Eve

silviana amethyst

Equation

\[ 0.5 x^2 + 2 x z^2 + 5 y^6 + 15 y^4 + 0.5 z^2 - (15 y^5 + 5 y^3)\]

Properties:

Some story

I love this surface. I had to hunt for the correct equation for it, and emailed Herwig Hauser about it, which was fun. Also, I like the way it makes me feel when I look at it. I like it so much, I put it on my CV this application season.

Bertini_real input files

input

% surface 'eve'
% http://homepage.univie.ac.at/herwig.hauser/bildergalerie/gallery.html
% http://homepage.univie.ac.at/herwig.hauser/bildergalerie/gallery/eve.jpg
% a degree six surface in three variables.
CONFIG
tracktype: 1;
%securitylevel:1
endpointfinitethreshold: 1e16;
sharpendigits: 30;
condnumthreshold: 1e300;
odepredictor: 7;
finaltol: 1e-16;
numsamplepoints: 6;
endgamenum: 2;
maxstepsbeforenewton: 0;
maxnewtonits: 2;
END;
INPUT

variable_group x, y, z;
function f;
%correct equation, from the other mirror...
%http://homepage.univie.ac.at/herwig.hauser/gallery.html
f = 0.5*x^2 + 2*x*z^2 + 5*y^6 + 15*y^4 + 0.5*z^2 - (15*y^5 + 5*y^3);
%incorrect equation from the gallery:
%f = 5 * (x^2 + y^6 + 3*y^4 + z^2) + 2*x*z^2 - 5*y^3*(3*y^2 + 1);
% in matlab, you can use f = @(x,y,z) 0.5*x.^2 + 2*x.*z.^2 + 5*y.^6 + 15*y.^4 + 0.5*z.^2 - (15*y.^5 + 5*y.^3);
END;