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Arithmetic Subgroups of \({\rm SL}_2({\bf Z})\)¶

This chapter describes the basic functionality for finite index subgroups of the modular group \({\rm SL}_2(\ZZ)\).

  • Arithmetic subgroups (finite index subgroups of \({\rm SL}_2(\ZZ)\))
    • ArithmeticSubgroup
    • is_ArithmeticSubgroup()
  • Arithmetic subgroups defined by permutations of cosets
    • ArithmeticSubgroup_Permutation()
    • ArithmeticSubgroup_Permutation_class
    • EvenArithmeticSubgroup_Permutation
    • HsuExample10()
    • HsuExample18()
    • OddArithmeticSubgroup_Permutation
    • eval_sl2z_word()
    • sl2z_word_problem()
    • word_of_perms()
  • Elements of Arithmetic Subgroups
    • ArithmeticSubgroupElement
  • Congruence arithmetic subgroups of \({\rm SL}_2(\ZZ)\)
    • CongruenceSubgroup
    • CongruenceSubgroupBase
    • CongruenceSubgroupFromGroup
    • CongruenceSubgroup_constructor()
    • is_CongruenceSubgroup()
  • Congruence Subgroup \(\Gamma_H(N)\)
    • GammaH_class
    • GammaH_constructor()
    • is_GammaH()
    • mumu()
  • Congruence Subgroup \(\Gamma_1(N)\)
    • Gamma1_class
    • Gamma1_constructor()
    • is_Gamma1()
  • Congruence Subgroup \(\Gamma_0(N)\)
    • Gamma0_class
    • Gamma0_constructor()
    • is_Gamma0()
  • Congruence Subgroup \(\Gamma(N)\)
    • Gamma_class
    • Gamma_constructor()
    • is_Gamma()
  • The modular group \({\rm SL}_2(\ZZ)\)
    • SL2Z_class
    • is_SL2Z()
  • Farey Symbol for arithmetic subgroups of \({\rm PSL}_2(\ZZ)\)
    • Farey
  • Cython helper functions for congruence subgroups
    • degeneracy_coset_representatives_gamma0()
    • degeneracy_coset_representatives_gamma1()
    • generators_helper()

Indices and Tables¶

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