Group

catdef.spad line 754 [edit on github]

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

TwoSidedRecip

unitsKnown