Types in Nemo

Nemo is fully compatible with AbstractAlgebra.jl, but specialises implementations of various commonly used rings with a highly optimised C implementation, provided by the C libraries wrapped by Nemo.

Below, we give a list of all of the specialised types available in Nemo that implement rings using a specialised C library. The types of elements of the respective rings and other mathematical structures are given, and in parentheses we list the types of the parent objects of the given rings and structures.

  • Flint

    • fmpz (FlintIntegerRing)
    • fmpq (FlintRationalField)
    • nmod (NmodRing)
    • fmpz_mod (FmpzModRing`)
    • fq_nmod (FqNmodFiniteField)
    • gfp_elem (GaloisField)
    • gfp_fmpz_elem (GaloisFmpzField)
    • fq (FqFiniteField)
    • padic (FlintPadicField)
    • qadic (FlintQadicField)
    • fmpz_poly (FmpzPolyRing)
    • fmpq_poly (FmpqPolyRing)
    • nmod_poly (NmodPolyRing)
    • fmpz_mod_poly (FmpzModPolyRing)
    • fq_poly (FqPolyRing)
    • fq_nmod_poly (FqNmodPolyRing)
    • fmpz_mpoly (FmpzMPolyRing)
    • fmpq_mpoly (FmpqMPolyRing)
    • nmod_mpoly (NmodMPolyRing)
    • fq_nmod_mpoly (FqNmodMPolyRing`)
    • gfp_poly (GFPPolyRing)
    • gfp_fmpz_poly (GFPFmpzPolyRing)
    • fmpz_rel_series (FmpzRelSeriesRing)
    • fmpz_abs_series (FmpzAbsSeriesRing)
    • fmpq_rel_series (FmpqRelSeriesRing)
    • fmpq_abs_series (FmpqAbsSeriesRing)
    • fmpz_mod_rel_series (FmpzModRelSeriesRing)
    • fmpz_mod_abs_series (FmpzModAbsSeriesRing)
    • nmod_rel_series (NmodRelSeriesRing)
    • nmod_abs_series (NmodAbsSeriesRing)
    • gfp_rel_series (GFPRelSeriesRing)
    • gfp_abs_series (GFPAbsSeriesRing)
    • gfp_fmpz_rel_series (GFPFmpzRelSeriesRing)
    • gfp_fmpz_abs_series (GFPFmpzAbsSeriesRing)
    • fq_nmod_rel_series (FqNmodRelSeriesRing)
    • fq_nmod_abs_series (FqNmodAbsSeriesRing)
    • fq_rel_series (FqRelSeriesRing)
    • fq_abs_series (FqAbsSeriesRing)
    • fmpz_mat (FmpzMatSpace)
    • fmpq_mat (FmpqMatSpace)
    • nmod_mat (NmodMatSpace)
    • fmpz_mod_mat (FmpzModMatSpace`)
    • fq_nmod_mat (FqNmodMatSpace)
    • fq_mat (FqMatSpace)
    • gfp_mat (GFPMatSpace)
    • perm (SymmetricGroup)
  • Antic

    • nf_elem (AnticNumberField)
  • Arb

    • arb (ArbField)
    • acb (AcbField)
    • arb_poly (ArbPolyRing)
    • acb_poly (AcbPolyRing)
    • arb_mat (ArbMatSpace)
    • acb_mat (AcbMatSpace)
  • Calcium

    • qqbar (CalciumQQBarField)
    • ca (CalciumField)