# polynomial

Discussion in 'VHDL' started by S.Muralidharan, Nov 4, 2004.

1. ### S.MuralidharanGuest

hi all,
could any one tell me how to factorize the polynomial (x^255 +1).
I need the factors of that polynomial.

S.Muralidharan, Nov 4, 2004

2. ### Tuukka ToivonenGuest

I think the answer really depends what domain you use, ie. is the x
real or complex or something else.

Something like Maxima (or Maple or Mathematica or Pari/GP can help):

(%i1) factor(x^255+1);

2 4 3 2
(%o1) (x + 1) (x - x + 1) (x - x + x - x + 1)

8 7 5 4 3 16 15 14 13 12 11 10 9
(x + x - x - x - x + x + 1) (x - x + x - x + x - x + x - x

8 7 6 5 4 3 2
+ x - x + x - x + x - x + x - x + 1)

32 31 29 28 26 25 23 22 20 19 17 16 15
(x + x - x - x + x + x - x - x + x + x - x - x - x

13 12 10 9 7 6 4 3
+ x + x - x - x + x + x - x - x + x + 1)

64 63 59 58 54 53 49 48 47 46 44 43 42
(x + x - x - x + x + x - x - x - x - x + x + x + x

41 39 38 37 36 34 33 32 31 30 28 27 26
+ x - x - x - x - x + x + x + x + x + x - x - x - x

25 23 22 21 20 18 17 16 15 11 10 6 5
- x + x + x + x + x - x - x - x - x + x + x - x - x

128 127 126 123 122 121 113 112 110 109
+ x + 1) (x - x + x + x - x + x - x + x - x + x

108 107 105 104 98 97 95 94 93 92 90 89
- x + x - x + x + x - x + x - x + x - x + x - x

83 82 80 79 78 76 75 74 72 71 70 68
- x + x - x + x - x + x - 2 x + x - x + x - x + x

67 65 64 63 61 60 58 57 56 54 53 52
- x + x - x + x - x + x - x + x - x + x - 2 x + x

50 49 48 46 45 39 38 36 35 34 33 31 30
- x + x - x + x - x - x + x - x + x - x + x - x + x

24 23 21 20 19 18 16 15 7 6 5 2
+ x - x + x - x + x - x + x - x + x - x + x + x - x + 1)

Tuukka Toivonen, Nov 4, 2004