TaylorSeries Coef

mts.spad line 310 [edit on github]

• Coef: Ring

TaylorSeries is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, Coef) -> %

from RightModule Coef

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

from RightModule Fraction Integer

*: (Coef, %) -> %

from LeftModule Coef

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

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

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

from AbelianMonoidRing(Coef, IndexedExponents Symbol)

=: (%, %) -> Boolean

from BasicType

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

from ElementaryFunctionCategory

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

from RadicalCategory

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

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

from ArcTrigonometricFunctionCategory

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

from ArcHyperbolicFunctionCategory

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

from ArcTrigonometricFunctionCategory

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

from ArcHyperbolicFunctionCategory

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

from ArcTrigonometricFunctionCategory

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

from ArcHyperbolicFunctionCategory

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

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

from ArcTrigonometricFunctionCategory

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

from ArcHyperbolicFunctionCategory

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

from ArcTrigonometricFunctionCategory

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

from ArcHyperbolicFunctionCategory

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

from EntireRing

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

from NonAssociativeRng

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

from ArcTrigonometricFunctionCategory

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

from ArcHyperbolicFunctionCategory

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

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

from CharacteristicNonZero

coefficient: (%, IndexedExponents Symbol) -> Coef

from AbelianMonoidRing(Coef, IndexedExponents Symbol)

coefficient: (%, List Symbol, List NonNegativeInteger) -> %

from MultivariateTaylorSeriesCategory(Coef, Symbol)

coefficient: (%, NonNegativeInteger) -> Polynomial Coef

coefficient(s, n) gives the terms of total degree n.

coefficient: (%, Symbol, NonNegativeInteger) -> %

from MultivariateTaylorSeriesCategory(Coef, Symbol)

coerce: % -> % if Coef has CommutativeRing

from Algebra %

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Coef -> % if Coef has CommutativeRing

from Algebra Coef

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

from Algebra Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: Polynomial Coef -> %

coerce(s) regroups terms of s by total degree and forms a series.

coerce: Symbol -> %

coerce(s) converts a variable to a Taylor series

commutator: (%, %) -> %

from NonAssociativeRng

complete: % -> %

from PowerSeriesCategory(Coef, IndexedExponents Symbol, Symbol)

construct: List Record(k: IndexedExponents Symbol, c: Coef) -> %

from IndexedProductCategory(Coef, IndexedExponents Symbol)

constructOrdered: List Record(k: IndexedExponents Symbol, c: Coef) -> %

from IndexedProductCategory(Coef, IndexedExponents Symbol)

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

from TrigonometricFunctionCategory

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

from HyperbolicFunctionCategory

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

from TrigonometricFunctionCategory

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

from HyperbolicFunctionCategory

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

from TrigonometricFunctionCategory

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

from HyperbolicFunctionCategory

D: (%, List Symbol) -> %

from PartialDifferentialRing Symbol

D: (%, List Symbol, List NonNegativeInteger) -> %

from PartialDifferentialRing Symbol

D: (%, Symbol) -> %

from PartialDifferentialRing Symbol

D: (%, Symbol, NonNegativeInteger) -> %

from PartialDifferentialRing Symbol

degree: % -> IndexedExponents Symbol

from PowerSeriesCategory(Coef, IndexedExponents Symbol, Symbol)

differentiate: (%, List Symbol) -> %

from PartialDifferentialRing Symbol

differentiate: (%, List Symbol, List NonNegativeInteger) -> %

from PartialDifferentialRing Symbol

differentiate: (%, Symbol) -> %

from PartialDifferentialRing Symbol

differentiate: (%, Symbol, NonNegativeInteger) -> %

from PartialDifferentialRing Symbol

eval: (%, %, %) -> %

from InnerEvalable(%, %)

eval: (%, Equation %) -> %

from Evalable %

eval: (%, List %, List %) -> %

from InnerEvalable(%, %)

eval: (%, List Equation %) -> %

from Evalable %

eval: (%, List Symbol, List %) -> %

from InnerEvalable(Symbol, %)

eval: (%, Symbol, %) -> %

from InnerEvalable(Symbol, %)

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

from ElementaryFunctionCategory

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

from EntireRing

extend: (%, NonNegativeInteger) -> %

from MultivariateTaylorSeriesCategory(Coef, Symbol)

fintegrate: (() -> %, Symbol, Coef) -> % if Coef has Algebra Fraction Integer

fintegrate(f, v, c) is the integral of f() with respect to v and having c as the constant of integration. The evaluation of f() is delayed.

integrate: (%, Symbol) -> % if Coef has Algebra Fraction Integer

from MultivariateTaylorSeriesCategory(Coef, Symbol)

integrate: (%, Symbol, Coef) -> % if Coef has Algebra Fraction Integer

integrate(s, v, c) is the integral of s with respect to v and having c as the constant of integration.

