QEtaAlgebraCachedPower(C, A)

qetaalg.spad line 298 [edit on github]

• C: CommutativeRing

• A: Join(Monoid, AbelianGroup) with

  *: (C, %) -> %

The domain QEtaAlgebraCachedPower(C, A) behaves like the given QEtaAlgebra A, but to each of its elements x a power x^n is never computed twice, but rather stored and then accessed from the cache. Although the implementation is formulated with weaker conditions on the input parameter, we assume that A forms a C algebra.

0: %

from QEtaAlgebra C

1: %

from QEtaAlgebra C

*: (%, %) -> %

from QEtaAlgebra C

*: (C, %) -> %

c * x return the product of a constant (from the coefficient domain) with x.

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from QEtaAlgebra C

-: % -> %

from QEtaAlgebra C

-: (%, %) -> %

from QEtaAlgebra C

/: (%, %) -> % if A has XEtaGradedAlgebra C and C has Field

from XEtaGradedAlgebra C

=: (%, %) -> Boolean

from BasicType

^: (%, NonNegativeInteger) -> %

from QEtaAlgebra C

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

coerce: % -> A

from CoercibleTo A

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: A -> %

from CoercibleFrom A

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

maxIndex: () -> PositiveInteger if A has XEtaGradedAlgebra C

from XEtaGradedAlgebra C

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

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 XEtaGradedAlgebra C

from XEtaGradedAlgebra C

qetaGrade: (%, PositiveInteger, Integer) -> Integer if A has XEtaGradedAlgebra C

from XEtaGradedAlgebra C

qetaGrades: % -> List Integer if A has XEtaGradedAlgebra C

from XEtaGradedAlgebra C

qetaIndex: % -> PositiveInteger if A has XEtaGradedAlgebra C

from XEtaGradedAlgebra C

qetaLeadingCoefficient: % -> C if A has QEtaGradedAlgebra C

from QEtaGradedAlgebra C

qetaLeadingCoefficient: (%, PositiveInteger) -> C if A has XEtaGradedAlgebra C

from XEtaGradedAlgebra C

recip: % -> Union(%, failed)

from MagmaWithUnit

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from MagmaWithUnit

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

from CancellationAbelianMonoid

traceout: NonNegativeInteger -> % -> OutputForm if A has QEtaGradedAlgebra C or A has XEtaGradedAlgebra C

from QEtaAlgebra C

zero?: % -> Boolean

from QEtaAlgebra C

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid

CoercibleFrom A

CoercibleTo A

CoercibleTo OutputForm

Magma

MagmaWithUnit

Monoid

QEtaAlgebra C if A has QEtaGradedAlgebra C or A has XEtaGradedAlgebra C

QEtaGradedAlgebra C if A has QEtaGradedAlgebra C

SemiGroup

SetCategory

XEtaGradedAlgebra C if A has XEtaGradedAlgebra C