ddg.geometry.lie_models module

Lie geometry module.

class ddg.geometry.lie_models.ProjectiveModel(dimension)[source]

Bases: CayleyKleinGeometry

Lie geometry.

Model space

The model space is the quadric with matrix diag([1,...,1, -1, -1]) in RP^{n+2}.

Points in this quadric correspond to oriented hyperspheres and hyperplanes in R^n.

Parameters:
dimensionint
Attributes:
dimensionint
property absolute

The absolute quadric with matrix diag([1,...,1, -1, -1]).

Returns:
Quadric
property ambient_dimension
cayley_klein_distance(v, w)

Alias for self.absolute.cayley_klein_distance.

cayley_klein_sphere(center, radius, subspace=None, atol=None, rtol=None)

Create a Cayley-Klein sphere.

Parameters:
centerPoint or numpy.ndarray of shape (n+1,)
radiusfloat

Cayley-Klein radius

subspaceSubspace or list of numpy.ndarray of shape (k,) (default=None)
Returns:
CayleyKleinSphere
generalized_cayley_klein_sphere(center, radius, subspace=None, atol=None, rtol=None)

Create a generalized Cayley-Klein sphere.

Parameters:
centerPoint or numpy.ndarray of shape (n+1,)
radiusfloat

Generalized radius

subspaceSubspace or list of numpy.ndarray of shape (k,) (default=None)
Returns:
GeneralizedCayleyKleinSphere
inner_product(v, w)

Alias for self.absolute.inner_product.