QGeneratingFunctionSpecification

qgenfunspec.spad line 364 [edit on github]

QGeneratingFunctionSpecification formally specifices dissections of generating functions it is a commutative (multiplicatively written) group of variables given by QGeneratingFunctionVariable.

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, QGeneratingFunctionVariable) -> %

*: (QGeneratingFunctionVariable, %) -> %

*: (QGeneratingFunctionVariable, QGeneratingFunctionVariable) -> %

/: (%, %) -> %

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

^: (QGeneratingFunctionVariable, Integer) -> %

~=: (%, %) -> Boolean

from BasicType

choose: (PositiveInteger, NonNegativeInteger, %) -> %

choose(m,t)(x) returns a specification that represents $sum_{n=0}^infty a(m n + t)$, if x is a specification that represents $sum_{n=0}^infty a(n)$. This function distributes over products, i.e. choose(m,t,x*y)=choose(m,t,x)*choose(m,t,y).

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: QGeneratingFunctionVariable -> %

from CoercibleFrom QGeneratingFunctionVariable

commutator: (%, %) -> %

from Group

conjugate: (%, %) -> %

from Group

denom: % -> %

from QGeneratingFunctionSpecificationCategory

dilate: (%, PositiveInteger) -> %

dilate(x,n) is the respective operation of replacing q by q^n. This function distributes over products, i.e. dilate(x*y,m)=dilate(x,m)*dilate(y,m).

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

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 commes with positive exponent and an “i” (for inverse) is prepended, if the dissection comes with a negative power.

numer: % -> %

from QGeneratingFunctionSpecificationCategory

one?: % -> Boolean

from MagmaWithUnit

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

from QGeneratingFunctionSpecificationCategory

quotient: % -> Fraction Polynomial Integer

quotient(x) returns monomial(numer(x))/monomial(denom(x)).

recip: % -> Union(%, failed)

from MagmaWithUnit

retract: % -> QGeneratingFunctionVariable

from RetractableTo QGeneratingFunctionVariable

retractIfCan: % -> Union(QGeneratingFunctionVariable, failed)

from RetractableTo QGeneratingFunctionVariable

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

CoercibleFrom QGeneratingFunctionVariable

CoercibleTo OutputForm

CommutativeStar

Comparable

Group

Hashable

Magma

MagmaWithUnit

Monoid

OrderedSet

PartialOrder

QGeneratingFunctionSpecificationCategory

RetractableTo QGeneratingFunctionVariable

SemiGroup

SetCategory

TwoSidedRecip

unitsKnown