Interval(R)

interval.spad line 41 [edit on github]

• R : Join(FloatingPointSystem, TranscendentalFunctionCategory)

+ Author: Mike Dewar + Date Created: November 1996 + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals.

* : (%, %) -> %

from Magma

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

< : (%, %) -> Boolean

from PartialOrder

<= : (%, %) -> Boolean

from PartialOrder

= : (%, %) -> Boolean

from BasicType

> : (%, %) -> Boolean

from PartialOrder

>= : (%, %) -> Boolean

from PartialOrder

^ : (%, %) -> %

from ElementaryFunctionCategory

^ : (%, Fraction(Integer)) -> %

from RadicalCategory

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

acos : % -> %

from ArcTrigonometricFunctionCategory

acosh : % -> %

from ArcHyperbolicFunctionCategory

acot : % -> %

from ArcTrigonometricFunctionCategory

acoth : % -> %

from ArcHyperbolicFunctionCategory

acsc : % -> %

from ArcTrigonometricFunctionCategory

acsch : % -> %

from ArcHyperbolicFunctionCategory

annihilate? : (%, %) -> Boolean

from Rng

antiCommutator : (%, %) -> %

from NonAssociativeSemiRng

asec : % -> %

from ArcTrigonometricFunctionCategory

asech : % -> %

from ArcHyperbolicFunctionCategory

asin : % -> %

from ArcTrigonometricFunctionCategory

asinh : % -> %

from ArcHyperbolicFunctionCategory

associates? : (%, %) -> Boolean

from EntireRing

associator : (%, %, %) -> %

from NonAssociativeRng

atan : % -> %

from ArcTrigonometricFunctionCategory

atanh : % -> %

from ArcHyperbolicFunctionCategory

characteristic : () -> NonNegativeInteger

from NonAssociativeRing

coerce : % -> %

from Algebra(%)

coerce : Integer -> %

from CoercibleFrom(Integer)

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

commutator : (%, %) -> %

from NonAssociativeRng

contains? : (%, R) -> Boolean

from IntervalCategory(R)

cos : % -> %

from TrigonometricFunctionCategory

cosh : % -> %

from HyperbolicFunctionCategory

cot : % -> %

from TrigonometricFunctionCategory

coth : % -> %

from HyperbolicFunctionCategory

csc : % -> %

from TrigonometricFunctionCategory

csch : % -> %

from HyperbolicFunctionCategory

exp : % -> %

from ElementaryFunctionCategory

exquo : (%, %) -> Union(%, "failed")

from EntireRing

gcd : (%, %) -> %

from GcdDomain

gcd : List(%) -> %

from GcdDomain

gcdPolynomial : (SparseUnivariatePolynomial(%), SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%)

from GcdDomain

inf : % -> R

from IntervalCategory(R)

interval : R -> %

from IntervalCategory(R)

interval : (R, R) -> %

from IntervalCategory(R)

interval : Fraction(Integer) -> %

from IntervalCategory(R)

latex : % -> String

from SetCategory

lcm : (%, %) -> %

from GcdDomain

lcm : List(%) -> %

from GcdDomain

lcmCoef : (%, %) -> Record(llcm_res : %, coeff1 : %, coeff2 : %)

from LeftOreRing

leftPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower : (%, PositiveInteger) -> %

from Magma

leftRecip : % -> Union(%, "failed")

from MagmaWithUnit

log : % -> %

from ElementaryFunctionCategory

max : (%, %) -> %

from OrderedSet

min : (%, %) -> %

from OrderedSet

negative? : % -> Boolean

from IntervalCategory(R)

nthRoot : (%, Integer) -> %

from RadicalCategory

one? : % -> Boolean

from MagmaWithUnit

opposite? : (%, %) -> Boolean

from AbelianMonoid

pi : () -> %

from TranscendentalFunctionCategory

plenaryPower : (%, PositiveInteger) -> %

from NonAssociativeAlgebra(%)

positive? : % -> Boolean

from IntervalCategory(R)

qinterval : (R, R) -> %

from IntervalCategory(R)

recip : % -> Union(%, "failed")

from MagmaWithUnit

retract : % -> Integer

from RetractableTo(Integer)

retractIfCan : % -> Union(Integer, "failed")

from RetractableTo(Integer)

rightPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower : (%, PositiveInteger) -> %

from Magma

rightRecip : % -> Union(%, "failed")

from MagmaWithUnit

sample : () -> %

from AbelianMonoid

sec : % -> %

from TrigonometricFunctionCategory

sech : % -> %

from HyperbolicFunctionCategory

sin : % -> %

from TrigonometricFunctionCategory

sinh : % -> %

from HyperbolicFunctionCategory

smaller? : (%, %) -> Boolean

from Comparable

sqrt : % -> %

from RadicalCategory

subtractIfCan : (%, %) -> Union(%, "failed")

from CancellationAbelianMonoid

sup : % -> R

from IntervalCategory(R)

tan : % -> %

from TrigonometricFunctionCategory

tanh : % -> %

from HyperbolicFunctionCategory

unit? : % -> Boolean

from EntireRing

unitCanonical : % -> %

from EntireRing

unitNormal : % -> Record(unit : %, canonical : %, associate : %)

from EntireRing

width : % -> R

from IntervalCategory(R)

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

IntegralDomain

Comparable

ElementaryFunctionCategory

Algebra(%)

noZeroDivisors

RightModule(%)

GcdDomain

Monoid

TranscendentalFunctionCategory

ArcTrigonometricFunctionCategory

CancellationAbelianMonoid

MagmaWithUnit

RetractableTo(Integer)

NonAssociativeAlgebra(%)

RadicalCategory

OrderedSet

Module(%)

SetCategory

LeftOreRing

TrigonometricFunctionCategory

CoercibleTo(OutputForm)

LeftModule(%)

CommutativeRing

TwoSidedRecip

Magma

NonAssociativeRing

SemiGroup

IntervalCategory(R)

Rng

PartialOrder

ArcHyperbolicFunctionCategory

CoercibleFrom(Integer)

unitsKnown

AbelianGroup

AbelianSemiGroup

AbelianMonoid

CommutativeStar

NonAssociativeSemiRing

Approximate

BiModule(%, %)

NonAssociativeRng

HyperbolicFunctionCategory

Ring

SemiRng

EntireRing

NonAssociativeSemiRng

BasicType

SemiRing