What is the easiest way to draw fundamental domains for congruence subgroups of $SL_2(\mathbb{Z})$ in sage?
1 Answer
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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:
FareySymbol(G).fundamental_domain()
This yields the following image:
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$\begingroup$ This helps a lot thank you! Is there a way to get a result what is symmetric in the y-axis? $\endgroup$– user360730Aug 23, 2016 at 8:42
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$\begingroup$ @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". $\endgroup$– Pjotr5Aug 23, 2016 at 15:56