Arithmetic Subgroups of \(\SL_2(\ZZ)\)

This chapter describes the basic functionality for finite index subgroups of the modular group \(\SL_2(\ZZ)\).

• Arithmetic subgroups (finite index subgroups of \(\SL_2(\ZZ)\))
  • 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 \(\SL_2(\ZZ)\)
  • 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 \(\SL_2(\ZZ)\)
  • SL2Z_class
  • is_SL2Z()
• Farey Symbol for arithmetic subgroups of \(\PSL_2(\ZZ)\)
  • Farey
• Cython helper functions for congruence subgroups
  • degeneracy_coset_representatives_gamma0()
  • degeneracy_coset_representatives_gamma1()
  • generators_helper()

Indices and Tables

• Index

• Module Index

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