QEtaPowerGradedAlgebra CΒΆ

qetaalg.spad line 178 [edit on github]

A domain implementing QEtaPowerGradedAlgebra(C) is supposed to work like the direct product of n=maxIndex() copies of a QEtaAlgebra.

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 C 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).

=: (%, %) -> Boolean

from BasicType

^: (%, NonNegativeInteger) -> %

from QEtaAlgebra C

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

maxIndex: () -> PositiveInteger

maxIndex() returns the number of components of this domain.

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

qetaGrade: (%, PositiveInteger) -> Integer

qetaGrade(x, k) returns the grade with the first nonzero entry in the k-th component. If the grade is not bounded from below this function might run into an infinite loop. qetaGrade(0, k) is undefined.

qetaGrade: (%, PositiveInteger, Integer) -> Integer

qetaGrade(x, k, mn) returns the maximum of qetaGrade(x, k) and mn. In particular, qetaGrade(0,k,mn)=mn.

qetaGrades: % -> List Integer

qetaGrades(x) returns [qetaGrade(x, k) for k in 1..maxIndex())] for nonzero x and [-1 for k in 1..maxIndex()] for x=0.

qetaIndex: % -> PositiveInteger

qetaIndex(x) for nonzero x returns k such that qetaGrade(x, k) = max [qetaGrade(x, j) for j in 1..maxIndex()] and k is minimal with this property. qetaIndex(0) is undefined.

qetaLeadingCoefficient: (%, PositiveInteger) -> C

qetaLeadingCoefficient(x, k) returns the coefficient in the k-th component corresponding to qetaGrade(x). The qetaLeadingCoefficient of 0 is undefined.

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

from QEtaAlgebra C

zero?: % -> Boolean

from QEtaAlgebra C

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid

CoercibleTo OutputForm

Magma

MagmaWithUnit

Monoid

QEtaAlgebra C

SemiGroup

SetCategory