Group

catdef.spad line 760 [edit on github]

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

* : (%, %) -> %

from Magma

/ : (%, %) -> %

x/y is the same as x times the inverse of y.

1 : () -> %

from MagmaWithUnit

= : (%, %) -> Boolean

from BasicType

^ : (%, Integer) -> %

x^n returns x raised to the integer power n.

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

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'.

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

~= : (%, %) -> Boolean

from BasicType

BasicType

CoercibleTo(OutputForm)

MagmaWithUnit

SemiGroup

TwoSidedRecip

unitsKnown

Magma

Monoid

SetCategory