Calypso

silviana amethyst

Equation ¶

\[ x^2+y^2 z - z^2 \]

Properties: ¶

degree 3
smooth, except a single singular point at the origin.

Some story ¶

Similar to calyx, calypso was easier to decompose using projection onto \(x\) and \(y\).

Bertini_real input files ¶

input

CONFIG
randomseed: 2;
tracktype: 1;
finaltol: 1e-15;
ampmaxprec: 3096;
ampsafetydigits1: 30;
ampsafetydigits2: 30;
maxnumbersteps: 50000;
pathtruncationthreshold: 1e30;
endpointfinitethreshold: 1e12;
sharpendigits: 60;
endgamenum: 2;
numsamplepoints: 20;
odepredictor: 2;
condnumthreshold: 1e300;
tracktolbeforeeg: 1e-8;
maxnewtonits: 2;
maxstepsbeforenewton: 0;
securitylevel: 1;
imagthreshold: 1e-7;
END;
INPUT

variable_group x, y, z;
function f1;
f1 = x^2+y^2*z - z^2;
END;

projection

sphere