Imaginary Projection

imaginary_projection(f; alg=Greedy(), grid=..., options...)

Compute the imaginary_projection of f with the given algorithm alg and a 2D or 3D grid. alg can be

• Greedy()
• Simple()

but you probably only want to use Greedy().

Examples

@polyvar x y

g = x^4 + im * x^3 - x^2 * y^2 + 3x^3 - 2im*x*y^2 + (4-2im)*x + 0.5*y^2 + 1.5
grid = Grid2D(xlims=(-4, 4), ylims=(-5, 5), res=(1200, 1200))
# This uses the `Greedy()` algorithm
imaginary_projection(g, grid=grid)

These algorithms are all approximations of the imaginary projection 𝐼(𝑓) based on a grid. This basically applies the membership test for different grid points. The grid can be passed explicitly, otherwise it will be computed based on a heuristic.

• membership_options=[MembershipTestOptions()](@ref): The options for the membership test.
• npasses=1: The Greedy() algorithm can make multiple passes to improve the quality.
• test_domain: A tuple (xmin, xmax, ymin, ymax, [zmin, zmax]) from which start values for the membership test are drawn.