ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 13 Jul 2017 23:22:32 +0200Plotting geodesics in $SL_2(\mathbb{Z})\backslash\mathbb{H}$https://ask.sagemath.org/question/38178/plotting-geodesics-in-sl_2mathbbzbackslashmathbbh/In [here](http://doc.sagemath.org/html/en/reference/hyperbolic_geometry/sage/geometry/hyperbolic_space/hyperbolic_geodesic.html) there are functions that allow to plot geodesics in the upper half plane (namely, half circles perpendicular to the x axis and vertical lines). Are there similar functions that do the same thing but only in the fundamental domain of $SL_2(\mathbb{Z})$, so that the geodesic is folded up into the domain $|x|<\frac{1}{2}$ and $x^2+y^2>1$?
What I would like to have is something like the picture in page 5 of [this paper](https://arxiv.org/pdf/1109.0413.pdf).
Wed, 05 Jul 2017 07:23:22 +0200https://ask.sagemath.org/question/38178/plotting-geodesics-in-sl_2mathbbzbackslashmathbbh/Comment by vdelecroix for <p>In <a href="http://doc.sagemath.org/html/en/reference/hyperbolic_geometry/sage/geometry/hyperbolic_space/hyperbolic_geodesic.html">here</a> there are functions that allow to plot geodesics in the upper half plane (namely, half circles perpendicular to the x axis and vertical lines). Are there similar functions that do the same thing but only in the fundamental domain of $SL_2(\mathbb{Z})$, so that the geodesic is folded up into the domain $|x|<\frac{1}{2}$ and $x^2+y^2>1$?</p>
<p>What I would like to have is something like the picture in page 5 of <a href="https://arxiv.org/pdf/1109.0413.pdf">this paper</a>.</p>
https://ask.sagemath.org/question/38178/plotting-geodesics-in-sl_2mathbbzbackslashmathbbh/?comment=38238#post-id-38238There is no straightforward function to do it. However a simple algorithm is not hard to implement. You just need to look at the next intersection with the boundary, and apply the appropriate isometry... though the intersection feature is broken: see [#23427](https://trac.sagemath.org/ticket/23427).Thu, 13 Jul 2017 23:22:32 +0200https://ask.sagemath.org/question/38178/plotting-geodesics-in-sl_2mathbbzbackslashmathbbh/?comment=38238#post-id-38238