InfiniteCyclicGroup gΒΆ

discrgrp.spad line 146

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
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 SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
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

CoercibleTo OutputForm

CommutativeStar

Comparable

ConvertibleTo SExpression

FinitelyGenerated

Group

Magma

MagmaWithUnit

Monoid

OrderedMonoid

OrderedSemiGroup

OrderedSet

PartialOrder

SemiGroup

SetCategory

unitsKnown