PowerSeriesCategory(Coef, Expon, Var)

pscat.spad line 1 [edit on github]

• Coef : Ring
• Expon : OrderedAbelianMonoid
• Var : OrderedSet

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

* : (%, %) -> %

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)

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

= : (%, %) -> Boolean

from BasicType

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

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 : 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 : % -> OutputForm

from CoercibleTo(OutputForm)

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.

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

from IndexedProductCategory(Coef, Expon)

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

from IndexedProductCategory(Coef, Expon)

degree : % -> Expon

degree(f) returns the exponent of the lowest order term of f.

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

from EntireRing

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.

leadingSupport : % -> Expon

from IndexedProductCategory(Coef, Expon)

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

from IndexedProductCategory(Coef, Expon)

leftPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower : (%, PositiveInteger) -> %

from Magma

leftRecip : % -> Union(%, "failed")

from MagmaWithUnit

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

from IndexedProductCategory(Coef, Expon)

monomial : (Coef, Expon) -> %

from IndexedProductCategory(Coef, Expon)

monomial? : % -> Boolean

from IndexedProductCategory(Coef, Expon)

one? : % -> Boolean

from MagmaWithUnit

opposite? : (%, %) -> Boolean

from AbelianMonoid

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

from NonAssociativeAlgebra(Coef)

pole? : % -> Boolean

pole?(f) determines if the power series f has a pole.

recip : % -> Union(%, "failed")

from MagmaWithUnit

reductum : % -> %

from IndexedProductCategory(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

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

CharacteristicNonZero

Module(Fraction(Integer))

Module(Coef)

noZeroDivisors

LeftModule(Coef)

LeftModule(Fraction(Integer))

Algebra(%)

RightModule(%)

Monoid

AbelianMonoid

CharacteristicZero

NonAssociativeSemiRng

NonAssociativeAlgebra(Fraction(Integer))

CancellationAbelianMonoid

MagmaWithUnit

NonAssociativeRing

RightModule(Fraction(Integer))

BiModule(%, %)

CoercibleTo(OutputForm)

RightModule(Coef)

LeftModule(%)

IndexedProductCategory(Coef, Expon)

SemiRng

Module(%)

SetCategory

AbelianProductCategory(Coef)

Algebra(Fraction(Integer))

Rng

CommutativeRing

IntegralDomain

TwoSidedRecip

Magma

SemiGroup

AbelianGroup

AbelianSemiGroup

CommutativeStar

NonAssociativeSemiRing

VariablesCommuteWithCoefficients

NonAssociativeAlgebra(%)

BiModule(Fraction(Integer), Fraction(Integer))

BiModule(Coef, Coef)

NonAssociativeRng

unitsKnown

Ring

Algebra(Coef)

EntireRing

AbelianMonoidRing(Coef, Expon)

BasicType

NonAssociativeAlgebra(Coef)

SemiRing