polynomial

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

  1. 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
    #1
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  2. 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
    #2
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