QEtaSpecificationExpression CΒΆ

qetaspecexpr.spad line 423 [edit on github]

QEtaSpecificationExpression contains functions to specify linear combinations of q-Pochammer quotients, eta-quotients and dissections of such.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, C) -> %

from RightModule C

*: (C, %) -> %

from LeftModule C

*: (C, QEtaSpecificationExpressionMonomial) -> %

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

*: (QEtaSpecification, %) -> %

*: (QGeneratingFunctionSpecification, %) -> %

*: (QGeneratingFunctionVariable, %) -> %

*: (QPochhammerSpecification, %) -> %

*: (XGeneratingFunctionSpecification, %) -> %

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, %) -> %

x/y returns x*inv(y).

=: (%, %) -> Boolean

from BasicType

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

associator: (%, %, %) -> %

from NonAssociativeRng

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

coefficient: (%, QEtaSpecificationExpressionMonomial) -> C

from FreeModuleCategory(C, QEtaSpecificationExpressionMonomial)

coefficients: % -> List C

from FreeModuleCategory(C, QEtaSpecificationExpressionMonomial)

coerce: % -> %

from Algebra %

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: C -> %

from CoercibleFrom C

coerce: Integer -> %

from NonAssociativeRing

coerce: List Record(k: QEtaSpecificationExpressionMonomial, c: C) -> %

from MonoidRingCategory(C, QEtaSpecificationExpressionMonomial)

coerce: QEtaSpecification -> %

from CoercibleFrom QEtaSpecification

coerce: QEtaSpecificationExpressionMonomial -> %

from CoercibleFrom QEtaSpecificationExpressionMonomial

coerce: QGeneratingFunctionSpecification -> %

from CoercibleFrom QGeneratingFunctionSpecification

coerce: QGeneratingFunctionVariable -> %

from CoercibleFrom QGeneratingFunctionVariable

coerce: QPochhammerSpecification -> %

from CoercibleFrom QPochhammerSpecification

coerce: XGeneratingFunctionSpecification -> %

from CoercibleFrom XGeneratingFunctionSpecification

commutator: (%, %) -> %

from NonAssociativeRng

construct: List Record(k: QEtaSpecificationExpressionMonomial, c: C) -> %

from IndexedProductCategory(C, QEtaSpecificationExpressionMonomial)

constructOrdered: List Record(k: QEtaSpecificationExpressionMonomial, c: C) -> %

from IndexedProductCategory(C, QEtaSpecificationExpressionMonomial)

convert: % -> InputForm if QEtaSpecificationExpressionMonomial has Finite and C has Finite

from ConvertibleTo InputForm

dilate: (%, PositiveInteger) -> %

dilate(x,n) is the respective operation of replacing q by q^n. It distributes over sums and products.

enumerate: () -> List % if QEtaSpecificationExpressionMonomial has Finite and C has Finite

from Finite

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).

hash: % -> SingleInteger if QEtaSpecificationExpressionMonomial has Finite and C has Finite

from Hashable

hashUpdate!: (HashState, %) -> HashState if QEtaSpecificationExpressionMonomial has Finite and C has Finite

from Hashable

index: PositiveInteger -> % if QEtaSpecificationExpressionMonomial has Finite and C has Finite

from Finite

inv: % -> %

inv(x) returns the recip(x)::% if recip(x) does not fail, otherwise the function aborts with an error. The functions is a support function for cases where the user knows that recip will not fail. An element is invertible if and only if it is a monomial with an invertible coefficient. In success cases it holds inv(inv(x))=x and inv(x)*x=1.

latex: % -> String

from SetCategory

leadingCoefficient: % -> C

from IndexedProductCategory(C, QEtaSpecificationExpressionMonomial)

leadingMonomial: % -> %

from IndexedProductCategory(C, QEtaSpecificationExpressionMonomial)

leadingSupport: % -> QEtaSpecificationExpressionMonomial

from IndexedProductCategory(C, QEtaSpecificationExpressionMonomial)

leadingTerm: % -> Record(k: QEtaSpecificationExpressionMonomial, c: C)

from IndexedProductCategory(C, QEtaSpecificationExpressionMonomial)

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

level: % -> PositiveInteger

level(x) returns the lcm of the levels of all parts.

linearExtend: (QEtaSpecificationExpressionMonomial -> C, %) -> C

from FreeModuleCategory(C, QEtaSpecificationExpressionMonomial)

listOfTerms: % -> List Record(k: QEtaSpecificationExpressionMonomial, c: C)

from IndexedDirectProductCategory(C, QEtaSpecificationExpressionMonomial)

lookup: % -> PositiveInteger if QEtaSpecificationExpressionMonomial has Finite and C has Finite

from Finite

map: (C -> C, %) -> %

from IndexedProductCategory(C, QEtaSpecificationExpressionMonomial)

monomial?: % -> Boolean

from IndexedProductCategory(C, QEtaSpecificationExpressionMonomial)

monomial: (C, QEtaSpecificationExpressionMonomial) -> %

from IndexedProductCategory(C, QEtaSpecificationExpressionMonomial)

monomials: % -> List %

from FreeModuleCategory(C, QEtaSpecificationExpressionMonomial)

numberOfMonomials: % -> NonNegativeInteger

from IndexedDirectProductCategory(C, QEtaSpecificationExpressionMonomial)

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra C

polynomial: % -> Polynomial C

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).

