QGeneratingFunctionSpecificationCategory

qgenfunspec.spad line 314 [edit on github]

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

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: % -> %

denom(x) returns the part of the specification that corresponds to negative exponents. It holds: x=numer(x)/denom(x).

exponent: (%, QGeneratingFunctionVariable) -> Integer

exponent(x, gfv) returns the exponent corresponding to gfv.

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

level(x) returns the lcm of the level of each variable of 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 sum_{n=0}^infty a(m*n+k) q^n.

numer: % -> %

numer(x) returns the part of the specification that corresponds to positive exponents.

one?: % -> Boolean

from MagmaWithUnit

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

parts(x) returns a list of dissections together with their exponents.

quotient: % -> Fraction Polynomial Integer

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

recip: % -> Union(%, failed)

from MagmaWithUnit

rhoInfinity: % -> Fraction Integer

rhoInfinity(x) returns the sum of e*rhoInfinity(p) for all parts p of x.

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

SemiGroup

SetCategory

TwoSidedRecip

unitsKnown