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
's
dangerous, because sums of eta-quotients might have zeros so that inverses of such function usually have poles not only at the cusps ofGamma_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 ofx
.- 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 tox
.
- 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 returnsk
.
- 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 wherex
representsb
.
- 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