chamanara

Chamanara’s surfaces which depend on a parameter \(\alpha\) less than one.

REFERENCES:

• Defined as \(X_\alpha\) in Chamanara, Reza, “Affine automorphism groups of surfaces of infinite type”, City University of New York, 2002.

EXAMPLES:

sage: from flatsurf import translation_surfaces
sage: s = translation_surfaces.chamanara(1/2)
sage: s.plot()
...Graphics object consisting of 129 graphics primitives

flatsurf.geometry.chamanara.ChamanaraPolygon(alpha)

class flatsurf.geometry.chamanara.ChamanaraSurface(alpha)

The Chamanara surface $X_{alpha}$.

EXAMPLES:

sage: from flatsurf.geometry.chamanara import ChamanaraSurface
sage: S = ChamanaraSurface(1/2); S
Chamanara surface with parameter 1/2

graphical_surface(**kwds)

is_cone_surface()

Return whether this surface is a cone surfaces, overrides flatsurf.geometry.categories.similarity_surfaces.SimilaritySurfaces.ParentMethods.is_cone_surface().

EXAMPLES:

sage: from flatsurf.geometry.chamanara import ChamanaraSurface
sage: S = ChamanaraSurface(1/2)
sage: S.is_cone_surface()
False

is_dilation_surface(positive=False)

Return whether this surface is a dilation surface, overrides flatsurf.geometry.categories.similarity_surfaces.SimilaritySurfaces.ParentMethods.is_dilation_surface().

EXAMPLES:

sage: from flatsurf.geometry.chamanara import ChamanaraSurface
sage: S = ChamanaraSurface(1/2)
sage: S.is_dilation_surface(positive=True)
False
sage: S.is_dilation_surface(positive=False)
True

is_mutable()

Return whether this surface is mutable which it is not.

EXAMPLES:

sage: from flatsurf.geometry.chamanara import ChamanaraSurface
sage: S = ChamanaraSurface(1/2)
sage: S.is_mutable()
False

is_translation_surface(positive=True)

Return whether this surfaces is a (half-)translation surface, overrides flatsurf.geometry.categories.similarity_surfaces.SimilaritySurfaces.ParentMethods.is_translation_surface().

EXAMPLES:

sage: from flatsurf.geometry.chamanara import ChamanaraSurface
sage: S = ChamanaraSurface(1/2)
sage: S.is_translation_surface(positive=True)
False
sage: S.is_translation_surface(positive=False)
False

labels()

Return the labels used to identify the polygons that make up this surface, i.e., the integers.

This overrides flatsurf.geometry.categories.polygonal_surfaces.PolygonalSurfaces.ParentMethods.labels()

EXAMPLES:

sage: from flatsurf.geometry.chamanara import ChamanaraSurface
sage: S = ChamanaraSurface(1/2)
sage: S.labels()
(0, 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, …)

opposite_edge(p, e)

polygon(lab)

EXAMPLES:

sage: from flatsurf import translation_surfaces
sage: C = translation_surfaces.chamanara(1/2)
sage: C.polygon(0)
Polygon(vertices=[(0, 0), (1, 0), (-1, 2), (-1, 1)])

roots()

Return a label in each connected component of this surface.

This overrides flatsurf.geometry.categories.polygonal_surfaces.PolygonalSurfaces.ParentMethods.roots().

EXAMPLES:

sage: from flatsurf.geometry.chamanara import ChamanaraSurface
sage: S = ChamanaraSurface(1/2)
sage: S.roots()
(0,)

class flatsurf.geometry.chamanara.ChamanaraTranslationSurface(alpha)

graphical_surface(**kwds)

flatsurf.geometry.chamanara.chamanara_half_dilation_surface(alpha, n=None)

Return Chamanara’s surface thought of as a Half Dilation surface.

EXAMPLES:

sage: from flatsurf.geometry.chamanara import chamanara_half_dilation_surface
sage: s = chamanara_half_dilation_surface(1/2)
sage: TestSuite(s).run()

flatsurf.geometry.chamanara.chamanara_surface(alpha, n=None)

Return Chamanara’s surface thought of as a translation surface.

EXAMPLES:

sage: from flatsurf.geometry.chamanara import chamanara_surface
sage: s = chamanara_surface(1/2)
sage: TestSuite(s).run()