Visualization

Set visualize to keep the certified boxes, and export them to TikZ with either two or three axes. The following example draws the certification boxes in (t, Re(x1), Im(x2)) coordinates and overlays the numerical HC.jl trace.

julia> @variables x y;
julia> CC = AcbField(128);
julia> F = [x^2 + 3*y - 4, y^2 + 3];
julia> G = [x^2 - 1, y^2 - 1];
julia> H = straight_line_homotopy(F, G, [x, y]; CCRing=CC, gamma=CC(0.5, 0.5));Compilation Done.
julia> cert = certify_posteriori(
           H,
           [CC(1), CC(-1)];
           max_step_size=Inf,
           max_depth=6,
           visualize=(axes=(:t, (1, :real), (2, :imag)), show_trace=true),
       )PosterioriPathResult(success=true, method=adaptive_local_parameter_endpoint_box, trace_points=10, original_segments=9, boxes=9, failed=0, max_depth=0, hc_status=success)
julia> certPosterioriPathResult(success=true, method=adaptive_local_parameter_endpoint_box, trace_points=10, original_segments=9, boxes=9, failed=0, max_depth=0, hc_status=success)
julia> cert.successtrue
julia> cert.total_boxes9
julia> length(path_boxes(cert))9
julia> export_path_tikz(
           cert,
           "posteriori_visualization.tex";
           axes=(:t, (1, :real), (2, :imag)),
           show_trace=true,
       )"posteriori_visualization.tex"