g * z : GrpPSL2Elt, [SpcHypElt] -> [SpcHypElt]
g * z : GrpPSL2Elt, SetCspElt -> SetCspElt
g * z : RngIntElt, SpcHypElt -> SpcHypElt
g * z : RngIntElt, [SpcHypElt] -> [SpcHypElt]
g * z : RngIntElt, SetCspElt -> SetCspElt
For z of type SpcHypElt, SetCspElt or [SpcHypElt],
and when g is an element of a projective linear group,
returns the image of z under the action of g. The type of
the image is the same as the type of z. If g is a
positive integer, returns
return az, which his is equivalent to acting on z with
the matrix pmatrix(a & 0
0 & 1)∈PGL2(R).
Returns a sequence of points in H fixed by the action of g.
If points a, b in the upper half plane are equivalent under the action
of the group G, returns true, and the matrix g in G such that g.a = b.
Otherwise returns false and the identity.
For the point x in the upper half plane, returns a point z in the
region with -1/2 < z ≤1/2 and |z| ≥1, and a matrix g in PSL2(Z)
with g*x = z
Returns a generator of the subgroup of G stabilizing a.
If g is an element of PSL2(Z) which is an involution,
this returns the end points in the real line of the arc
fixed by g, with mid point of the arc also fixed by g.
Note that for any point b, the arc from b to g.b is fixed
by g.
z + a : SpcHypElt, FldRatElt -> SpcHypElt
z - a : SpcHypElt, RngIntElt -> SpcHypElt
z - a : SpcHypElt, FldRatElt -> SpcHypElt
For any integer a, and element z in the upper half plane,
this returns the element z + a in the same copy of the upper half plane.
z * a : SpcHypElt, RngElt -> SpcHypElt
a * z : RngIntElt, SetCspElt -> SetCspElt
a * z : FldRatElt, SetCspElt -> SetCspElt
a * seq : RngElt, [SpcHypElt] -> [SpcHypElt]
a * z : RngIntElt, [SetCspElt] -> [SetCspElt]
a * z : FldRatElt, [SetCspElt] -> [SetCspElt]
z * a : SpcHypElt, RngIntElt -> SpcHypElt
z * a : SpcHypElt, RngIntElt -> SpcHypElt
z * a : SpcHypElt, RngIntElt -> SpcHypElt
z * a : SpcHypElt, RngIntElt -> SpcHypElt
z * a : SpcHypElt, RngIntElt -> SpcHypElt
z / a : SpcHypElt, RngIntElt -> SpcHypElt
Given an element z (or a sequence of elements) in the upper half plane,
and a positive rational number a, this returns the product
(or products) in the same copy of the upper half plane.
Precision: RngIntElt Default:
Returns the hyperbolic distance between z and w.
Precision: RngIntElt Default:
Returns the angle of the tangent at x of the geodescic from x to y,
with given precision.
Precision: RngIntElt Default:
Given two sequences e1 = [z1, z2] and e2 = [z1, z3], where
z1, z2, z3 are elements of the upper half plane, this returns
the angle between the geodesics at z1.
Given elements z1, z2 in the upper half plane H, this extends the
geodesic between z1 and z2 to a semicircle with endpoints on the real
line, and returns the two real endpoints as elements of H.
GeodesicsIntersection(x1,x2) : [SetCspElt], [SetCspElt]) -> SeqEnum
The intersection in the upper half plane of the two geodesics
whose endpoints are given by the sequences x1 and x2.
If the geodesics intersect along a line, the empty sequence is returned.
V2.28, 13 July 2023