galois.typing.ElementLike¶

galois.typing.ElementLike¶

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.

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

  In [3]: GF("x^2 + 2x + 2")
  Out[3]: GF(17, order=3^5)
  
  # Add explicit * for multiplication
  In [4]: GF("x^2 + 2*x + 2")
  Out[4]: GF(17, order=3^5)
  
  # No spaces
  In [5]: GF("x^2+2x+2")
  Out[5]: GF(17, order=3^5)
  
  # ** instead of ^
  In [6]: GF("x**2 + 2x + 2")
  Out[6]: GF(17, order=3^5)
  
  # Different indeterminate
  In [7]: GF("α^2 + 2α + 2")
  Out[7]: GF(17, order=3^5)
  
  # Ascending degrees
  In [8]: GF("2 + 2x + x^2")
  Out[8]: GF(17, order=3^5)
  

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

Alias

alias of Union[int, str, Array]