Plotting Algebraic Curves in Julia

Question

I'm looking to visualize some algebraic curves in Julia

I have the polynomials:

f1=(x^4+y^4-1)(x^2+y^2-2)+x^5y

f2 = x^2+2xy^2-2y^2-1/2

and I would like to plot V(f1) and V(f2) so I can see their common intersections. I have tried using contour plot in Gadfly.jl but it seems to only allow me to plot one curve at a time. Is there a way to plot both curves in Gadfly.jl or doing it in another Julia package?

Here is what I have so far.

Answer 1

Gadfly is using a handy composite item: Layers

https://gadflyjl.org/stable/man/compositing/#Layers

These are freely accessible through the plot as plot_name.layers and can be manually appended ( e.g. using append!(p.layers, new_layer) ). A personal favorite is building both layers prior to calling plot() and implementing any necessary figure labels within the plot() function:

using Gadfly

pol_one = layer(z=(x,y) -> (x^4 + y^4 - 1) * (x^2+y^2-2) + x^5 * y,
               xmin=[-2], xmax=[2], ymin=[-2], ymax=[2],
               Geom.contour(levels=[0;]))

pol_two = layer(z=(x,y) -> x^2 + 2x*y^2 - 2y^2 - 1/2,
               xmin=[-2], xmax=[2], ymin=[-2], ymax=[2],
               Geom.contour(levels=[0;]))

plot(p_layer, q_layer, Guide.xlabel("x"), Guide.ylabel("y"))

which will produce the following figure: