# Thread: Lagrange reduction - rank and signature

1. ## 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?

2. Originally Posted by mitch_nufc
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?

3. =
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

4. See below

5. See below...

6. Originally Posted by mitch_nufc
=
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.

7. 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

8. Originally Posted by mitch_nufc
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.

9. You seem pretty bright are you a uni student or A-level?

10. Originally Posted by mitch_nufc
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?

11. 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

12. Originally Posted by mitch_nufc
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.

13. 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

14. Originally Posted by mitch_nufc
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