A Union representing objects that can be coerced into a Galois field array.

Union¶

• IterableLike: A recursive iterable of iterables of elements.

  Integer Polynomial Power

  In [1]: GF = galois.GF(3**5)
  
  In [2]: GF([[17, 4], [148, 205]])
  Out[2]: 
  GF([[ 17,   4],
      [148, 205]], order=3^5)
  
  # Mix and match integers and strings
  In [3]: GF([["x^2 + 2x + 2", 4], ["x^4 + 2x^3 + x^2 + x + 1", 205]])
  Out[3]: 
  GF([[ 17,   4],
      [148, 205]], order=3^5)
  

  In [4]: GF = galois.GF(3**5, repr="poly")
  
  In [5]: GF([[17, 4], [148, 205]])
  Out[5]: 
  GF([[             α^2 + 2α + 2,                     α + 1],
      [ α^4 + 2α^3 + α^2 + α + 1, 2α^4 + α^3 + α^2 + 2α + 1]], order=3^5)
  
  # Mix and match integers and strings
  In [6]: GF([["x^2 + 2x + 2", 4], ["x^4 + 2x^3 + x^2 + x + 1", 205]])
  Out[6]: 
  GF([[             α^2 + 2α + 2,                     α + 1],
      [ α^4 + 2α^3 + α^2 + α + 1, 2α^4 + α^3 + α^2 + 2α + 1]], order=3^5)
  

  In [7]: GF = galois.GF(3**5, repr="power")
  
  In [8]: GF([[17, 4], [148, 205]])
  Out[8]: 
  GF([[α^222,  α^69],
      [ α^54,  α^24]], order=3^5)
  
  # Mix and match integers and strings
  In [9]: GF([["x^2 + 2x + 2", 4], ["x^4 + 2x^3 + x^2 + x + 1", 205]])
  Out[9]: 
  GF([[α^222,  α^69],
      [ α^54,  α^24]], order=3^5)
  

• ndarray: A NumPy array of integers, representing finite field elements in their integer representation.

  Integer Polynomial Power

  In [10]: x = np.array([[17, 4], [148, 205]]); x
  Out[10]: 
  array([[ 17,   4],
         [148, 205]])
  
  In [11]: GF(x)
  Out[11]: 
  GF([[ 17,   4],
      [148, 205]], order=3^5)
  

  In [12]: x = np.array([[17, 4], [148, 205]]); x
  Out[12]: 
  array([[ 17,   4],
         [148, 205]])
  
  In [13]: GF(x)
  Out[13]: 
  GF([[             α^2 + 2α + 2,                     α + 1],
      [ α^4 + 2α^3 + α^2 + α + 1, 2α^4 + α^3 + α^2 + 2α + 1]], order=3^5)
  

  In [14]: x = np.array([[17, 4], [148, 205]]); x
  Out[14]: 
  array([[ 17,   4],
         [148, 205]])
  
  In [15]: GF(x)
  Out[15]: 
  GF([[α^222,  α^69],
      [ α^54,  α^24]], order=3^5)
  

• Array: A previously created Array object. No coercion is necessary.

Alias¶

alias of Union[Sequence[Union[int, str, Array]], Sequence[IterableLike], ndarray, Array]