The dual_pairs package

The SageMath package dual_pairs implements computations with finite locally free group schemes and Galois representations in the form of dual pairs of algebras. See the preprint Dual pairs of algebras and finite commutative group schemes for details.

Author

Peter Bruin <P.J.Bruin@math.leidenuniv.nl>

Installation

The package can be installed using

$ sage --pip install dual_pairs

Source code

The source code is available at <https://gitlab.com/pbruin/dual-pairs>.

Documentation of the modules

The documentation pages in the table below are automatically generated from the source code.

Dual pairs of algebras

• Dual pairs of algebras
  • DualPairFactory
  • DualPair_class
• Constructing a dual pair of algebras from a dihedral field
  • dual_pair_from_dihedral_field()
• Constructing a dual pair of algebras from a table
  • algebra_and_points_from_action()
  • dual_pair_from_table()
• Importing a dual pair of algebras from a file
  • dual_pair_import()
• Dual pairs of algebras over the rationals
  • DualPair_rational
  • lift_to_prime()

Finite flat algebras

• Finite flat algebras
  • FiniteFlatAlgebraFactory
  • FiniteFlatAlgebra_base
  • FiniteFlatAlgebra_generic
  • FiniteFlatAlgebra_monogenic
  • FiniteFlatAlgebra_product
• Elements of finite flat algebras
  • FiniteFlatAlgebraElement
  • FiniteFlatAlgebraElement_generic
  • FiniteFlatAlgebraElement_monogenic
  • FiniteFlatAlgebraElement_product
• Modules over finite flat algebras
  • FiniteFlatAlgebraModule
  • FiniteFlatAlgebraModuleElement
• Class groups of finite flat algebras
  • class_group()
• Unit groups of finite flat algebras
  • roots_of_unity()
  • unit_group()
• Selmer groups of finite flat algebras
  • selmer_group()

Torsors and extension groups

• Extension class groups
  • ExtGroup
  • ExtGroupElement
  • ExtGroupGm()
  • ExtGroup_mu_n()
• Torsor class groups
  • Torsor
  • TorsorClassGroup
• Torsor modules
  • TorsorPair
• Sheaves of Abelian groups
  • AbelianSheaf
  • MultiplicativeGroup
  • RootsOfUnity
• Simplicial sheaves
  • SimplicialSheaf

Miscellaneous

• Homomorphisms of finitely generated Abelian groups
  • AbelianGroupHomomorphism
  • homology()
  • solve_mod()
  • solve_mod_right()
• Example: easy extensions
  • extension()
• Utility functions for finite Abelian groups
  • find_group_structure()
  • find_group_structure_old()
  • find_perm()
  • mod1()
  • standard_group_structure()
• Utility functions for p-adic polynomials
  • integral_basis_generator()
  • kummer_dedekind()
  • lift_root()
  • padic_aut()
  • padic_roots()
  • reduce_element()
  • reduce_poly()
  • rootpadic()
  • roots_mod_m()
• Smith normal form for Abelian groups

Indices and tables

• Index

• Module Index

• Search Page