3 ms·
It's not straightforward to get a useful visual plot, but the article does include a somewhat artistic one (w/o labeled axes) in the banner image at the top. It
by _delirium 9y ago
It's not straightforward to get a useful visual plot, but the article does include a somewhat artistic one (w/o labeled axes) in the banner image at the top. It's a polynomial in 3 variables, so plotting the polynomial itself is 4-dimensional, and the roots are in 3 dimensions. The visualization at the top of the article is a 3d plot of the locations of the roots.
The seven rational solutions are given on p. 30 of the paper, and are: (x,y,z) = (1,1,1), (1,1,2), (0,0,1), (-3,3,2), (1,1,0), (0,2,1), (-1,1,0). Those were already known though. The new result of the paper is to prove that there aren't any others.
- enriquto 9y agoIt is a curve in homogeneous coordinates. You can set z=1 to obtain an affine view of it, and draw it as a regular curve in the plane. Points with z=0 are points at infinity (directions). The two rational points with z=0 that you describe mean that the curve has two asymptotes at 45 and -45 degrees.