Conics meeting 8 lines
Zachary Griffin and Jonathan Hauenstein
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Given eight lines in general position in space, there are 92 conics which meet the lines.
The remainder of this page shows that there exists 8 real lines such that all 92 conics are real.
Directions
Before you begin, you will need to have a working binary of
alphaCertified on your machine.
We present the computation for one of the two sets of a point and lines and provide the files for the other below.
- Save the files polySys_92real and points_92real in the same directory.
The file points_92real_float contains the floating points approximations computed by Bertini.
Perusing it, we see that the last three coordinates of each point are at least 0.01 units apart.
- Execute the command
> alphaCertified polySys_92real points_92real
from the directory.
- Here is the output displayed to the screen. Perusing it, we see that alphaCertified does certify that there are 92 real solutions.
- Here is the constantValues file computed by alphaCertified. Perusing it, we see that the second constant (corresponding
to β) is bounded above by 1.06e-53 so that the distance between the approximation and the corresponding solution is bounded above by 2.12e-53.
Additional Files
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