QEtaAlgebraCachedSamba(C, A)ΒΆ

qetaalg.spad line 328 [edit on github]

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 of Gamma_0(m). No check is made whether the result actually is an element of the domains, it is simply assumed.

=: (%, %) -> Boolean

from BasicType

^: (%, NonNegativeInteger) -> %

from QEtaAlgebra C

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

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 x represents b.

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

from CancellationAbelianMonoid

traceout: NonNegativeInteger -> % -> OutputForm

from QEtaAlgebra C

zero?: % -> Boolean

from QEtaAlgebra C

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid

CoercibleTo OutputForm

Magma

MagmaWithUnit

Monoid

QEtaAlgebra C

QEtaGradedAlgebra C if A has QEtaGradedAlgebra C

QEtaPowerGradedAlgebra C if A has QEtaPowerGradedAlgebra C

SemiGroup

SetCategory