Finite Rings

Finite Rings

• Ring \(\ZZ/n\ZZ\) of integers modulo \(n\)
  • IntegerModFactory
  • IntegerModRing_generic
  • crt()
  • is_IntegerModRing()
• Elements of \(\ZZ/n\ZZ\)
  • Int_to_IntegerMod
  • IntegerMod()
  • IntegerMod_abstract
  • IntegerMod_gmp
  • IntegerMod_hom
  • IntegerMod_int
  • IntegerMod_int64
  • IntegerMod_to_Integer
  • IntegerMod_to_IntegerMod
  • Integer_to_IntegerMod
  • Mod()
  • NativeIntStruct
  • is_IntegerMod()
  • lucas()
  • lucas_q1()
  • makeNativeIntStruct
  • mod()
  • square_root_mod_prime()
  • square_root_mod_prime_power()

Finite Fields

• Finite fields
  • FiniteFieldFactory
  • is_PrimeFiniteField()
• Base class for finite fields
  • FiniteField
  • is_FiniteField()
  • unpickle_FiniteField_ext()
  • unpickle_FiniteField_prm()
• Base class for finite field elements
  • Cache_base
  • FinitePolyExtElement
  • FiniteRingElement
  • is_FiniteFieldElement()
• Homset for finite fields
  • FiniteFieldHomset
• Finite field morphisms
  • FiniteFieldHomomorphism_generic
  • FrobeniusEndomorphism_finite_field
  • SectionFiniteFieldHomomorphism_generic

Prime Fields

• Finite prime fields
  • FiniteField_prime_modn
• Finite field morphisms for prime fields
  • FiniteFieldHomomorphism_prime
  • FrobeniusEndomorphism_prime
  • SectionFiniteFieldHomomorphism_prime

Finite Fields Using Pari

• Finite fields implemented via PARI’s FFELT type
  • FiniteField_pari_ffelt
• Finite field elements implemented via PARI’s FFELT type
  • FiniteFieldElement_pari_ffelt
  • unpickle_FiniteFieldElement_pari_ffelt()

Finite Fields Using Givaro

• Givaro finite fields
  • FiniteField_givaro
• Givaro finite field elements
  • Cache_givaro
  • FiniteField_givaroElement
  • FiniteField_givaro_iterator
  • unpickle_Cache_givaro()
  • unpickle_FiniteField_givaroElement()
• Givaro finite field morphisms
  • FiniteFieldHomomorphism_givaro
  • FrobeniusEndomorphism_givaro
  • SectionFiniteFieldHomomorphism_givaro

Finite Fields of Characteristic 2 Using NTL

• Finite fields of characteristic 2
  • FiniteField_ntl_gf2e
  • late_import()
• Finite field of characteristic 2 elements
  • Cache_ntl_gf2e
  • FiniteField_ntl_gf2eElement
  • unpickleFiniteField_ntl_gf2eElement()

Miscellaneous

• Finite residue fields
  • LiftingMap
  • ReductionMap
  • ResidueFieldFactory
  • ResidueFieldHomomorphism_global
  • ResidueField_generic
  • ResidueFiniteField_givaro
  • ResidueFiniteField_ntl_gf2e
  • ResidueFiniteField_pari_ffelt
  • ResidueFiniteField_prime_modn
• Algebraic closures of finite fields
  • AlgebraicClosureFiniteField()
  • AlgebraicClosureFiniteFieldElement
  • AlgebraicClosureFiniteField_generic
  • AlgebraicClosureFiniteField_pseudo_conway
• Routines for Conway and pseudo-Conway polynomials
  • PseudoConwayLattice
  • conway_polynomial()
  • exists_conway_polynomial()

Indices and Tables

• Index

• Module Index

• Search Page