latex: % -> String

from SetCategory

leadingCoefficient: % -> Coef

from PowerSeriesCategory(Coef, IndexedExponents Symbol, Symbol)

leadingMonomial: % -> %

from PowerSeriesCategory(Coef, IndexedExponents Symbol, Symbol)

leadingSupport: % -> IndexedExponents Symbol

from IndexedProductCategory(Coef, IndexedExponents Symbol)

leadingTerm: % -> Record(k: IndexedExponents Symbol, c: Coef)

from IndexedProductCategory(Coef, IndexedExponents Symbol)

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

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

from ElementaryFunctionCategory

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

from IndexedProductCategory(Coef, IndexedExponents Symbol)

monomial?: % -> Boolean

from IndexedProductCategory(Coef, IndexedExponents Symbol)

monomial: (%, List Symbol, List NonNegativeInteger) -> %

from MultivariateTaylorSeriesCategory(Coef, Symbol)

monomial: (%, Symbol, NonNegativeInteger) -> %

from MultivariateTaylorSeriesCategory(Coef, Symbol)

monomial: (Coef, IndexedExponents Symbol) -> %

from IndexedProductCategory(Coef, IndexedExponents Symbol)

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

from RadicalCategory

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: (%, Symbol) -> NonNegativeInteger

from MultivariateTaylorSeriesCategory(Coef, Symbol)

order: (%, Symbol, NonNegativeInteger) -> NonNegativeInteger

from MultivariateTaylorSeriesCategory(Coef, Symbol)

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

from TranscendentalFunctionCategory

plenaryPower: (%, PositiveInteger) -> % if Coef has CommutativeRing or Coef has Algebra Fraction Integer

from NonAssociativeAlgebra Coef

pole?: % -> Boolean

from PowerSeriesCategory(Coef, IndexedExponents Symbol, Symbol)

polynomial: (%, NonNegativeInteger) -> Polynomial Coef

from MultivariateTaylorSeriesCategory(Coef, Symbol)

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

from MultivariateTaylorSeriesCategory(Coef, Symbol)

recip: % -> Union(%, failed)

from MagmaWithUnit

reductum: % -> %

from IndexedProductCategory(Coef, IndexedExponents Symbol)

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

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

from TrigonometricFunctionCategory

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

from HyperbolicFunctionCategory

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

from TrigonometricFunctionCategory

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

from HyperbolicFunctionCategory

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

from RadicalCategory

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

from CancellationAbelianMonoid

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

from TrigonometricFunctionCategory

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

from HyperbolicFunctionCategory

unit?: % -> Boolean if Coef has IntegralDomain

from EntireRing

unitCanonical: % -> % if Coef has IntegralDomain

from EntireRing

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

from EntireRing

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianMonoidRing(Coef, IndexedExponents Symbol)

AbelianProductCategory Coef

AbelianSemiGroup

Algebra % if Coef has CommutativeRing

Algebra Coef if Coef has CommutativeRing

Algebra Fraction Integer if Coef has Algebra Fraction Integer

ArcHyperbolicFunctionCategory if Coef has Algebra Fraction Integer

ArcTrigonometricFunctionCategory if Coef has Algebra Fraction Integer

BasicType

BiModule(%, %)

BiModule(Coef, Coef)

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

CancellationAbelianMonoid

CharacteristicNonZero if Coef has CharacteristicNonZero

CharacteristicZero if Coef has CharacteristicZero

CoercibleTo OutputForm

CommutativeRing if Coef has CommutativeRing

CommutativeStar if Coef has CommutativeRing

ElementaryFunctionCategory if Coef has Algebra Fraction Integer

EntireRing if Coef has IntegralDomain

Evalable %

HyperbolicFunctionCategory if Coef has Algebra Fraction Integer

IndexedProductCategory(Coef, IndexedExponents Symbol)

InnerEvalable(%, %)

InnerEvalable(Symbol, %)

IntegralDomain if Coef has IntegralDomain

LeftModule %

LeftModule Coef

LeftModule Fraction Integer if Coef has Algebra Fraction Integer

Magma

MagmaWithUnit

Module % if Coef has CommutativeRing

Module Coef if Coef has CommutativeRing

Module Fraction Integer if Coef has Algebra Fraction Integer

Monoid

MultivariateTaylorSeriesCategory(Coef, Symbol)

NonAssociativeAlgebra % if Coef has CommutativeRing

NonAssociativeAlgebra Coef if Coef has CommutativeRing

NonAssociativeAlgebra Fraction Integer if Coef has Algebra Fraction Integer

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if Coef has IntegralDomain

PartialDifferentialRing Symbol

PowerSeriesCategory(Coef, IndexedExponents Symbol, Symbol)

RadicalCategory if Coef has Algebra Fraction Integer

RightModule %

RightModule Coef

RightModule Fraction Integer if Coef has Algebra Fraction Integer

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TranscendentalFunctionCategory if Coef has Algebra Fraction Integer

TrigonometricFunctionCategory if Coef has Algebra Fraction Integer

TwoSidedRecip if Coef has CommutativeRing

unitsKnown

VariablesCommuteWithCoefficients