QEtaAlgebraCachedSamba(C, A)ΒΆ
qetaalg.spad line 328 [edit on github]
- A: QEtaAlgebra C 
The domain QEtaAlgebraCachedSamba(C, A) behaves like the given QEtaAlgebra A, but it cached any product of two elements.
- 0: %
- from QEtaAlgebra C 
- 1: %
- from QEtaAlgebra C 
- *: (%, %) -> %
- from QEtaAlgebra C 
- *: (C, %) -> %
- from QEtaAlgebra C 
- *: (Integer, %) -> %
- from AbelianGroup 
- *: (NonNegativeInteger, %) -> %
- from AbelianMonoid 
- *: (PositiveInteger, %) -> %
- from AbelianSemiGroup 
- +: (%, %) -> %
- from QEtaAlgebra C 
- -: % -> %
- from QEtaAlgebra C 
- -: (%, %) -> %
- from QEtaAlgebra C 
- /: (%, %) -> % if A has QEtaPowerGradedAlgebra C and C has Field or A has /: (A, A) -> A
- Division. It - 'sdangerous, because sums of eta-quotients might have zeros so that inverses of such function usually have poles not only at the cusps of- Gamma_0(- m). No check is made whether the result actually is an element of the domains, it is simply assumed.
- ^: (%, NonNegativeInteger) -> %
- from QEtaAlgebra C 
- ^: (%, PositiveInteger) -> %
- from Magma 
- clearCache!: () -> Void
- clearCache!()removes any cache data and resets this domain to a situation as it was at creation time. That invalidates any existing element.
- coerce: % -> A
- coerce(x)returns forgets the cache of- x.
- coerce: % -> OutputForm
- from CoercibleTo OutputForm 
- embed: A -> %
- embed(a)creates a new element with value a and a (new) positive identifier.
getCache: () -> XHashTable(Product(Integer, Integer), Record(idpow: Product(Integer, Integer), val: A))
- identifier: % -> Integer
- identifier(x)returns the identifier connected to- x.
- latex: % -> String
- from SetCategory 
- leftPower: (%, NonNegativeInteger) -> %
- from MagmaWithUnit 
- leftPower: (%, PositiveInteger) -> %
- from Magma 
- leftRecip: % -> Union(%, failed)
- from MagmaWithUnit 
- maxIndex: () -> PositiveInteger if A has QEtaPowerGradedAlgebra C
- from QEtaPowerGradedAlgebra C 
nextIdentifier: () -> Integer
- one?: % -> Boolean
- from MagmaWithUnit 
- opposite?: (%, %) -> Boolean
- from AbelianMonoid 
- power: % -> Integer
- power(x)for an element of form b*t^k returns- k.
- qetaCoefficient: (%, Integer) -> C if A has QEtaGradedAlgebra C
- from QEtaGradedAlgebra C 
- qetaGrade: % -> Integer if A has QEtaGradedAlgebra C
- from QEtaGradedAlgebra C 
- qetaGrade: (%, PositiveInteger) -> Integer if A has QEtaPowerGradedAlgebra C
- from QEtaPowerGradedAlgebra C 
- qetaGrade: (%, PositiveInteger, Integer) -> Integer if A has QEtaPowerGradedAlgebra C
- from QEtaPowerGradedAlgebra C 
- qetaGrades: % -> List Integer if A has QEtaPowerGradedAlgebra C
- from QEtaPowerGradedAlgebra C 
- qetaIndex: % -> PositiveInteger if A has QEtaPowerGradedAlgebra C
- from QEtaPowerGradedAlgebra C 
- qetaLeadingCoefficient: % -> C if A has QEtaGradedAlgebra C
- from QEtaGradedAlgebra C 
- qetaLeadingCoefficient: (%, PositiveInteger) -> C if A has QEtaPowerGradedAlgebra C
- from QEtaPowerGradedAlgebra C 
- recip: % -> Union(%, failed)
- from MagmaWithUnit 
- rightPower: (%, NonNegativeInteger) -> %
- from MagmaWithUnit 
- rightPower: (%, PositiveInteger) -> %
- from Magma 
- rightRecip: % -> Union(%, failed)
- from MagmaWithUnit 
- sample: %
- from MagmaWithUnit 
- setCache!: (%, Integer, A) -> %
- setCache!(x, n, a)sets that b*t^n is equal to a where- xrepresents- b.
- subtractIfCan: (%, %) -> Union(%, failed)
- traceout: NonNegativeInteger -> % -> OutputForm
- from QEtaAlgebra C 
- zero?: % -> Boolean
- from QEtaAlgebra C 
QEtaGradedAlgebra C if A has QEtaGradedAlgebra C
QEtaPowerGradedAlgebra C if A has QEtaPowerGradedAlgebra C