gf(2) Find polynomial factors
Find all the irreducible factors of f
f = b0110011001110111111000100000000101000110010100001000111110110111
f = 0x6677e20146508fb7
f = x62 + x61 + x58 + x57 + x54 + x53 + x52 + x50 + x49 + x48 + x47 + x46 + x45 + x41 + x32 + x30 + x26 + x25 + x22 + x20 + x15 + x11 + x10 + x9 + x8 + x7 + x5 + x4 + x2 + x + 1
Factor out any squareable factors in f.
f = (b0110011001110111111000100000000101000110010100001000111110110111)
f = (0x6677e20146508fb7)
f = (x62 + x61 + x58 + x57 + x54 + x53 + x52 + x50 + x49 + x48 + x47 + x46 + x45 + x41 + x32 + x30 + x26 + x25 + x22 + x20 + x15 + x11 + x10 + x9 + x8 + x7 + x5 + x4 + x2 + x + 1)
For each factor found, factor into irreducible polynomials.
f0 = b0110011001110111111000100000000101000110010100001000111110110111
f0 = 0x6677e20146508fb7
f0 = x62 + x61 + x58 + x57 + x54 + x53 + x52 + x50 + x49 + x48 + x47 + x46 + x45 + x41 + x32 + x30 + x26 + x25 + x22 + x20 + x15 + x11 + x10 + x9 + x8 + x7 + x5 + x4 + x2 + x + 1
Find irreducible factors of f0f00 = b0000000000000000000000000000000010110000110000010101001011111001
f00 = 0x00000000b0c152f9
f00 = x31 + x29 + x28 + x23 + x22 + x16 + x14 + x12 + x9 + x7 + x6 + x5 + x4 + x3 + 1
f01 = b0000000000000000000000000000000011101011111100101000001100011111
f01 = 0x00000000ebf2831f
f01 = x31 + x30 + x29 + x27 + x25 + x24 + x23 + x22 + x21 + x20 + x17 + x15 + x9 + x8 + x4 + x3 + x2 + x + 1
f factored, powers expanded:
f = (b10110000110000010101001011111001)(b11101011111100101000001100011111)
f = (0xb0c152f9)(0xebf2831f)
f = (x31 + x29 + x28 + x23 + x22 + x16 + x14 + x12 + x9 + x7 + x6 + x5 + x4 + x3 + 1)(x31 + x30 + x29 + x27 + x25 + x24 + x23 + x22 + x21 + x20 + x17 + x15 + x9 + x8 + x4 + x3 + x2 + x + 1)