QEtaTaylorSeriesCategory CΒΆ

qetaser.spad line 114 [edit on github]

QEtaTaylorSeriesCategory is a UnivariateTaylorSeriesCategory extended by a few functions that we need in the computation of our package.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from LeftModule %

*: (%, C) -> %

from RightModule C

*: (%, Fraction Integer) -> % if C has Algebra Fraction Integer

from RightModule Fraction Integer

*: (C, %) -> %

from LeftModule C

*: (Fraction Integer, %) -> % if C has Algebra Fraction Integer

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, C) -> % if C has Field

from AbelianMonoidRing(C, NonNegativeInteger)

=: (%, %) -> Boolean

from BasicType

^: (%, %) -> % if C has Algebra Fraction Integer

from ElementaryFunctionCategory

^: (%, C) -> % if C has Field

from UnivariateTaylorSeriesCategory C

^: (%, Fraction Integer) -> % if C has Algebra Fraction Integer

from RadicalCategory

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

acos: % -> % if C has Algebra Fraction Integer

from ArcTrigonometricFunctionCategory

acosh: % -> % if C has Algebra Fraction Integer

from ArcHyperbolicFunctionCategory

acot: % -> % if C has Algebra Fraction Integer

from ArcTrigonometricFunctionCategory

acoth: % -> % if C has Algebra Fraction Integer

from ArcHyperbolicFunctionCategory

acsc: % -> % if C has Algebra Fraction Integer

from ArcTrigonometricFunctionCategory

acsch: % -> % if C has Algebra Fraction Integer

from ArcHyperbolicFunctionCategory

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

approximate: (%, NonNegativeInteger) -> C if C has coerce: Symbol -> C and C has ^: (C, NonNegativeInteger) -> C

from UnivariatePowerSeriesCategory(C, NonNegativeInteger)

asec: % -> % if C has Algebra Fraction Integer

from ArcTrigonometricFunctionCategory

asech: % -> % if C has Algebra Fraction Integer

from ArcHyperbolicFunctionCategory

asin: % -> % if C has Algebra Fraction Integer

from ArcTrigonometricFunctionCategory

asinh: % -> % if C has Algebra Fraction Integer

from ArcHyperbolicFunctionCategory

associates?: (%, %) -> Boolean if C has IntegralDomain

from EntireRing

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

from NonAssociativeRng

atan: % -> % if C has Algebra Fraction Integer

from ArcTrigonometricFunctionCategory

atanh: % -> % if C has Algebra Fraction Integer

from ArcHyperbolicFunctionCategory

center: % -> C

from UnivariatePowerSeriesCategory(C, NonNegativeInteger)

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

charthRoot: % -> Union(%, failed) if C has CharacteristicNonZero

from CharacteristicNonZero

coefficient: (%, NonNegativeInteger) -> C

from AbelianMonoidRing(C, NonNegativeInteger)

coefficients: % -> Stream C

from UnivariateTaylorSeriesCategory C

coerce: % -> % if C has CommutativeRing

from Algebra %

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: % -> UnivariateTaylorSeries(C, QUOTE q, Sel(C, Zero))

coerce(x) interprets x as a univariate Taylor series in the variable q about the center 0.

coerce: C -> % if C has CommutativeRing

from Algebra C

coerce: Fraction Integer -> % if C has Algebra Fraction Integer

from Algebra Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: UnivariateTaylorSeries(C, QUOTE q, Sel(C, Zero)) -> %

coerce(x) interpret a univariate Taylor series in q with a center at 0 as an element of this domain. No check is made.

commutator: (%, %) -> %

from NonAssociativeRng

complete: % -> %

from PowerSeriesCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

construct: List Record(k: NonNegativeInteger, c: C) -> %

from IndexedProductCategory(C, NonNegativeInteger)

constructOrdered: List Record(k: NonNegativeInteger, c: C) -> %

from IndexedProductCategory(C, NonNegativeInteger)

cos: % -> % if C has Algebra Fraction Integer

from TrigonometricFunctionCategory

cosh: % -> % if C has Algebra Fraction Integer

from HyperbolicFunctionCategory

cot: % -> % if C has Algebra Fraction Integer

from TrigonometricFunctionCategory

coth: % -> % if C has Algebra Fraction Integer

from HyperbolicFunctionCategory

csc: % -> % if C has Algebra Fraction Integer

from TrigonometricFunctionCategory

csch: % -> % if C has Algebra Fraction Integer

from HyperbolicFunctionCategory

D: % -> % if C has *: (NonNegativeInteger, C) -> C

from DifferentialRing

D: (%, List Symbol) -> % if C has PartialDifferentialRing Symbol and C has *: (NonNegativeInteger, C) -> C

