spheres.relativity.mobius¶
-
spheres.relativity.
mobius
(abcd)[source]¶ Given parameters \(\begin{pmatrix} a & b \\ b & c \end{pmatrix}\), arranged in a 2x2 matrix, returns a function which implements the corresponding Möbius transformation
\[f(z) = \frac{az+b}{cz+d}\]which acts on the extended complex plane. Note that if \(c \neq 0\), we have:
\[ \begin{align}\begin{aligned}f(-\frac{d}{c}) = \infty\\f(\infty) = \frac{a}{c}\end{aligned}\end{align} \]And if \(c = 0\), we have:
\[f(\infty) = \infty\]- Parameters
abcd (np.ndarray or qt.Qobj) – 2x2 matrix representing Möbius parameters.
- Returns
mobius – A function which takes an extended complex coordinate as input, and returns an extended complex coordinate as output.
- Return type
func
- Raises
Exception – If \(ad = bc\), then \(f(z) = \frac{a}{c}\), a constant function, which doesn’t qualify as a Möbius transformation.