OrderedCompletion RΒΆ

complet.spad line 1

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
~=: (%, %) -> Boolean
from BasicType
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: Fraction Integer -> % if R has RetractableTo Fraction Integer
from RetractableTo Fraction Integer
coerce: Integer -> % if R has RetractableTo Integer
from RetractableTo Integer
coerce: R -> %
from RetractableTo R
finite?: % -> Boolean
finite?(x) tests if x is finite.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
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: % -> Fraction Integer if R has RetractableTo Fraction Integer
from RetractableTo Fraction Integer
retract: % -> Integer if R has RetractableTo Integer
from RetractableTo Integer
retract: % -> R
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
retractIfCan: % -> Union(R, failed)
from RetractableTo R
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.

BasicType

CoercibleTo OutputForm

Comparable if R has OrderedSet

FullyRetractableTo R

OrderedSet if R has OrderedSet

PartialOrder if R has OrderedSet

RetractableTo Fraction Integer if R has RetractableTo Fraction Integer

RetractableTo Integer if R has RetractableTo Integer

RetractableTo R

SetCategory