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]