from PartialDifferentialRing Symbol

D: (%, List Symbol, List NonNegativeInteger) -> % if C has PartialDifferentialRing Symbol and C has *: (NonNegativeInteger, C) -> C

from PartialDifferentialRing Symbol

D: (%, NonNegativeInteger) -> % if C has *: (NonNegativeInteger, C) -> C

from DifferentialRing

D: (%, Symbol) -> % if C has PartialDifferentialRing Symbol and C has *: (NonNegativeInteger, C) -> C

from PartialDifferentialRing Symbol

D: (%, Symbol, NonNegativeInteger) -> % if C has PartialDifferentialRing Symbol and C has *: (NonNegativeInteger, C) -> C

from PartialDifferentialRing Symbol

degree: % -> NonNegativeInteger

from PowerSeriesCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

differentiate: % -> % if C has *: (NonNegativeInteger, C) -> C

from DifferentialRing

differentiate: (%, List Symbol) -> % if C has PartialDifferentialRing Symbol and C has *: (NonNegativeInteger, C) -> C

from PartialDifferentialRing Symbol

differentiate: (%, List Symbol, List NonNegativeInteger) -> % if C has PartialDifferentialRing Symbol and C has *: (NonNegativeInteger, C) -> C

from PartialDifferentialRing Symbol

differentiate: (%, NonNegativeInteger) -> % if C has *: (NonNegativeInteger, C) -> C

from DifferentialRing

differentiate: (%, Symbol) -> % if C has PartialDifferentialRing Symbol and C has *: (NonNegativeInteger, C) -> C

from PartialDifferentialRing Symbol

differentiate: (%, Symbol, NonNegativeInteger) -> % if C has PartialDifferentialRing Symbol and C has *: (NonNegativeInteger, C) -> C

from PartialDifferentialRing Symbol

elt: (%, %) -> %

from Eltable(%, %)

elt: (%, NonNegativeInteger) -> C

from UnivariatePowerSeriesCategory(C, NonNegativeInteger)

eval: (%, C) -> Stream C if C has ^: (C, NonNegativeInteger) -> C

from UnivariatePowerSeriesCategory(C, NonNegativeInteger)

exp: % -> % if C has Algebra Fraction Integer

from ElementaryFunctionCategory

exquo: (%, %) -> Union(%, failed) if C has IntegralDomain

from EntireRing

extend: (%, NonNegativeInteger) -> %

from UnivariatePowerSeriesCategory(C, NonNegativeInteger)

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

integrate: % -> % if C has Algebra Fraction Integer

from UnivariateSeriesWithRationalExponents(C, NonNegativeInteger)

integrate: (%, Symbol) -> % if C has variables: C -> List Symbol and C has Algebra Fraction Integer and C has integrate: (C, Symbol) -> C

from UnivariateSeriesWithRationalExponents(C, NonNegativeInteger)

latex: % -> String

from SetCategory

leadingCoefficient: % -> C

from PowerSeriesCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

leadingMonomial: % -> %

from PowerSeriesCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

leadingSupport: % -> NonNegativeInteger

from IndexedProductCategory(C, NonNegativeInteger)

leadingTerm: % -> Record(k: NonNegativeInteger, c: C)

from IndexedProductCategory(C, NonNegativeInteger)

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

log: % -> % if C has Algebra Fraction Integer

from ElementaryFunctionCategory

map: (C -> C, %) -> %

from IndexedProductCategory(C, NonNegativeInteger)

monomial?: % -> Boolean

from IndexedProductCategory(C, NonNegativeInteger)

monomial: (C, NonNegativeInteger) -> %

from IndexedProductCategory(C, NonNegativeInteger)

multiplyCoefficients: (Integer -> C, %) -> %

from UnivariateTaylorSeriesCategory C

multiplyExponents: (%, PositiveInteger) -> %

from UnivariatePowerSeriesCategory(C, NonNegativeInteger)

multisect: (Integer, Integer, %) -> %

multisect(a, b, x} selects the coefficients of q^((a+b)*n+a) and changes this monomial to q^n.

nthRoot: (%, Integer) -> % if C has Algebra Fraction Integer

from RadicalCategory

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> NonNegativeInteger

from UnivariatePowerSeriesCategory(C, NonNegativeInteger)

order: (%, NonNegativeInteger) -> NonNegativeInteger

from UnivariatePowerSeriesCategory(C, NonNegativeInteger)

pi: () -> % if C has Algebra Fraction Integer

from TranscendentalFunctionCategory

pole?: % -> Boolean

from PowerSeriesCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

polynomial: (%, NonNegativeInteger) -> Polynomial C

from UnivariateTaylorSeriesCategory C

polynomial: (%, NonNegativeInteger, NonNegativeInteger) -> Polynomial C

from UnivariateTaylorSeriesCategory C

quoByVar: % -> %

from UnivariateTaylorSeriesCategory C

recip: % -> Union(%, failed)

from MagmaWithUnit

reductum: % -> %

from IndexedProductCategory(C, NonNegativeInteger)

revert: % -> %

revert(f(x)) returns a Taylor series g(x) such that f(g(x)) = g(f(x)) = x. Series f(x) should have constant coefficient 0 and invertible 1st order coefficient.

