DihedralGroup(n, a, b)

discrgrp.spad line 201 [edit on github]

• n : PositiveInteger
• a : Symbol
• b : Symbol

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

* : (%, %) -> %

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)

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 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

TwoSidedRecip

FiniteGroup

BasicType

unitsKnown

Magma

CoercibleTo(OutputForm)

Group

SetCategory

Comparable

Hashable

MagmaWithUnit

Monoid

ConvertibleTo(InputForm)