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Math Help - Factoring a polynomial

  1. #1
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    Factoring a polynomial

    Ive got a little problem with this. How do i factor a polynomial over a ternary field? I know how to do it in binary...

    in binary: x^7 - 1 = x^7 - 1 = (x+1)(x^3 + x + 1)(x^3 + x^2 + 1)

    i get that

    and now the question is how do i do it for ternary field

    x^5 - 1 = ???


    thx a lot for help
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  2. #2
    Junior Member
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    Oct 2008
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    First in any ring you can write
    x^5-1=(x-1)(x^4+x^3+x^2+1)

    Confince yourself that x^4+x^3+x^2+1 has no linear factor by checking that this polynom has no ternary root.

    It mean either this polynomial can't be factor anymore or
    x^4+x^3+x^2+1=(x^2+Ax+B)(x^2+C+D)
    Since BD=1 then B=D=1 or B+D=-1.

    Now you can playing around with A,C and see whether we can find a suitable A and C.
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  3. #3
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    one more thing...do any special rules apply like in the binary case? For example in the binary field i could say that x + x = 0...

    can i do the same for ternary field?
    Last edited by merlin1x1; October 11th 2008 at 10:12 AM.
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