IntervalCategory RΒΆ

interval.spad line 1

  • 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 Magma
*: (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
^: (%, %) -> %
from ElementaryFunctionCategory
^: (%, Fraction Integer) -> %
from RadicalCategory
^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
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: % -> OutputForm
from CoercibleTo OutputForm
coerce: Integer -> %
from RetractableTo Integer
commutator: (%, %) -> %
from NonAssociativeRng
contains?: (%, R) -> Boolean
contains?(i, f) returns true if f is contained within the interval i, false otherwise.
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
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
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, in] 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: % -> %
from ElementaryFunctionCategory
max: (%, %) -> %
from OrderedSet
min: (%, %) -> %
from OrderedSet
negative?: % -> Boolean
negative?(u) returns true if every element of u is negative, false otherwise.
nthRoot: (%, Integer) -> %
from RadicalCategory
one?: % -> Boolean
from MagmaWithUnit
opposite?: (%, %) -> Boolean
from AbelianMonoid
pi: () -> %
from TranscendentalFunctionCategory
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
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
sup(u) returns the supremum of u.
tan: % -> %
from TrigonometricFunctionCategory
tanh: % -> %
from HyperbolicFunctionCategory
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

Algebra %

Approximate

ArcHyperbolicFunctionCategory

ArcTrigonometricFunctionCategory

BasicType

BiModule(%, %)

CancellationAbelianMonoid

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ElementaryFunctionCategory

EntireRing

GcdDomain

HyperbolicFunctionCategory

IntegralDomain

LeftModule %

LeftOreRing

Magma

MagmaWithUnit

Module %

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

OrderedSet

PartialOrder

RadicalCategory

RetractableTo Integer

RightModule %

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TranscendentalFunctionCategory

TrigonometricFunctionCategory

unitsKnown