Determinant for V = 12h³ - 6ah² + ha²

Mathematics about graphical computing
Glen
Posts: 67
Joined: Fri Jan 25, 2008 4:11 am
Location: Australia

Determinant for V = 12h³ - 6ah² + ha²

Postby Glen » Sat Dec 15, 2012 4:35 pm

Spotted the question here:

http://math.stackexchange.com/questions ... r-nomogram

I can see how to do this much: -V + 12h³ - 6ah² easily enough, and probably any two of the terms on the RHS can be done the same way.

This doesn't look like it's necessarily impossible, but it might require playing with terms in all three columns.

Can anyone get that to come out?
jasonwalker
Posts: 27
Joined: Sun Sep 11, 2011 3:54 pm

Re: Determinant for V = 12h³ - 6ah² + ha²

Postby jasonwalker » Sun Dec 16, 2012 11:39 pm

Not often I get to be the clever one around here.

Determinant:
0__________V_________1
1__________[6a-a²]_______1
[h/(h+1)]__[12h³/(h+1)]___1

It's a standard type 4 determinant as described by Levens, or Genus 1 as described by Alcock and Jones. The formula just translates directly across.

Jason
Glen
Posts: 67
Joined: Fri Jan 25, 2008 4:11 am
Location: Australia

Re: Determinant for V = 12h³ - 6ah² + ha²

Postby Glen » Sun Dec 16, 2012 11:58 pm

Hi Jason

That determinant seems to be V = 12h³ - 6ah + ha²

Unfortunately, the equation is V = 12h³ - 6ah² + ha² (--- note middle term is a little different)

A comment in Hall seems to suggest that without a common factor (as there is in the first one), 3-terms in two RHS variables usually doesn't work; this may be an example of a case where it doesn't.

I appreciate the effort; your suggestion is a bit neater than one I had and gives me more room to play with it.
jasonwalker
Posts: 27
Joined: Sun Sep 11, 2011 3:54 pm

Re: Determinant for V = 12h³ - 6ah² + ha²

Postby jasonwalker » Mon Dec 17, 2012 7:28 am

Oh bother. Thought I had it!

:)

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