gf(2) Square-free factorization (sff)
Find and remove all squared factors from f.
f = b0000000000000000000000000000000000000000000000000000000001100111
f = 0x0000000000000067
f = x6 + x5 + x2 + x + 1
Find the derivative of f (f')
f' = b0000000000000000000000000000000000000000000000000000000000010001
f' = 0x0000000000000011
f' = x4 + 1
Since f' does not equal zero, find g=gcd(f,f')
g = b0000000000000000000000000000000000000000000000000000000000000001
g = 0x0000000000000001
g = 1
Since g equals one, f has no square factors.
Result (f factored into square-free factors)
f = (b0000000000000000000000000000000000000000000000000000000001100111)2
f = (0x0000000000000067)2
f = (x6 + x5 + x2 + x + 1)2
See also: