PowerSeriesCategory(Coef, Expon, Var)ΒΆ

pscat.spad line 1

PowerSeriesCategory is the most general power series category with exponents in an ordered abelian monoid.

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, Expon)
=: (%, %) -> Boolean
from BasicType
^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
annihilate?: (%, %) -> Boolean
from Rng
antiCommutator: (%, %) -> %
from NonAssociativeSemiRng
associates?: (%, %) -> Boolean if Coef has IntegralDomain
from EntireRing
associator: (%, %, %) -> %
from NonAssociativeRng
characteristic: () -> NonNegativeInteger
from NonAssociativeRing
charthRoot: % -> Union(%, failed) if Coef has CharacteristicNonZero
from CharacteristicNonZero
coefficient: (%, Expon) -> Coef
from AbelianMonoidRing(Coef, Expon)
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
commutator: (%, %) -> %
from NonAssociativeRng
complete: % -> %
complete(f) causes all terms of f to be computed. Note: this results in an infinite loop if f has infinitely many terms.
degree: % -> Expon
degree(f) returns the exponent of the lowest order term of f.
exquo: (%, %) -> Union(%, failed) if Coef has IntegralDomain
from EntireRing
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
latex: % -> String
from SetCategory
leadingCoefficient: % -> Coef
leadingCoefficient(f) returns the coefficient of the lowest order term of f
leadingMonomial: % -> %
leadingMonomial(f) returns the monomial of f of lowest order.
leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
leftPower: (%, PositiveInteger) -> %
from Magma
leftRecip: % -> Union(%, failed)
from MagmaWithUnit
map: (Coef -> Coef, %) -> %
from AbelianMonoidRing(Coef, Expon)
monomial: (%, List Var, List Expon) -> %
monomial(a, [x1, .., xk], [n1, .., nk]) computes a * x1^n1 * .. * xk^nk.
monomial: (%, Var, Expon) -> %
monomial(a, x, n) computes a*x^n.
monomial: (Coef, Expon) -> %
from AbelianMonoidRing(Coef, Expon)
monomial?: % -> Boolean
from AbelianMonoidRing(Coef, Expon)
one?: % -> Boolean
from MagmaWithUnit
opposite?: (%, %) -> Boolean
from AbelianMonoid
pole?: % -> Boolean
pole?(f) determines if the power series f has a pole.
recip: % -> Union(%, failed)
from MagmaWithUnit
reductum: % -> %
from AbelianMonoidRing(Coef, Expon)
rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
rightPower: (%, PositiveInteger) -> %
from Magma
rightRecip: % -> Union(%, failed)
from MagmaWithUnit
sample: %
from AbelianMonoid
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
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
variables(f) returns a list of the variables occurring in the power series f.
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianMonoidRing(Coef, Expon)

AbelianSemiGroup

Algebra % if Coef has CommutativeRing

Algebra Coef if Coef has CommutativeRing

Algebra Fraction Integer 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

EntireRing if Coef has IntegralDomain

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

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if Coef has IntegralDomain

RightModule %

RightModule Coef

RightModule Fraction Integer if Coef has Algebra Fraction Integer

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

unitsKnown

VariablesCommuteWithCoefficients