  
  [1X1 [33X[0;0YIntroduction[133X[101X
  
  
  [1X1.1 [33X[0;0YGeneral aims of the [5XModularGroup[105X[101X[1X package[133X[101X
  
  [33X[0;0YThis  [5XGAP[105X package provides methods for computing with finite-index subgroups
  of  the  modular  groups  [22XSL_2(ℤ)[122X  and  [22XPSL_2(ℤ)[122X.  This includes, but is not
  limited  to,  computation of the generalized level, index or cusp widths. It
  also  implements algorithms described in [Hsu96] and [HL14] for testing if a
  given  group  is a congruence subgroup. Hence it differs from the Congruence
  ([7Xhttps://gap-packages.github.io/congruence/[107X)  package [DJKV18], which can be
  used  -  among other things - to construct canonical congruence subgroups of
  [22XSL_2(ℤ)[122X.[133X
  
  
  [1X1.2 [33X[0;0YTechnicalities[133X[101X
  
  [33X[0;0YA  convenient  way  to  represent  finite-index  subgroups  of [22XSL_2(ℤ)[122X is by
  specifying  the  action of generator matrices of [22XSL_2(ℤ)[122X on the right cosets
  by right multiplication. For example, one could choose the generators[133X
  
                   [ 0 -1 ]            [ 1  1 ]
               S = [ 1  0 ],       T = [ 0  1 ]
  
  [33X[0;0Yand  represent  a  subgroup  as a tuple of transitive permutations [22X(σ_S,σ_T)[122X
  describing  the  action  of  [22XS[122X  and  [22XT[122X. This is exactly the way this package
  internally  treats  such subgroups. We use the convention that [22X1[122X corresponds
  to  the  coset  of the identity matrix. Note that such a representation as a
  tuple  of  permutations is only unique up to relabelling of the cosets, i.e.
  up  to  simultaneous  conjugation (fixing the [22X1[122X coset by our convention). To
  not  restrict  [5XModularGroup[105X to right multiplication on right cosets, getters
  and  setters  are  defined  in  two versions: one by right multiplication on
  right  cosets  ("[10XViaRightAction[110X")  and  one  by  left multiplication on left
  cosets ("[10XViaLeftAction[110X").[133X
  
