gf(2) Square-free factorization (sff)

Find and remove all squared factors from f.

f = b0000000000000000111101111101100100100100100111111111001100111111 f = 0x0000f7d9249ff33f f = x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁸ + x³⁶ + x³⁵ + x³² + x²⁹ + x²⁶ + x²³ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x⁹ + x⁸ + x⁵ + x⁴ + x³ + x² + x + 1

Find the derivative of f (f')

f' = b0000000000000000010100010100010000010000010001010101000100010101 f' = 0x0000514410455115 f' = x⁴⁶ + x⁴⁴ + x⁴⁰ + x³⁸ + x³⁴ + x²⁸ + x²² + x¹⁸ + x¹⁶ + x¹⁴ + x¹² + x⁸ + x⁴ + x² + 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 = (b0000000000000000111101111101100100100100100111111111001100111111) f = (0x0000f7d9249ff33f) f = (x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴⁴ + x⁴² + x⁴¹ + x⁴⁰ + x³⁹ + x³⁸ + x³⁶ + x³⁵ + x³² + x²⁹ + x²⁶ + x²³ + x²⁰ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹⁴ + x¹³ + x¹² + x⁹ + x⁸ + x⁵ + x⁴ + x³ + x² + x + 1)