CyclicGroup(n, g)ΒΆ

discrgrp.spad line 71 [edit on github]

A domain for finite cyclic groups.

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

/: (%, %) -> %

from Group

=: (%, %) -> Boolean

from BasicType

^: (%, Integer) -> %

from Group

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

commutator: (%, %) -> %

from Group

conjugate: (%, %) -> %

from Group

convert: % -> InputForm

from ConvertibleTo InputForm

convert: % -> SExpression

from ConvertibleTo SExpression

enumerate: () -> List %

from Finite

exponent: % -> Integer

exponent(g^k) returns the representative integer $k$.

generator: () -> %

generator() returns the generator.

generators: () -> List %

from FinitelyGenerated

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

index: PositiveInteger -> %

from Finite

inv: % -> %

from Group

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

lookup: % -> PositiveInteger

from Finite

one?: % -> Boolean

from MagmaWithUnit

order: % -> Integer

from FiniteGroup

random: () -> %

from Finite

recip: % -> Union(%, failed)

from MagmaWithUnit

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from MagmaWithUnit

size: () -> NonNegativeInteger

from Finite

smaller?: (%, %) -> Boolean

from Comparable

BasicType

CoercibleTo OutputForm

CommutativeStar

Comparable

ConvertibleTo InputForm

ConvertibleTo SExpression

Finite

FiniteGroup

FinitelyGenerated

Group

Magma

MagmaWithUnit

Monoid

SemiGroup

SetCategory

TwoSidedRecip

unitsKnown