I got a headache just looking at your post
Hi,
I have this system of equations
From here on I'm only working with +ve x, y and z integers where
For any given x i've found the maximum value of y is
and that for y from 1 to this limit, z has a lower range and higher range of limits
and
I had thought that y had a lower limit of 1
but when x gets to 31622777 and y = 1 there are no valid values of Z that satisfy the equations.
There are valid values for z when x = 31622777 and y = 2
So somewhere in these equations I should be able to find this lower y limit
My problem? I can't
Any help would be greatly appreciated
Pro
Hi,
First my apologies for not using a relevant title.
Yes, all of the equations can have factored out and yes, some of them are equivalent. I presented them in their entirety so I could be sure I hadn't misfactored somewhere along the way.
Anyway, I have a feeling that the result I got could simply be a computer rounding error, so I'm off to find a pencil and piece of paper.
Thanks
Yes,
Sorry folks, it was a rounding error
Excel reports
31622777^2=1000000025191730 not the correct 1000000025191729
Moral of the story; Don't trust Micro$oft with anything you care about
Sigh, back to the grindstone
Pro
I was about to say that this is a limitation of double precision floating point, since 16 decimal digits in the mantissa is close to the limit of double precision floating point, but checking 31622777^2 is just inside the limits for exact integer arithmetic in DP floating point, indeed Gnumeric gets this right.
(to some extent I am incredulous that MS can get this wrong since they are supposed to be implementing the IEEE floating point specification, and it is not a fault with the MS C/C++ compiler since I have a couple of applications built with that which get 31622777^2 right)
CB
Well, if your equation (9) is set to zero, and solved for y:
2y^2 - 4xy + x^2 = 0
y = x[2 - SQRT(2)] / 2
which is same as your y = x[1 - 1/SQRT(2)]
So there really was nothing to be "found"; all that's needed is set (9) to
zero and solve for y, as I'm showing; ...am I missing something?
I'm still perplexed by those first 8 equations of yours; there's really only 2:
10xy - 6xz - 5y^2 + 3z^2 < 0
-4xy + 2xz + 2y^2 - 1z^2 < 0
And I see nothing wrong with adding 'em up to get:
6xy - 4xz - 3y^2 + 2z^2 < 0
Exactly
Not at all, that's exactly where I 'found' it...am I missing something?
As I replied to TheChaz, I only included them all for completeness sake, in case I had overlooked something. It appears I hadn'tI'm still perplexed by those first 8 equations of yours; there's really only 2:
10xy - 6xz - 5y^2 + 3z^2 < 0
-4xy + 2xz + 2y^2 - 1z^2 < 0
Again, you are quite right, nothing at all wrong with thatAnd I see nothing wrong with adding 'em up to get:
6xy - 4xz - 3y^2 + 2z^2 < 0
My problem was with the result I was getting at x=31622777, but as I updated, it turns out that Excel can't count and I can't read. I had the equations set up in Excel so it would indicate for a given x, y and z if they were all true. In this particular instance I took it on blind faith that it was correctly reporting one or more of them was false so looked to the equations for a reason. If I'd had the sense to look at Excel's output for the individual equations, I would have noticed that (31622777)² couldn't end with a zero
Thanks,
Pro