MoebiusTransform(F)

moebius.spad line 1 [edit on github]

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

* : (%, %) -> %
from Magma
/ : (%, %) -> %
from Group
1 : () -> %
from MagmaWithUnit
= : (%, %) -> Boolean
from BasicType
^ : (%, Integer) -> %
from Group
^ : (%, NonNegativeInteger) -> %
from MagmaWithUnit
^ : (%, PositiveInteger) -> %
from Magma
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).

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

recip : % -> %

recip(m) = recip() * m

recip : % -> Union(%, "failed")
from MagmaWithUnit
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.

~= : (%, %) -> Boolean
from BasicType

Group

CoercibleTo(OutputForm)

SetCategory

unitsKnown

Monoid

MagmaWithUnit

TwoSidedRecip

SemiGroup

Magma

BasicType