Macaulay2 error: expected a $0$-dimensional system

Question

What does the error stdio:28:6:(3): error: expected a 0-dimensional system mean and how to avoid it?

Thanks in advance for any help!

Below is the code:

needsPackage "NumericalAlgebraicGeometry"
NumericalAlgebraicGeometry
Package
R = QQ[sa,sb,sc,sd,se,ca,cb,cc,cd,ce]
system = {-cb sa - cd sa - ce sa + ca sb + ca sd + ca se, 
 cb sa - ca sb - cc sb - cd sb - ce sb + cb sc + cb sd + cb se, 
 cc sb - cb sc - cd sc - ce sc + cc sd + cc se, 
 cd sa + cd sb + cd sc - ca sd - cb sd - cc sd - ce sd + cd se, 
 ce sa + ce sb + ce sc + ce sd - ca se - cb se - cc se - cd se, -1 + 
  ca^2 + sa^2, -1 + cb^2 + sb^2, -1 + cc^2 + sc^2, -1 + cd^2 + sd^2}

Answer 1

Numerical algebraic geometry focuses a lot on finding single "witness" solutions to a set of equations. Often the methods ask for the solution set to be only a finite set of points. This is called a "0-dimensional" system. If the solution set is a finite set of curves it is 1-dimensional, a finite set of surfaces is 2-dimensional, and so on.

So when the package tells you your system is not 0-dimensional it means there are infinitely many solutions and you need more equations for the algorithms to work. As a rule, you need at least as many equations as you have variables. You have 9 equations and 10 variables which one expects will form a 1-dimensional solution set.