From b9b20293df80d84c5f6846abb56d3ff33b3e8094 Mon Sep 17 00:00:00 2001 From: aodesky Date: Mon, 18 Nov 2019 15:15:45 -0500 Subject: [PATCH] Updated doc to include an example with the embedding specified for splitting the Galois orbits of critical points. --- .../dynamics/arithmetic_dynamics/projective_ds.py | 12 ++++++++---- 1 file changed, 8 insertions(+), 4 deletions(-) diff --git a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py index 694500df683..55e3f5d27ce 100644 --- a/src/sage/dynamics/arithmetic_dynamics/projective_ds.py +++ b/src/sage/dynamics/arithmetic_dynamics/projective_ds.py @@ -3087,14 +3087,17 @@ def critical_points(self, R=None): def ramification_type(self,R=None): r""" - Return the ramification type of a self-map of the - projective line. Only branch points defined over ``R`` + Return the ramification type of endomorphisms of + `\mathbb{P}^1`. Only branch points defined over ``R`` contribute to the ramification type if specified, otherwise ``R`` is the ring of definition for self. + Note that branch points defined over ``R`` may not + be geometric points. + INPUT: - - ``R`` -- (optional) + - ``R`` -- ring or morphism (optional) OUTPUT: @@ -3125,7 +3128,8 @@ def ramification_type(self,R=None): sage: F = DynamicalSystem_projective([x^3-2*x*y^2 + 2*y^3, y^3]) sage: F.ramification_type() [[2], [3]] - sage: F.ramification_type(F.field_of_definition_critical()) + sage: L,phi = F.field_of_definition_critical(return_embedding=True) + sage: F.ramification_type(phi) [[2], [2], [3]] """