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Quadratic again. may be tricky

  1. Nov 28, 2007 #1
    hi, i think this one is a bit trickier.

    for an odd prime number "p", let [itex]F_p[/itex] be the field with "p" elements. i.e. the integers {0,....p-1} with addition and multiplication defined modulo "p".
    So how many quadratic forms are there on the vector space [itex]F^n_p[/itex] and why?

    any clues here please?
     
    Last edited: Nov 28, 2007
  2. jcsd
  3. Dec 1, 2007 #2

    CompuChip

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    Can you write down the general form of such a quadratic form?
    E.g., for n = 1, 2, 3 it would be
    [tex]a x^2; \quad a x^2 + b x y + c y^2; \quad a x^2 + b x y + c x z + d y^2 + e y z + f z^2[/tex] --
    do you know of a general formula?

    (By the way, you probably don't need the general formula, just the number of terms occurring in it. So in the above example, 1, 3 and 6 respectively).
     
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