DihedralGroup(n, a, b)ΒΆ

discrgrp.spad line 201

DihedralGroup(n, a, b) is the dihedral group generated by a rotation a of order n and a reflection b.

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
enumerate: () -> List %
from Finite
expa: % -> IntegerMod n
expa(x) returns the exponent of the rotation a in the normal form of x
expb: % -> IntegerMod 2
expa(x) returns the exponent of the reflection b in the normal form of x
exponenta: % -> Integer
exponenta(x) returns the exponent of the rotation a in the normal form of x as integer
exponentb: % -> Integer
exponentb(x) returns the exponent of the reflection b in the normal form of x as integer
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

Comparable

ConvertibleTo InputForm

Finite

FiniteGroup

FinitelyGenerated

Group

Magma

MagmaWithUnit

Monoid

SemiGroup

SetCategory

unitsKnown