gflib

Description

Python library of finite field calculator

Usage

This library contains 2 classes 'gf' and 'gfex'.

At first, you need to type as follows.

from gflib import gf,gfex

gf class

gf class has one class variable 'gf.space'

You can get the surplus of gf.space if you operate two gf object each other.

>>> gf.space=7
>>> gf(3)+gf(5)
1
>>> gf(3)-gf(5)
5
>>> gf(3)*gf(5)
1
>>> gf(3)/gf(5)
2

gfex class

You have to set the constant before using this class by calling 'gfex.set_const(m,p,ply)'. and you can get the table of the elements by using 'gfex.info()'.

>>> gfex.set_const(2,3,[1,1,0])
>>> gfex.info()
[1, 0, 0] 0
[0, 1, 0] 1
[0, 0, 1] 2
[1, 1, 0] 3
[0, 1, 1] 4
[1, 1, 1] 5
[1, 0, 1] 6
[1, 0, 0] 0

extension field: p and m value can be set by 1st and 2nd arguments.

3rd argument means the coefficient of primitive polynomial. (You need to transposition all item except highest degree item)

gfex class supports '+,-,*,/' operators as well.

>>> gfex(2)+gfex(4)
[0, 1, 0] 1
>>> gfex(2)-gfex(4)
[0, 1, 0] 1
>>> gfex(2)*gfex(4)
[1, 0, 1] 6
>>> gfex(2)/gfex(4)
[1, 1, 1] 5

If you wanna use 0, you need to initialize gfex() by passing -1.

>>> zero = gfex(-1)
>>> zero
[0, 0, 0] -1
>>> gfex(3)*zero
[0, 0, 0] -1
>>> gfex(3)+zero
[1, 1, 0] 3