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

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Fraction Integer -> % if R has RetractableTo Fraction Integer

from CoercibleFrom Fraction Integer

coerce: Integer -> % if R has RetractableTo Integer

from CoercibleFrom Integer

coerce: R -> %

from CoercibleFrom R

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?: % -> Boolean if R has IntegerNumberSystem

rational?(x) tests if x is a finite rational number.

rational: % -> Fraction Integer if R has IntegerNumberSystem

rational(x) returns x as a finite rational number. Error: if x cannot be so converted.

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

CoercibleFrom Fraction Integer if R has RetractableTo Fraction Integer

CoercibleFrom Integer if R has RetractableTo Integer

CoercibleFrom R

CoercibleTo OutputForm

Comparable if R has OrderedSet

ConvertibleTo InputForm if R has ConvertibleTo InputForm

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