Define Poly.__index__() to support bin(), oct(), and hex()

docs/basic-usage/poly-creation.rst

@@ -10,15 +10,15 @@ Create a polynomial by specifying its coefficients in degree-descending order an
 
 .. ipython:: python
 
-  GF = galois.GF(2**8)
-  galois.Poly([1, 0, 0, 55, 23], field=GF)
+ GF = galois.GF(2**8)
+ galois.Poly([1, 0, 0, 55, 23], field=GF)
 
 Or pass a *Galois field array* of coefficients without explicitly specifying the finite field.
 
 .. ipython:: python
 
-  coeffs = GF([1, 0, 0, 55, 23]); coeffs
-  galois.Poly(coeffs)
+ coeffs = GF([1, 0, 0, 55, 23]); coeffs
+ galois.Poly(coeffs)
 
 Element representation
 ----------------------
@@ -28,18 +28,18 @@ by setting the `display` keyword argument of :func:`galois.GF` or using the :fun
 
 .. ipython:: python
 
-  GF = galois.GF(3**5)
+ GF = galois.GF(3**5)
 
-  # Display f using the default integer representation
-  f = galois.Poly([13, 0, 4, 2], field=GF); f
+ # Display f using the default integer representation
+ f = galois.Poly([13, 0, 4, 2], field=GF); f
 
-  # Display f using the polynomial representation
-  GF.display("poly"); f
+ # Display f using the polynomial representation
+ GF.display("poly"); f
 
-  # Display f using the power representation
-  GF.display("power"); f
+ # Display f using the power representation
+ GF.display("power"); f
 
-  GF.display("int");
+ GF.display("int");
 
 See :ref:`Field Element Representation` for more details.
 
@@ -56,26 +56,49 @@ Create a polynomial by specifying its non-zero degrees and coefficients using :f
 
 .. ipython:: python
 
-  galois.Poly.Degrees([8, 1], coeffs=[1, 179], field=GF)
+ galois.Poly.Degrees([8, 1], coeffs=[1, 179], field=GF)
 
-Create a polynomial from its integer representation using :func:`galois.Poly.Int`.
+Create a polynomial from its integer representation using :func:`galois.Poly.Int`. Additionally, one may create a polynomial from
+a binary, octal, or hexadecimal string of its integer representation.
 
-.. ipython:: python
+.. tab-set::
+
+ .. tab-item:: Integer
+
+ .. ipython:: python
+
+ galois.Poly.Int(268, field=GF)
+
+ .. tab-item:: Binary string
+
+ .. ipython:: python
+
+ galois.Poly.Int(int("0b1011", 2))
+
+ .. tab-item:: Octal string
+
+ .. ipython:: python
+
+ galois.Poly.Int(int("0o5034", 8), field=galois.GF(2**3))
+
+ .. tab-item:: Hex string
+
+ .. ipython:: python
 
- galois.Poly.Int(268, field=GF)
+  galois.Poly.Int(int("0xf700a275", 16), field=galois.GF(2**8))
 
 Create a polynomial from its string representation using :func:`galois.Poly.Str`.
 
 .. ipython:: python
 
-  galois.Poly.Str("x^5 + 143", field=GF)
+ galois.Poly.Str("x^5 + 143", field=GF)
 
 Create a polynomial from its roots using :func:`galois.Poly.Roots`.
 
 .. ipython:: python
 
-  f = galois.Poly.Roots([137, 22, 51], field=GF); f
-  f.roots()
+ f = galois.Poly.Roots([137, 22, 51], field=GF); f
+ f.roots()
 
 Simple polynomials
 ..................
@@ -85,9 +108,9 @@ simple polynomials. They are included for convenience.
 
 .. ipython:: python
 
-  galois.Poly.Zero(GF)
-  galois.Poly.One(GF)
-  galois.Poly.Identity(GF)
+ galois.Poly.Zero(GF)
+ galois.Poly.One(GF)
+ galois.Poly.Identity(GF)
 
 Random polynomials
 ..................
@@ -96,7 +119,7 @@ Random polynomials of a given degree are easily created with :func:`galois.Poly.
 
 .. ipython:: python
 
-  galois.Poly.Random(4, field=GF)
+ galois.Poly.Random(4, field=GF)
 
 Methods
 -------
@@ -107,15 +130,15 @@ Compute the derivative of a polynomial using :func:`galois.Poly.derivative`.
 
 .. ipython:: python
 
-  GF = galois.GF(7)
-  f = galois.Poly([1, 0, 5, 2, 3], field=GF); f
-  f.derivative()
+ GF = galois.GF(7)
+ f = galois.Poly([1, 0, 5, 2, 3], field=GF); f
+ f.derivative()
 
 Compute the roots of a polynomial using :func:`galois.Poly.roots`.
 
 .. ipython:: python
 
-  f.roots()
+ f.roots()
 
 Properties
 ----------
@@ -127,22 +150,48 @@ and :obj:`galois.Poly.nonzero_coeffs`.
 
 .. ipython:: python
 
-  GF = galois.GF(7)
-  f = galois.Poly([1, 0, 3], field=GF); f
-  f.nonzero_degrees
-  f.nonzero_coeffs
+ GF = galois.GF(7)
+ f = galois.Poly([1, 0, 3], field=GF); f
+ f.nonzero_degrees
+ f.nonzero_coeffs
 
-Find the integer equivalent of the polynomial using :func:`galois.Poly.__int__`.
+Find the integer equivalent of the polynomial using :func:`int`, see :func:`galois.Poly.__int__`. Additionally, one may
+convert a polynomial into the binary, octal, or hexadecimal string of its integer representation.
 
-.. ipython:: python
+.. tab-set::
+
+ .. tab-item:: Integer
+
+ .. ipython:: python
+
+ int(f)
+
+ .. tab-item:: Binary string
+
+ .. ipython:: python
+
+ g = galois.Poly([1, 0, 1, 1]); g
+ bin(g)
+
+ .. tab-item:: Octal string
+
+ .. ipython:: python
+
+ g = galois.Poly([5, 0, 3, 4], field=galois.GF(2**3)); g
+ oct(g)
+
+ .. tab-item:: Hex string
+
+ .. ipython:: python
 
- int(f)
+ g = galois.Poly([0xf7, 0x00, 0xa2, 0x75], field=galois.GF(2**8)); g
+ hex(g)
 
 Get the string representation of the polynomial using :func:`str`.
 
 .. ipython:: python
 
-  str(f)
+ str(f)
 
 Special polynomials
 -------------------
@@ -153,18 +202,18 @@ Find one or all irreducible polynomials with :func:`galois.irreducible_poly` and
 
 .. ipython:: python
 
-  galois.irreducible_poly(3, 3)
-  galois.irreducible_polys(3, 3)
+ galois.irreducible_poly(3, 3)
+ galois.irreducible_polys(3, 3)
 
 Find one or all primitive polynomials with :func:`galois.primitive_poly` and :func:`galois.primitive_polys`.
 
 .. ipython:: python
 
-  galois.primitive_poly(3, 3)
-  galois.primitive_polys(3, 3)
+ galois.primitive_poly(3, 3)
+ galois.primitive_polys(3, 3)
 
 Find the Conway polynomial using :func:`galois.conway_poly`.
 
 .. ipython:: python
 
-  galois.conway_poly(3, 3)
+ galois.conway_poly(3, 3)

galois/_fields/_main.py

@@ -3164,7 +3164,7 @@ def Str(cls, string: str, field: Optional[FieldClass] = GF2) -> "Poly":
  str(f)
  """
  if not isinstance(string, str):
- raise TypeError(f"Argument `string` be an string, not {type(string)}")
+ raise TypeError(f"Argument `string` be a string, not {type(string)}")
 
  return Poly.Degrees(*str_to_sparse_poly(string), field=field)
 
@@ -3189,22 +3189,55 @@ def Int(cls, integer: int, field: Optional[FieldClass] = GF2) -> "Poly":
 
  Examples
  --------
- Construct a polynomial over :math:`\mathrm{GF}(2)` from its integer representation.
+ .. tab-set::
 
- .. ipython:: python
+  .. tab-item:: Integer
 
- f = galois.Poly.Int(5); f
- int(f)
+ Construct a polynomial over :math:`\mathrm{GF}(2)` from its integer representation.
 
- Construct a polynomial over :math:`\mathrm{GF}(3^5)` from its integer representation.
+  .. ipython:: python
 
- .. ipython:: python
+ f = galois.Poly.Int(5); f
+ int(f)
 
- GF = galois.GF(3**5)
- f = galois.Poly.Int(186535908, field=GF); f
- int(f)
- # The polynomial/integer equivalence
- int(f) == 13*GF.order**3 + 117
+ Construct a polynomial over :math:`\mathrm{GF}(3^5)` from its integer representation.
+
+ .. ipython:: python
+
+ GF = galois.GF(3**5)
+ f = galois.Poly.Int(186535908, field=GF); f
+ int(f)
+ # The polynomial/integer equivalence
+ int(f) == 13*GF.order**3 + 117
+
+ .. tab-item:: Binary string
+
+ Construct a polynomial over :math:`\mathrm{GF}(2)` from its binary string.
+
+ .. ipython:: python
+
+ f = galois.Poly.Int(int("0b1011", 2)); f
+ bin(f)
+
+ .. tab-item:: Octal string
+
+ Construct a polynomial over :math:`\mathrm{GF}(2^3)` from its octal string.
+
+ .. ipython:: python
+
+ GF = galois.GF(2**3)
+ f = galois.Poly.Int(int("0o5034", 8), field=GF); f
+ oct(f)
+
+ .. tab-item:: Hex string
+
+ Construct a polynomial over :math:`\mathrm{GF}(2^8)` from its hexadecimal string.
+
+ .. ipython:: python
+
+ GF = galois.GF(2**8)
+ f = galois.Poly.Int(int("0xf700a275", 16), field=GF); f
+ hex(f)
  """
  if not isinstance(integer, (int, np.integer)):
  raise TypeError(f"Argument `integer` be an integer, not {type(integer)}")
@@ -3729,6 +3762,10 @@ def __str__(self) -> str:
  """
  return sparse_poly_to_str(self.nonzero_degrees, self.nonzero_coeffs)
 
+ def __index__(self) -> int:
+ # Define __index__ to enable use of bin(), oct(), and hex()
+ return sparse_poly_to_integer(self.nonzero_degrees, self.nonzero_coeffs, self.field.order)
+
  def __int__(self) -> int:
  r"""
  The integer representation of the polynomial.
@@ -3753,7 +3790,7 @@ def __int__(self) -> int:
  int(f)
  int(f) == 3*GF.order**3 + 5*GF.order**1 + 2*GF.order**0
  """
- return sparse_poly_to_integer(self.nonzero_degrees, self.nonzero_coeffs, self.field.order)
+ return self.__index__()
 
  def __hash__(self):
  t = tuple([self.field.order,] + self.nonzero_degrees.tolist() + self.nonzero_coeffs.tolist())

tests/polys/test_operations.py

@@ -138,6 +138,23 @@ def test_int():
  assert int(poly) == 4295000729
 
 
+def test_bin():
+ poly = galois.Poly([1, 0, 1, 1])
+ assert bin(poly) == "0b1011"
+
+
+def test_oct():
+ GF = galois.GF(2**3)
+ poly = galois.Poly([5, 0, 3, 4], field=GF)
+ assert oct(poly) == "0o5034"
+
+
+def test_hex():
+ GF = galois.GF(2**8)
+ poly = galois.Poly([0xf7, 0x00, 0xa2, 0x75], field=GF)
+ assert hex(poly) == "0xf700a275"
+
+
 def test_equal(field):
  # NOTE: GF(11) is not included in the `field` pytest fixture
  c = field.Random(6)