Automorphism R

ore.spad line 291 [edit on github]

• R: Ring

Automorphism R is the multiplicative group of automorphisms of R.

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

/: (%, %) -> %

from Group

=: (%, %) -> Boolean

from BasicType

^: (%, Integer) -> %

from Group

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

commutator: (%, %) -> %

from Group

conjugate: (%, %) -> %

from Group

elt: (%, R) -> R

from Eltable(R, R)

inv: % -> %

from Group

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

morphism: ((R, Integer) -> R) -> %

morphism(f) returns the morphism given by f^n(x) = f(x, n).

morphism: (R -> R) -> %

morphism(f) returns the non-invertible morphism given by f.

morphism: (R -> R, R -> R) -> %

morphism(f, g) returns the invertible morphism given by f, where g is the inverse of f..

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

Eltable(R, R)

Group

Magma

MagmaWithUnit

Monoid

SemiGroup

SetCategory

TwoSidedRecip

unitsKnown