Introduction

draw_curve_tikz(filename::String, f_in; solver_precision::Int=128, graph::Bool=false, custom_edge_plot=nothing)

Takes a polynomial in two variables and constructs a plot of the resulting real algebraic curve in TikZ.

The algorithm is based on the critical points of $f$, points where both $f$ and its $y$-derivative vanish. If there are no such points, e.g. if $f$ is strictly positive everywhere or consists of a bunch of parallel lines, currently an NotImplementedError is thrown.

The red points are the singularities of $f$ and the blue points are the places where the tangent is parallel to the $y$-axis. However, a random transformation may have been applied beforehand, so the blue points may not be critical points in the original coordinate system.

Keyword arguments:

• transform::Union{MatrixElem, AbstractMatrix}: Provide a matrix such that transforming the curve with said transformation results in a curve with generic set of critical points, i.e. distinct $x$-coordinates. The default is to loop over a hard-coded list of transformation matrices.
• ntries::Int: Apply transform repeatedly to reach generic critical points, but at most ntries times.
• graph::Bool=false: Only draw isotopy graph.

Examples

julia> fn = tempname();

julia> R, (x, y) = polynomial_ring(QQ, [:x, :y])
(Multivariate polynomial ring in 2 variables over QQ, QQMPolyRingElem[x, y])

julia> f = (x^2+y^2-1)*((x-1)^2+y^2-1)
x^4 - 2*x^3 + 2*x^2*y^2 - x^2 - 2*x*y^2 + 2*x + y^4 - y^2

julia> b = draw_curve_tikz(fn, f)

Restarting with another random linear form
Restarting with a non-random linear form
Restarting with another random linear form
Restarting with a non-random linear formtrue

julia> b
true