MultivariateTaylorSeriesCategory(Coef, Var)ΒΆ

pscat.spad line 524

MultivariateTaylorSeriesCategory is the most general multivariate Taylor series category.

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 Var)
=: (%, %) -> 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 Var) -> Coef
from AbelianMonoidRing(Coef, IndexedExponents Var)
coefficient: (%, List Var, List NonNegativeInteger) -> %
coefficient(f, [x1, x2, ..., xk], [n1, n2, ..., nk]) returns the coefficient of x1^n1 * ... * xk^nk in f.
coefficient: (%, Var, NonNegativeInteger) -> %
coefficient(f, x, n) returns the coefficient of x^n in f.
coerce: % -> % if Coef has IntegralDomain
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
commutator: (%, %) -> %
from NonAssociativeRng
complete: % -> %
from PowerSeriesCategory(Coef, IndexedExponents Var, Var)
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 Var) -> %
from PartialDifferentialRing Var
D: (%, List Var, List NonNegativeInteger) -> %
from PartialDifferentialRing Var
D: (%, Var) -> %
from PartialDifferentialRing Var
D: (%, Var, NonNegativeInteger) -> %
from PartialDifferentialRing Var
degree: % -> IndexedExponents Var
from PowerSeriesCategory(Coef, IndexedExponents Var, Var)
differentiate: (%, List Var) -> %
from PartialDifferentialRing Var
differentiate: (%, List Var, List NonNegativeInteger) -> %
from PartialDifferentialRing Var
differentiate: (%, Var) -> %
from PartialDifferentialRing Var
differentiate: (%, Var, NonNegativeInteger) -> %
from PartialDifferentialRing Var
eval: (%, %, %) -> %
from InnerEvalable(%, %)
eval: (%, Equation %) -> %
from Evalable %
eval: (%, List %, List %) -> %
from InnerEvalable(%, %)
eval: (%, List Equation %) -> %
from Evalable %
eval: (%, List Var, List %) -> %
from InnerEvalable(Var, %)
eval: (%, Var, %) -> %
from InnerEvalable(Var, %)
exp: % -> % if Coef has Algebra Fraction Integer
from ElementaryFunctionCategory
exquo: (%, %) -> Union(%, failed) if Coef has IntegralDomain
from EntireRing
extend: (%, NonNegativeInteger) -> %
extend(f, n) causes all terms of f of degree <= n to be computed.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
integrate: (%, Var) -> % if Coef has Algebra Fraction Integer
integrate(f, x) returns the anti-derivative of the power series f(x) with respect to the variable x with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.
latex: % -> String
from SetCategory
leadingCoefficient: % -> Coef
from PowerSeriesCategory(Coef, IndexedExponents Var, Var)
leadingMonomial: % -> %
from PowerSeriesCategory(Coef, IndexedExponents Var, Var)
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 AbelianMonoidRing(Coef, IndexedExponents Var)
monomial: (%, List Var, List IndexedExponents Var) -> %
from PowerSeriesCategory(Coef, IndexedExponents Var, Var)
monomial: (%, List Var, List NonNegativeInteger) -> %
monomial(a, [x1, x2, ..., xk], [n1, n2, ..., nk]) returns a * x1^n1 * ... * xk^nk.
monomial: (%, Var, IndexedExponents Var) -> %
from PowerSeriesCategory(Coef, IndexedExponents Var, Var)
monomial: (%, Var, NonNegativeInteger) -> %
monomial(a, x, n) returns a*x^n.
monomial: (Coef, IndexedExponents Var) -> %
from AbelianMonoidRing(Coef, IndexedExponents Var)
monomial?: % -> Boolean
from AbelianMonoidRing(Coef, IndexedExponents Var)
nthRoot: (%, Integer) -> % if Coef has Algebra Fraction Integer
from RadicalCategory
one?: % -> Boolean
from MagmaWithUnit
opposite?: (%, %) -> Boolean
from AbelianMonoid
order: (%, Var) -> NonNegativeInteger
order(f, x) returns the order of f viewed as a series in x may result in an infinite loop if f has no non-zero terms.
order: (%, Var, NonNegativeInteger) -> NonNegativeInteger
order(f, x, n) returns min(n, order(f, x)).
pi: () -> % if Coef has Algebra Fraction Integer
from TranscendentalFunctionCategory
pole?: % -> Boolean
from PowerSeriesCategory(Coef, IndexedExponents Var, Var)
polynomial: (%, NonNegativeInteger) -> Polynomial Coef
polynomial(f, k) returns a polynomial consisting of the sum of all terms of f of degree <= k.
polynomial: (%, NonNegativeInteger, NonNegativeInteger) -> Polynomial Coef
polynomial(f, k1, k2) returns a polynomial consisting of the sum of all terms of f of degree d with k1 <= d <= k2.
recip: % -> Union(%, failed)
from MagmaWithUnit
reductum: % -> %
from AbelianMonoidRing(Coef, IndexedExponents Var)
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
variables: % -> List Var
from PowerSeriesCategory(Coef, IndexedExponents Var, Var)
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianMonoidRing(Coef, IndexedExponents Var)

AbelianSemiGroup

Algebra % if Coef has IntegralDomain

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

InnerEvalable(%, %)

InnerEvalable(Var, %)

IntegralDomain if Coef has IntegralDomain

LeftModule %

LeftModule Coef

LeftModule Fraction Integer if Coef has Algebra Fraction Integer

Magma

MagmaWithUnit

Module % if Coef has IntegralDomain

Module Coef if Coef has CommutativeRing

Module Fraction Integer if Coef has Algebra Fraction Integer

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if Coef has IntegralDomain

PartialDifferentialRing Var

PowerSeriesCategory(Coef, IndexedExponents Var, Var)

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

unitsKnown

VariablesCommuteWithCoefficients