QEtaExtendedAlgebra(C, A, B)

qetaalg.spad line 214 [edit on github]

• C: CommutativeRing

• A: QEtaAlgebra C

• B: Join(Monoid, AbelianGroup) with

  *: (C, %) -> %

The domain QEtaExtendedAlgebra(C, A, B) behaves like the given QEtaAlgebra A, but every algebra operation is executed on the (hidden) B part as well and can later be extracted. The purpose of this domain is to record the computation trace of its elements, i.e. how an element is represented in terms of initial 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 XEtaGradedAlgebra C and C has Field or A has Field and B has Field

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

coerce: % -> OutputForm

from CoercibleTo OutputForm

embed: (A, B) -> %

embed(a, b) attaches the element b to the element a.

first: % -> A

first(x) returns the (main) algebra element from x.

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

second: % -> B

second(x) returns the attached part of x.

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

SemiGroup

SetCategory

XEtaGradedAlgebra C if A has XEtaGradedAlgebra C