MoebiusTransform FΒΆ

moebius.spad line 1

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
from CoercibleTo 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

CoercibleTo OutputForm

Group

Magma

MagmaWithUnit

Monoid

SemiGroup

SetCategory

unitsKnown