# IntervalCategory RΒΆ

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

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from LeftModule %

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

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

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

acos: % -> %
acosh: % -> %
acot: % -> %
acoth: % -> %
acsc: % -> %
acsch: % -> %
annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %
asec: % -> %
asech: % -> %
asin: % -> %
asinh: % -> %
associates?: (%, %) -> Boolean

from EntireRing

associator: (%, %, %) -> %
atan: % -> %
atanh: % -> %
characteristic: () -> NonNegativeInteger
coerce: % -> %

from Algebra %

coerce: % -> OutputForm
coerce: Integer -> %
commutator: (%, %) -> %
contains?: (%, R) -> Boolean

contains?(i, f) returns true if f is contained within the interval i, false otherwise.

cos: % -> %
cosh: % -> %
cot: % -> %
coth: % -> %
csc: % -> %
csch: % -> %
exp: % -> %
exquo: (%, %) -> Union(%, failed)

from EntireRing

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

inf: % -> R

inf(u) returns the infinum of u.

interval: (R, R) -> %

interval(inf, sup) creates a new interval, either [inf, sup] if inf <= sup or [sup, inf] otherwise.

interval: Fraction Integer -> %

interval(f) creates a new interval around f.

interval: R -> %

interval(f) creates a new interval around f.

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: % -> %
max: (%, %) -> %

from OrderedSet

min: (%, %) -> %

from OrderedSet

negative?: % -> Boolean

negative?(u) returns true if every element of u is negative, false otherwise.

nthRoot: (%, Integer) -> %

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

pi: () -> %
plenaryPower: (%, PositiveInteger) -> %
positive?: % -> Boolean

positive?(u) returns true if every element of u is positive, false otherwise.

qinterval: (R, R) -> %

qinterval(inf, sup) creates a new interval [inf, sup], without checking the ordering on the elements.

recip: % -> Union(%, failed)

from MagmaWithUnit

retract: % -> Integer
retractIfCan: % -> Union(Integer, failed)
rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sec: % -> %
sech: % -> %
sin: % -> %
sinh: % -> %
smaller?: (%, %) -> Boolean

from Comparable

sqrt: % -> %

subtractIfCan: (%, %) -> Union(%, failed)
sup: % -> R

sup(u) returns the supremum of u.

tan: % -> %
tanh: % -> %
unit?: % -> Boolean

from EntireRing

unitCanonical: % -> %

from EntireRing

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

from EntireRing

width: % -> R

width(u) returns sup(u) - inf(u).

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Approximate

ArcHyperbolicFunctionCategory

ArcTrigonometricFunctionCategory

BasicType

BiModule(%, %)

CancellationAbelianMonoid

CommutativeRing

CommutativeStar

Comparable

ElementaryFunctionCategory

EntireRing

GcdDomain

HyperbolicFunctionCategory

IntegralDomain

LeftOreRing

Magma

MagmaWithUnit

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

OrderedSet

PartialOrder

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TranscendentalFunctionCategory

TrigonometricFunctionCategory

TwoSidedRecip

unitsKnown