XGeneratingFunctionSpecification

qgenfunspec.spad line 557 [edit on github]

XGeneratingFunctionSpecification formally specifices dissections of generating functions it is a commutative (multiplicatively written) group of variables given by QGeneratingFunctionVariable where each variable v is actually understood as representing q^rho*v with $rho=rhoInfinity(v)$. XGeneratingFunctionSpecification is just a reinterpretation of the same data (and representation of QGeneratingFunctionSpecification.

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

/: (%, %) -> %

from Group

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

^: (%, Integer) -> %

from Group

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

commutator: (%, %) -> %

from Group

conjugate: (%, %) -> %

from Group

denom: % -> %

from QGeneratingFunctionSpecificationCategory

exponent: (%, QGeneratingFunctionVariable) -> Integer

from QGeneratingFunctionSpecificationCategory

hash: % -> SingleInteger

from Hashable

hashUpdate!: (HashState, %) -> HashState

from Hashable

inv: % -> %

from Group

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

level: % -> PositiveInteger

from QGeneratingFunctionSpecificationCategory

lift: QGeneratingFunctionSpecification -> %

lift(x) interprets x as q^r*x where r=rhoInfinity(x).

lift: QGeneratingFunctionVariable -> %

lift(x) interprets x as q^r*x where r=rhoInfinity(x).

max: (%, %) -> %

from OrderedSet

min: (%, %) -> %

from OrderedSet

monomial: % -> Polynomial Integer

monomial(x) returns 1 if x is constant. Otherwise, it returns a power product of variables where each variable is the respective symbol for the dissection, if it comes with positive exponent and an “i” (for inverse) is prepended, if the dissection comes with a negative power. A variable like am_k should be interpreted with the meaning q^r*sum_{n=0}^infty a(m*n+k) q^n where r=rhoInfinity(v) and v is an element of QGeneratingFunctionVariable corresponding to sum_{n=0}^infty a(m*n+k) q^n.

numer: % -> %

from QGeneratingFunctionSpecificationCategory

one?: % -> Boolean

from MagmaWithUnit

parts: % -> List Record(key: QGeneratingFunctionVariable, entry: Integer)

from QGeneratingFunctionSpecificationCategory

project: % -> QGeneratingFunctionSpecification

project(x) returns y such that x=lift(y), i.e. forgets the q^r factor where r=rhoInfinity(x).

quotient: % -> Fraction Polynomial Integer

from QGeneratingFunctionSpecificationCategory

recip: % -> Union(%, failed)

from MagmaWithUnit

rhoInfinity: % -> Fraction Integer

from QGeneratingFunctionSpecificationCategory

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from MagmaWithUnit

smaller?: (%, %) -> Boolean

from Comparable

BasicType

CoercibleTo OutputForm

CommutativeStar

Comparable

Group

Hashable

Magma

MagmaWithUnit

Monoid

OrderedSet

PartialOrder

QGeneratingFunctionSpecificationCategory

SemiGroup

SetCategory

TwoSidedRecip

unitsKnown