InfiniteCyclicGroup(g)

discrgrp.spad line 146 [edit on github]

• g : Symbol

Infinite cyclic groups.

* : (%, %) -> %

from Magma

/ : (%, %) -> %

from Group

1 : () -> %

from MagmaWithUnit

< : (%, %) -> Boolean

from PartialOrder

<= : (%, %) -> Boolean

from PartialOrder

= : (%, %) -> Boolean

from BasicType

> : (%, %) -> Boolean

from PartialOrder

>= : (%, %) -> Boolean

from PartialOrder

^ : (%, Integer) -> %

from Group

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

commutator : (%, %) -> %

from Group

conjugate : (%, %) -> %

from Group

convert : % -> SExpression

from ConvertibleTo(SExpression)

exponent : % -> Integer

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

generator : () -> %

generator() returns the generator.

generators : () -> List(%)

from FinitelyGenerated

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

~= : (%, %) -> Boolean

from BasicType

FinitelyGenerated

Monoid

SemiGroup

CommutativeStar

TwoSidedRecip

BasicType

unitsKnown

CoercibleTo(OutputForm)

OrderedSet

Group

Magma

SetCategory

Comparable

Hashable

OrderedMonoid

PartialOrder

OrderedSemiGroup

MagmaWithUnit

ConvertibleTo(SExpression)