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sec: % -> % if C has Algebra Fraction Integer

from TrigonometricFunctionCategory

sech: % -> % if C has Algebra Fraction Integer

from HyperbolicFunctionCategory

series: Stream C -> %

from UnivariateTaylorSeriesCategory C

series: Stream Record(k: NonNegativeInteger, c: C) -> %

from UnivariateTaylorSeriesCategory C

sin: % -> % if C has Algebra Fraction Integer

from TrigonometricFunctionCategory

sinh: % -> % if C has Algebra Fraction Integer

from HyperbolicFunctionCategory

sqrt: % -> % if C has Algebra Fraction Integer

from RadicalCategory

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

from CancellationAbelianMonoid

tan: % -> % if C has Algebra Fraction Integer

from TrigonometricFunctionCategory

tanh: % -> % if C has Algebra Fraction Integer

from HyperbolicFunctionCategory

terms: % -> Stream Record(k: NonNegativeInteger, c: C)

from UnivariatePowerSeriesCategory(C, NonNegativeInteger)

truncate: (%, NonNegativeInteger) -> %

from UnivariatePowerSeriesCategory(C, NonNegativeInteger)

truncate: (%, NonNegativeInteger, NonNegativeInteger) -> %

from UnivariatePowerSeriesCategory(C, NonNegativeInteger)

unit?: % -> Boolean if C has IntegralDomain

from EntireRing

unitCanonical: % -> % if C has IntegralDomain

from EntireRing

unitNormal: % -> Record(unit: %, canonical: %, associate: %) if C has IntegralDomain

from EntireRing

variable: % -> Symbol

from UnivariatePowerSeriesCategory(C, NonNegativeInteger)

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianMonoidRing(C, NonNegativeInteger)

AbelianProductCategory C

AbelianSemiGroup

Algebra % if C has CommutativeRing

Algebra C if C has CommutativeRing

Algebra Fraction Integer if C has Algebra Fraction Integer

ArcHyperbolicFunctionCategory if C has Algebra Fraction Integer

ArcTrigonometricFunctionCategory if C has Algebra Fraction Integer

BasicType

BiModule(%, %)

BiModule(C, C)

BiModule(Fraction Integer, Fraction Integer) if C has Algebra Fraction Integer

CancellationAbelianMonoid

CharacteristicNonZero if C has CharacteristicNonZero

CharacteristicZero if C has CharacteristicZero

CoercibleTo OutputForm

CommutativeRing if C has CommutativeRing

CommutativeStar if C has CommutativeRing

DifferentialRing if C has *: (NonNegativeInteger, C) -> C

ElementaryFunctionCategory if C has Algebra Fraction Integer

Eltable(%, %)

EntireRing if C has IntegralDomain

HyperbolicFunctionCategory if C has Algebra Fraction Integer

IndexedProductCategory(C, NonNegativeInteger)

IntegralDomain if C has IntegralDomain

LeftModule %

LeftModule C

LeftModule Fraction Integer if C has Algebra Fraction Integer

Magma

MagmaWithUnit

Module % if C has CommutativeRing

Module C if C has CommutativeRing

Module Fraction Integer if C has Algebra Fraction Integer

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if C has IntegralDomain

PartialDifferentialRing Symbol if C has PartialDifferentialRing Symbol and C has *: (NonNegativeInteger, C) -> C

PowerSeriesCategory(C, NonNegativeInteger, SingletonAsOrderedSet)

RadicalCategory if C has Algebra Fraction Integer

RightModule %

RightModule C

RightModule Fraction Integer if C has Algebra Fraction Integer

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TranscendentalFunctionCategory if C has Algebra Fraction Integer

TrigonometricFunctionCategory if C has Algebra Fraction Integer

TwoSidedRecip if C has CommutativeRing

unitsKnown

UnivariatePowerSeriesCategory(C, NonNegativeInteger)

UnivariateSeriesWithRationalExponents(C, NonNegativeInteger)

UnivariateTaylorSeriesCategory C

VariablesCommuteWithCoefficients