from SetCategory
- max : (%, %) -> % if R has OrderedSet
- from OrderedSet
- min : (%, %) -> % if R has OrderedSet
- from OrderedSet
- minusInfinity : () -> %
minusInfinity() returns -infinity.
- plusInfinity : () -> %
plusInfinity() returns +infinity.
- rational : % -> Fraction(Integer) if R has IntegerNumberSystem
rational(x) returns x as a finite rational number. Error: if x cannot be so converted.
- rational? : % -> Boolean if R has IntegerNumberSystem
rational?(x) tests if x is a finite rational number.
- rationalIfCan : % -> Union(Fraction(Integer), "failed") if R has IntegerNumberSystem
rationalIfCan(x) returns x as a finite rational number if it is one and "failed" otherwise.
- retract : % -> R
- from RetractableTo(R)
- retract : % -> Fraction(Integer) if R has RetractableTo(Fraction(Integer))
- from RetractableTo(Fraction(Integer))
- retract : % -> Integer if R has RetractableTo(Integer)
- from RetractableTo(Integer)
- retractIfCan : % -> Union(R, "failed")
- from RetractableTo(R)
- retractIfCan : % -> Union(Fraction(Integer), "failed") if R has RetractableTo(Fraction(Integer))
- from RetractableTo(Fraction(Integer))
- retractIfCan : % -> Union(Integer, "failed") if R has RetractableTo(Integer)
- from RetractableTo(Integer)
- smaller? : (%, %) -> Boolean if R has OrderedSet
- from Comparable
- whatInfinity : % -> SingleInteger
whatInfinity(x) returns 0 if x is finite, 1 if x is +infinity, and -1 if x is -infinity.
- ~= : (%, %) -> Boolean
- from BasicType
RetractableTo(Integer)
FullyRetractableTo(R)
CoercibleTo(OutputForm)
BasicType
CoercibleFrom(R)
RetractableTo(Fraction(Integer))
ConvertibleTo(InputForm)
OrderedSet
CoercibleFrom(Fraction(Integer))
SetCategory
Comparable
CoercibleFrom(Integer)
PartialOrder
RetractableTo(R)