algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety algebraic set; component of solutions; diagonal homotopy; embedding; equation-by-equation solver; generic point; homotopy continuation; irreducible component; numerical irreducible decomposition; numerical algebraic geometry; path following; polynomial system; witness point; positive dimensional solution; product decomposition; incremental regeneration; polyhedral homotopy; diagonal homotopy 