QEtaGradedAlgebra C

qetaalg.spad line 146 [edit on github]

• C: CommutativeRing

QEtaGradedAlgebra(C) lists the minimal signatures for running the functions in the QEtaPackage. Mathematically seen is it a C-algebra that is ZZ-graded. Simplest example is a univariate polynomial ring over C, but since it is expected that respective domains will be created on the fly, we list here only the functions that are actually used in QEtaSambaPackage.

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

=: (%, %) -> 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

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

qetaCoefficient: (%, Integer) -> C

qetaCoefficient(x, n) returns the coefficient corresponding to grade n.

qetaGrade: % -> Integer

qetaGrade(x) returns the grade of an element. The qetaGrade of 0 is undefined. Any element x with qetaGrade(x)<0 will be considered to be zero.

qetaLeadingCoefficient: % -> C

qetaLeadingCoefficient(x) returns qetaCoefficient(x, 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