What is the easiest way to draw fundamental domains for congruence subgroups of $SL_2(\mathbb{Z})$ in sage?


An easy way is to use FareySymbol. You can for example define the congruence subgroup $\Gamma_1(5)$ like this:

G = Gamma1(5)

Then use this to plot a fundamental domain:


This yields the following image:

enter image description here

  • $\begingroup$ This helps a lot thank you! Is there a way to get a result what is symmetric in the y-axis? $\endgroup$ – user360730 Aug 23 '16 at 8:42
  • $\begingroup$ @mathmarseille There might be, but I don't know how to! The only options I could find were "fill", "linestyle", "color", "show_pairing", "tesselation", "color_even", "thickness" and "ymax". $\endgroup$ – Pjotr5 Aug 23 '16 at 15:56

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