# InfiniteCyclicGroup gΒΆ

Infinite cyclic groups.

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

/: (%, %) -> %

from Group

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

^: (%, Integer) -> %

from Group

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm
commutator: (%, %) -> %

from Group

conjugate: (%, %) -> %

from Group

convert: % -> SExpression
exponent: % -> Integer

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

generator: () -> %

`generator()` returns the generator.

generators: () -> List %
hash: % -> SingleInteger

from Hashable

hashUpdate!: (HashState, %) -> HashState

from Hashable

inv: % -> %

from Group

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

max: (%, %) -> %

from OrderedSet

min: (%, %) -> %

from OrderedSet

one?: % -> Boolean

from MagmaWithUnit

recip: % -> Union(%, failed)

from MagmaWithUnit

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from MagmaWithUnit

smaller?: (%, %) -> Boolean

from Comparable

BasicType

CommutativeStar

Comparable

FinitelyGenerated

Group

Hashable

Magma

MagmaWithUnit

Monoid

OrderedMonoid

OrderedSemiGroup

OrderedSet

PartialOrder

SemiGroup

SetCategory

TwoSidedRecip

unitsKnown