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

Scalars are 0-D Array objects.

Union¶

• int: A finite field element in its integer representation.

  Integer Polynomial Power

  In [1]: GF = galois.GF(3**5)
  
  In [2]: GF(17)
  Out[2]: GF(17, order=3^5)
  

  In [3]: GF = galois.GF(3**5, repr="poly")
  
  In [4]: GF(17)
  Out[4]: GF(α^2 + 2α + 2, order=3^5)
  

  In [5]: GF = galois.GF(3**5, repr="power")
  
  In [6]: GF(17)
  Out[6]: GF(α^222, order=3^5)
  

• str: A finite field element in its polynomial representation. Many string conventions are accepted, including: with/without *, with/without spaces, ^ or **, any indeterminate variable, increasing/decreasing degrees, etc. Or any combination of the above.

  Integer Polynomial Power

  In [7]: GF("x^2 + 2x + 2")
  Out[7]: GF(17, order=3^5)
  
  # Add explicit * for multiplication
  In [8]: GF("x^2 + 2*x + 2")
  Out[8]: GF(17, order=3^5)
  
  # No spaces
  In [9]: GF("x^2+2x+2")
  Out[9]: GF(17, order=3^5)
  
  # ** instead of ^
  In [10]: GF("x**2 + 2x + 2")
  Out[10]: GF(17, order=3^5)
  
  # Different indeterminate
  In [11]: GF("α^2 + 2α + 2")
  Out[11]: GF(17, order=3^5)
  
  # Ascending degrees
  In [12]: GF("2 + 2x + x^2")
  Out[12]: GF(17, order=3^5)
  

  In [13]: GF("x^2 + 2x + 2")
  Out[13]: GF(α^2 + 2α + 2, order=3^5)
  
  # Add explicit * for multiplication
  In [14]: GF("x^2 + 2*x + 2")
  Out[14]: GF(α^2 + 2α + 2, order=3^5)
  
  # No spaces
  In [15]: GF("x^2+2x+2")
  Out[15]: GF(α^2 + 2α + 2, order=3^5)
  
  # ** instead of ^
  In [16]: GF("x**2 + 2x + 2")
  Out[16]: GF(α^2 + 2α + 2, order=3^5)
  
  # Different indeterminate
  In [17]: GF("α^2 + 2α + 2")
  Out[17]: GF(α^2 + 2α + 2, order=3^5)
  
  # Ascending degrees
  In [18]: GF("2 + 2x + x^2")
  Out[18]: GF(α^2 + 2α + 2, order=3^5)
  

  In [19]: GF("x^2 + 2x + 2")
  Out[19]: GF(α^222, order=3^5)
  
  # Add explicit * for multiplication
  In [20]: GF("x^2 + 2*x + 2")
  Out[20]: GF(α^222, order=3^5)
  
  # No spaces
  In [21]: GF("x^2+2x+2")
  Out[21]: GF(α^222, order=3^5)
  
  # ** instead of ^
  In [22]: GF("x**2 + 2x + 2")
  Out[22]: GF(α^222, order=3^5)
  
  # Different indeterminate
  In [23]: GF("α^2 + 2α + 2")
  Out[23]: GF(α^222, order=3^5)
  
  # Ascending degrees
  In [24]: GF("2 + 2x + x^2")
  Out[24]: GF(α^222, order=3^5)
  

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

Alias¶

alias of Union[int, str, Array]