Lie symmetries

scaling_symmetries(X::AbstractAlgebraicVariety)

Given an AbstractAlgebraicVariety X returns the group of scaling symmetries of X.

julia> @var x y a b c;

julia> X = AlgebraicVariety([x^4+a^2+1, y^2+b+c]; variables=[x,y,a,b,c]);

julia> scaling_symmetries(X)
ScalingGroup isomorphic to ℂˣ × ℤ₄ × ℤ₂
 1 Lie scaling:
  y ↦ y*λ, b ↦ b*λ^2, c ↦ c*λ^2

 modular scalings:
  1 of order 4:
   x ↦ -im*x, y ↦ im*y, b ↦ -b, c ↦ -c
  1 of order 2:
   x ↦ -x, y ↦ -y, a ↦ -a

ScalingGroup

A ScalingGroup is the result of the scaling_symmetries computation.