CyclicGroup(n, g)

discrgrp.spad line 71 [edit on github]

A domain for finite cyclic groups.

* : (%, %) -> %
from Magma
/ : (%, %) -> %
from Group
1 : () -> %
from MagmaWithUnit
= : (%, %) -> Boolean
from BasicType
^ : (%, Integer) -> %
from Group
^ : (%, NonNegativeInteger) -> %
from MagmaWithUnit
^ : (%, PositiveInteger) -> %
from Magma
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 Hashable
hashUpdate! : (HashState, %) -> HashState
from Hashable
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
~= : (%, %) -> Boolean
from BasicType

FinitelyGenerated

Finite

SemiGroup

CommutativeStar

TwoSidedRecip

MagmaWithUnit

FiniteGroup

BasicType

unitsKnown

Magma

CoercibleTo(OutputForm)

Group

SetCategory

Comparable

Hashable

ConvertibleTo(SExpression)

Monoid

ConvertibleTo(InputForm)