Q: SymbolicUtils.PolyForm() -> StaticPolynomials.Polynomial(). Variable order at evaluation?

[Audrius-St]

The MWE code below converts a Symbolics polynomial expression to a StaticPolynomials one for fast and accurate evaluation [the actual polynomial expression has many more terms and will evaluated repeatedly].

At the point where the StaticPolynomial expression is evaluated, what is the order of the variables; in the case of the example q1, p1, q2, p2, t? Currently I'm testing the MWE using a random vector.

    # Test array
    x = @SVector rand(5)

    StaticPolynomials.evaluate(p_static, x)

excerpted from

# test_symbolics_to_staticpolynomials.jl
using StaticArrays
using StaticPolynomials
using Symbolics

function main()
    # Indexed array variables
    @variables q[1:2], p[1:2]

    # Time variable
    @variables t

    # Generate the numbered variables {qi, pi | i = 1, 2,  . . .}
    variables_cv_str = "variables_array = @variables"

    for i = 1:2
        variables_cv_str = string(variables_cv_str, " ", "q", string(i), " ", "p", string(i))
    end
    variables_cv_str = string(variables_cv_str, " t")

    eval(Meta.parse(variables_cv_str))
    @show typeof(variables_array)

    # Test expression
    expr = 
        p[1] - q[1]*t - (1//2)*p[1]*(t^2) - (2//1)*q[1]*q[2]*t -
        p[1]*q[2]*(t^2) - p[2]*q[1]*(t^2) + (1//6)*q[1]*(t^3) -
        (2//3)*p[1]*p[2]*(t^3)

    # Substitute {q[i] => qi | i = 1, 2, . . .}
    expr = 
        substitute(
            expr, 
            Dict(
                [q[i] => Num(eval(Symbol("q$(i)"))) for i = 1:2]
            )
        )

    # Substitute {p[i] => pi | i = 1, 2, . . .}
    expr = 
        substitute(
            expr, 
            Dict(
                [p[i] => Num(eval(Symbol("p$(i)"))) for i = 1:2]
            )
        )

    # Convert Symbolics polynomial to DynamicPolynomials form
    @show pf_expr = PolyForm(Symbolics.unwrap(expr))

    # Convert the DynamicPolynomials form to StaticPolynomials
    @show p_static = StaticPolynomials.Polynomial(pf_expr.p)

    # Test array 
    x = @SVector rand(5)

    # Evaluate
    @show @time StaticPolynomials.evaluate(p_static, x)
end

begin
    main()
end