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Math Help - Lagrange reduction - rank and signature

  1. #1
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    Lagrange reduction - rank and signature

    Can anyone explain in more simple terms what rank and signature mean in terms of quadratics in x,y,z in lagrange reductions. My lecturers notes arent too clear and I missed this section. I can do the computation but i dont get what the rank and signature mean? something about the radicals of the squares i assume?
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  2. #2
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    Quote Originally Posted by mitch_nufc View Post
    Can anyone explain in more simple terms what rank and signature mean in terms of quadratics in x,y,z in lagrange reductions. My lecturers notes arent too clear and I missed this section. I can do the computation but i dont get what the rank and signature mean? something about the radicals of the squares i assume?
    Perhaps you could post your notes so we can see these terms being used in context?
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  3. #3
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    =
    2(x + 2y 3z)^23(y 7z)^2+ 148z^2.

    Thus rank
    = 3 and signature 2 1 = 1.

    The
    rank of a quadratic form is the number of squares (here
    the rank is 3), and the
    signature is the number of positive
    squares minus the number of negative squares (here the

    signature is 2
    1 = 1.

    Could you just explain what it actually means, I'm probably being stupid lol but I'd appreciate it, thanks
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  4. #4
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    See below
    Last edited by Mush; December 20th 2008 at 03:19 PM. Reason: ...
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  5. #5
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    See below...
    Last edited by Mush; December 20th 2008 at 03:19 PM. Reason: Bollocks...
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  6. #6
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    Quote Originally Posted by mitch_nufc View Post
    =
    2(x + 2y 3z)^23(y 7z)^2+ 148z^2.

    Thus rank
    = 3 and signature 2 1 = 1.

    The
    rank of a quadratic form is the number of squares (here
    the rank is 3), and the
    signature is the number of positive
    squares minus the number of negative squares (here the

    signature is 2
    1 = 1.

    Could you just explain what it actually means, I'm probably being stupid lol but I'd appreciate it, thanks


    If you look at the equation there are THREE terms which are squared. ie  (something)^2. So that is the rank. Signature is the number of these which are positive minus the number of these which are negative. ie  -(something)^2 and +(something)^2.


    It's as simple as that really. Your expression can be boiled down to:

     2A^2 -3B^2+148C^2

    Where:

    A=x+2y-3z
     B = y-7z
     C=z



    Hence there are two positive squared terms and 1 negative squared term. Signature is 1.
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  7. #7
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    I feel stupid now lol, I was over complicating it far too much! I was thinking my signature was the individual squares i.e. z^2 y^2 etc, thanks for clearing this up
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  8. #8
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    Quote Originally Posted by mitch_nufc View Post
    I feel stupid now lol, I was over complicating it far too much! I was thinking my signature was the individual squares i.e. z^2 y^2 etc, thanks for clearing this up
    Yes well... thinking intuitively I would assume that the rank and signature for an expression should be the same whether you multiply it out or not. I'm not really familiar with the material, but it seems to be the case that the rank and signature only apply once you have factorised fully.
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  9. #9
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    You seem pretty bright are you a uni student or A-level?
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  10. #10
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    Quote Originally Posted by mitch_nufc View Post
    You seem pretty bright are you a uni student or A-level?
    I'm a 2nd Year Aeronautical Engineering student at the University of Glasgow. Or Rocket Science, as I like to call it :P.

    Yourself?
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  11. #11
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    Rocket science? I like it haha

    I'm in my first year at Newcastle doing Pure Maths, signed up for the 4 years, ouch lol
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  12. #12
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    Quote Originally Posted by mitch_nufc View Post
    Rocket science? I like it haha

    I'm in my first year at Newcastle doing Pure Maths, signed up for the 4 years, ouch lol
    I signed up for 5...

    Pure Maths is my pet interest on the side. I wish I could pursue it at degree level, but I suppose I've made my decision! Too late to switch, I think.
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  13. #13
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    You could change I think, but It would all depend on the level of mathematics you've already been taught? Do you have MSN? I can message you all kinds of problems I'll be having haha :O
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  14. #14
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    Quote Originally Posted by mitch_nufc View Post
    You could change I think, but It would all depend on the level of mathematics you've already been taught? Do you have MSN? I can message you all kinds of problems I'll be having haha :O
    Mushet@hotmail.co.uk
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