Hello Jeroen,
> Is there any way in Sage to compute with the action of SL(2,Z) (or
> similar groups) on the upper half plane? The group SL2Z exists in Sage,
> but I couldn't find how to make it act on stuff with the rule
> g(x) = (a*x + b)/(c*x + d).
#9439: hyperbolic spaces (I opened it a long time ago and it ended up
going nowhere)
For Hecke groups that generalizes SL(2,Z) the action is somehow not a
proper action but is indeed implemented in the elements (#16883,
#16936, #16976).
> Another obvious question is how to reduce elements to the usual
> fundamental domain.
Not sure what you meant. But for fundamental domains, the best way to
obtain them is not very handy (see #11709 and a long list that follow)
{{{
sage: G = Gamma1(3)
sage: F = FareySymbol(G)
sage: F.fundamental_domain() # beautiful picture
}}}
and you can play with F to obtain further informations.
Vincent
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