QEtaSpecificationExpressionMonomial

qetaspecexpr.spad line 163 [edit on github]

QEtaSpecificationExpressionMonomial is a combination (a product) of the different types of specifications, i.e. a QPochhammerSpecification, a QEtaSpecification, and a QGeneratingFunctionSpecification.

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (QEtaSpecification, %) -> %

*: (QGeneratingFunctionSpecification, %) -> %

*: (QGeneratingFunctionVariable, %) -> %

*: (QPochhammerSpecification, %) -> %

*: (QPochhammerSpecification, QEtaSpecification) -> %

*: (XGeneratingFunctionSpecification, %) -> %

/: (%, %) -> %

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

coerce: QEtaSpecification -> %

from CoercibleFrom QEtaSpecification

coerce: QGeneratingFunctionSpecification -> %

from CoercibleFrom QGeneratingFunctionSpecification

coerce: QGeneratingFunctionVariable -> %

from CoercibleFrom QGeneratingFunctionVariable

coerce: QPochhammerSpecification -> %

from CoercibleFrom QPochhammerSpecification

coerce: XGeneratingFunctionSpecification -> %

from CoercibleFrom XGeneratingFunctionSpecification

commutator: (%, %) -> %

from Group

conjugate: (%, %) -> %

from Group

denom: % -> %

from QEtaSpecificationCategory

dilate: (%, PositiveInteger) -> %

from QEtaSpecificationCategory

etaExpression: % -> %

etaExpression(x) tries to replace q-Pochhammer quotients by eta-Quotients. Since not every q-Pochhammer quotient can be translated into an eta-quotient, there might be q-Pochhammer symbols or (fractional) powers of q remaining in the expression. This function is idempotent and it holds etaExpression(qExpression(x))=etaExpression(x).

etaPart: % -> QEtaSpecification

etaPart(x) returns the eta-quotient part of the monomial.

gfPart: % -> QGeneratingFunctionSpecification

gfPart(x) returns the (dissected) generating function part of the monomial.

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 QEtaSpecificationCategory

max: (%, %) -> %

from OrderedSet

min: (%, %) -> %

from OrderedSet

monomial: % -> Polynomial Integer

from QEtaSpecificationCategory

monomial: (%, String, String) -> Polynomial Integer

from QEtaSpecificationCategory

numer: % -> %

from QEtaSpecificationCategory

one?: % -> Boolean

from MagmaWithUnit

purify: % -> %

purify(x) applies purify to all specifications that are part of x.

qExpression: % -> %

qExpression(x) replaces any eta-quotient by the respective quotient of q-Pochhammer symbols. This function is idempotent and it holds qExpression(etaExpression(x))=qExpression(x).

qMonomial: % -> Polynomial Integer

qmonomial(x) returns monomial(qExpression(x))$QPochhammerSpecification, if x corresponds to a q-Pochhammer specification. This function is the inverse of qSpecification.

qMonomial: (%, String, String) -> Polynomial Integer

qMonomial(x,u,v) returns monomial(qExpression(x),u,v), if x corresponds to a q-Pochhammer specification. This function is the inverse of qSpecification.

qPochhammerPart: % -> QPochhammerSpecification

qPochhammerPart(x) returns the q-Pochhammer part of the monomial.

qQuotient: % -> Fraction Polynomial Integer

qQuotient(x) returns quotient(qExpression(x),e)$QPochhammerSpecification, if x corresponds to a q-Pochhammer specification. This function is the inverse of qSpecification.

qQuotient: (%, String) -> Fraction Polynomial Integer

qQuotient(x,u) returns qMonomial(numer(x),u)/qMonomial(denom(x),u).

qSpecification: (Fraction Polynomial Integer, String) -> %

qSpecification(f,e) returns nspec/dspec for nspec:=qSpecification(numer(f),e) and dspec:=qSpecification(denom(f),e).

qSpecification: (Polynomial Integer, String) -> %

qSpecification(p,e) returns specification(p,e)$QPochhammerSpecification coerced to this domain.

qSpecification: Fraction Polynomial Integer -> %

qSpecification(f) returns nspec/dspec for nspec:=qSpecification(numer(f)) and dspec:=qSpecification(denom(f)).

qSpecification: Polynomial Integer -> %

qSpecification(p) returns specification(p,e)$QPochhammerSpecification coerced to this domain.

quotient: % -> Fraction Polynomial Integer

from QEtaSpecificationCategory

quotient: (%, String) -> Fraction Polynomial Integer

from QEtaSpecificationCategory

recip: % -> Union(%, failed)

from MagmaWithUnit

retract: % -> QEtaSpecification

from RetractableTo QEtaSpecification

retract: % -> QGeneratingFunctionSpecification

from RetractableTo QGeneratingFunctionSpecification

retract: % -> QGeneratingFunctionVariable

from RetractableTo QGeneratingFunctionVariable

retract: % -> QPochhammerSpecification

from RetractableTo QPochhammerSpecification

retract: % -> XGeneratingFunctionSpecification

from RetractableTo XGeneratingFunctionSpecification

retractIfCan: % -> Union(QEtaSpecification, failed)

from RetractableTo QEtaSpecification

retractIfCan: % -> Union(QGeneratingFunctionSpecification, failed)

from RetractableTo QGeneratingFunctionSpecification

retractIfCan: % -> Union(QGeneratingFunctionVariable, failed)

from RetractableTo QGeneratingFunctionVariable

retractIfCan: % -> Union(QPochhammerSpecification, failed)

from RetractableTo QPochhammerSpecification

retractIfCan: % -> Union(XGeneratingFunctionSpecification, failed)

from RetractableTo XGeneratingFunctionSpecification

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from MagmaWithUnit

smaller?: (%, %) -> Boolean

from Comparable

specification: (Fraction Polynomial Integer, String) -> %

from QEtaSpecificationCategory

specification: (Polynomial Integer, String) -> %

from QEtaSpecificationCategory

specification: Fraction Polynomial Integer -> %

from QEtaSpecificationCategory

specification: Polynomial Integer -> %

from QEtaSpecificationCategory

xgfPart: % -> XGeneratingFunctionSpecification

xgfPart(x) returns the (dissected) generating function part of the monomial multiplied by q^rhoInfinity(gfPart(x)).

BasicType

CoercibleFrom QEtaSpecification

CoercibleFrom QGeneratingFunctionSpecification

CoercibleFrom QGeneratingFunctionVariable

CoercibleFrom QPochhammerSpecification

CoercibleFrom XGeneratingFunctionSpecification

CoercibleTo OutputForm

CommutativeStar

Comparable

Group

Hashable

Magma

MagmaWithUnit

Monoid

OrderedSet

PartialOrder

QEtaSpecificationCategory

RetractableTo QEtaSpecification

RetractableTo QGeneratingFunctionSpecification

RetractableTo QGeneratingFunctionVariable

RetractableTo QPochhammerSpecification

RetractableTo XGeneratingFunctionSpecification

SemiGroup

SetCategory

TwoSidedRecip

unitsKnown