Add FieldClass.quadratic_non_residues

galois/_fields/_main.py

@@ -698,6 +698,35 @@ def quadratic_residues(cls) -> "FieldArray":
  is_quadratic_residue = x.is_quadratic_residue()
  return x[is_quadratic_residue]
 
+ @property
+ def quadratic_non_residues(cls) -> "FieldArray":
+ r"""
+ galois.FieldArray: All quadratic non-residues in the Galois field.
+
+ An element :math:`x` in :math:`\mathrm{GF}(p^m)` is a *quadratic non-residue* if there does not exist a :math:`y` such that
+ :math:`y^2 = x` in the field.
+
+ In fields with characteristic 2, no elements are quadratic non-residues. In fields with characteristic greater than 2,
+ exactly half of the nonzero elements are quadratic non-residues.
+
+ See also :func:`FieldArray.is_quadratic_residue`.
+
+ Examples
+ --------
+ .. ipython:: python
+
+ GF = galois.GF(11)
+ GF.quadratic_non_residues
+
+ .. ipython:: python
+
+ GF = galois.GF(2**4)
+ GF.quadratic_non_residues
+ """
+ x = cls.Elements()
+ is_quadratic_residue = x.is_quadratic_residue()
+ return x[~is_quadratic_residue]
+
  @property
  def is_prime_field(cls) -> bool:
  """