# MoebiusTransform FΒΆ

MoebiusTransform(F) is the domain of fractional linear (Moebius) transformations over F.

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

/: (%, %) -> %

from Group

=: (%, %) -> Boolean

from BasicType

^: (%, Integer) -> %

from Group

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm
commutator: (%, %) -> %

from Group

conjugate: (%, %) -> %

from Group

eval: (%, F) -> F

eval(m, x) returns (a*x + b)/(c*x + d) where m = moebius(a, b, c, d) (see moebius).

eval: (%, OnePointCompletion F) -> OnePointCompletion F

eval(m, x) returns (a*x + b)/(c*x + d) where m = moebius(a, b, c, d) (see moebius).

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

moebius: (F, F, F, F) -> %

moebius(a, b, c, d) returns matrix [[a, b], [c, d]].

one?: % -> Boolean

from MagmaWithUnit

recip: % -> %

recip(m) = recip() * m

recip: % -> Union(%, failed)

from MagmaWithUnit

recip: () -> %

recip() returns matrix [[0, 1], [1, 0]] representing the map x -> 1 / x.

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from MagmaWithUnit

scale: (%, F) -> %

scale(m, h) returns scale(h) * m (see shift).

scale: F -> %

scale(k) returns matrix [[k, 0], [0, 1]] representing the map x -> k * x.

shift: (%, F) -> %

shift(m, h) returns shift(h) * m (see shift).

shift: F -> %

shift(k) returns matrix [[1, k], [0, 1]] representing the map x -> x + k.

BasicType

Group

Magma

MagmaWithUnit

Monoid

SemiGroup

SetCategory

TwoSidedRecip

unitsKnown