GroupΒΆ

catdef.spad line 754

The class of multiplicative groups, i.e. monoids with multiplicative inverses.

1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
/: (%, %) -> %
x/y is the same as x times the inverse of y.
=: (%, %) -> Boolean
from BasicType
^: (%, Integer) -> %
x^n returns x raised to the integer power n.
^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
coerce: % -> OutputForm
from CoercibleTo OutputForm
commutator: (%, %) -> %
commutator(p, q) computes inv(p) * inv(q) * p * q.
conjugate: (%, %) -> %
conjugate(p, q) computes inv(q) * p * q; this is ‘right action by conjugation’.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
inv: % -> %
inv(x) returns the inverse of x.
latex: % -> String
from SetCategory
leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
leftPower: (%, PositiveInteger) -> %
from Magma
leftRecip: % -> Union(%, failed)
from MagmaWithUnit
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

BasicType

CoercibleTo OutputForm

Magma

MagmaWithUnit

Monoid

SemiGroup

SetCategory

unitsKnown