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

qSpecification: (Polynomial C, String) -> %

qSpecification: Fraction Polynomial C -> %

qSpecification: Polynomial C -> %

random: () -> % if QEtaSpecificationExpressionMonomial has Finite and C has Finite

from Finite

rationalFunction: % -> Fraction Polynomial C

recip: % -> Union(%, failed)

from MagmaWithUnit

reductum: % -> %

from IndexedProductCategory(C, QEtaSpecificationExpressionMonomial)

retract: % -> C

from RetractableTo C

retract: % -> QEtaSpecification

from RetractableTo QEtaSpecification

retract: % -> QEtaSpecificationExpressionMonomial

from RetractableTo QEtaSpecificationExpressionMonomial

retract: % -> QGeneratingFunctionSpecification

from RetractableTo QGeneratingFunctionSpecification

retract: % -> QGeneratingFunctionVariable

from RetractableTo QGeneratingFunctionVariable

retract: % -> QPochhammerSpecification

from RetractableTo QPochhammerSpecification

retract: % -> XGeneratingFunctionSpecification

from RetractableTo XGeneratingFunctionSpecification

retractIfCan: % -> Union(C, failed)

from RetractableTo C

retractIfCan: % -> Union(QEtaSpecification, failed)

from RetractableTo QEtaSpecification

retractIfCan: % -> Union(QEtaSpecificationExpressionMonomial, failed)

from RetractableTo QEtaSpecificationExpressionMonomial

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 AbelianMonoid

size: () -> NonNegativeInteger if QEtaSpecificationExpressionMonomial has Finite and C has Finite

from Finite

smaller?: (%, %) -> Boolean if C has Comparable

from Comparable

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

specification: (Polynomial C, String) -> %

specification: (Polynomial C, String, List QEtaSpecification) -> %

specification(p,m,specs) replaces each of the variables mi in p by the respective element specs.i and thus creates a formal linear combination of specifications.

specification: Fraction Polynomial C -> %

specification: Polynomial C -> %

subtractIfCan: (%, %) -> Union(%, failed)

from CancellationAbelianMonoid

support: % -> List QEtaSpecificationExpressionMonomial

from FreeModuleCategory(C, QEtaSpecificationExpressionMonomial)

terms: % -> List Record(k: QEtaSpecificationExpressionMonomial, c: C)

from MonoidRingCategory(C, QEtaSpecificationExpressionMonomial)

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianProductCategory C

AbelianSemiGroup

Algebra %

Algebra C

BasicType

BiModule(%, %)

BiModule(C, C)

CancellationAbelianMonoid

CharacteristicNonZero if C has CharacteristicNonZero

CharacteristicZero if C has CharacteristicZero

CoercibleFrom C

CoercibleFrom QEtaSpecification

CoercibleFrom QEtaSpecificationExpressionMonomial

CoercibleFrom QGeneratingFunctionSpecification

CoercibleFrom QGeneratingFunctionVariable

CoercibleFrom QPochhammerSpecification

CoercibleFrom XGeneratingFunctionSpecification

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable if C has Comparable

ConvertibleTo InputForm if QEtaSpecificationExpressionMonomial has Finite and C has Finite

Finite if QEtaSpecificationExpressionMonomial has Finite and C has Finite

FreeModuleCategory(C, QEtaSpecificationExpressionMonomial)

Hashable if QEtaSpecificationExpressionMonomial has Finite and C has Finite

IndexedDirectProductCategory(C, QEtaSpecificationExpressionMonomial)

IndexedProductCategory(C, QEtaSpecificationExpressionMonomial)

LeftModule %

LeftModule C

Magma

MagmaWithUnit

Module %

Module C

Monoid

MonoidRingCategory(C, QEtaSpecificationExpressionMonomial)

NonAssociativeAlgebra %

NonAssociativeAlgebra C

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

RetractableTo C

RetractableTo QEtaSpecification

RetractableTo QEtaSpecificationExpressionMonomial

RetractableTo QGeneratingFunctionSpecification

RetractableTo QGeneratingFunctionVariable

RetractableTo QPochhammerSpecification

RetractableTo XGeneratingFunctionSpecification

RightModule %

RightModule C

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TwoSidedRecip

unitsKnown