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: