I demonstrate what I mean with this using HomotopyContinuation.jl.
using HomotopyContinuation
@var x
f = System([4*x^4+3*x^3+2*x^2+x-5])Given a symbolic system of polynomials f, in HC.jl there are two ways
to optimize them for numerical evaluation.
First the expression is optimized with similar techniques as you do (common subexpression elimination and then a simple multivariate horner-schema).
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| using HomotopyContinuation, LinearAlgebra | |
| @polyvar x y z p[1:3] | |
| F = [ | |
| x + 3 + 2y + 2 * y^2 - p[1], | |
| (x - 2 + 5y) * z + 4 - p[2] * z, | |
| (x + 2 + 4y) * z + 5 - p[3] * z, | |
| ] |
| parsePolynomial = p -> replace("ii","im",replace("p[0-9]+","0",toExternalString p)) | |
| writeSystem = method(Options=>{}) | |
| writeSystem (List, File) := o -> (P,f) -> ( | |
| R := ring first P; | |
| vars := apply(gens R, toString); | |
| concatenate(mingle(vars, (#vars-1):1)); | |
| f << "# This file was auto generated from Macaulay2.\n"; | |
| f << "# For more information about HomotopyContinuation.jl visit:\n"; | |
| f << "# https://www.JuliaHomotopyContinuation.org\n"; |