homotopy_continuation_jl.m2

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";
    f << "using HomotopyContinuation";
    f << "\n\n";
    f << "@polyvar " | concatenate(mingle(vars, #vars:1));
    eqnCommas:=(#P-1):", ";
    f << "\n";
    f <<"f = [" | concatenate mingle(
	apply(P,e->parsePolynomial e), eqnCommas)| "];\n";
    f << "\n";
    f << "result = solve(f)";
    )
writeSystem (List, String) :=o -> (P,filename) -> (
    f := openOut filename;
    writeSystem(P,f);
    close f;
    )
writeSystem (Ideal, String) := o -> (I,f) -> (
    writeSystem(first entries gens I, f)
    )