Compatibility with DynamicPolynomials.jl

[gescholt]

Hello

I am pretty new to programming with types in Julia. I would like to generate Legendre polynomials in the @polyvar x environment of the DynamicPolynomial.jl package.

If someone has some pointers on how to do this, I would be glad to try to implement it myself.

all the best
Georgy

[HMegh]

I might be able to help more if you could explain what you want to achieve. If you want to generate Legendre polynomials using the DynamicPolynomials package, you can use the recurrence relation directly:

function p(n::Integer)
    @polyvar x
    n==0 && return 1
    n==1 && return x
    y0=1
    y1=x
    for k=1:n-1
        y0,y1=y1,(2k+1)//(k+1)*x*y1 -k//(k+1)*y0
    end
    return y1
end

For example,

julia> p(10)
-63//256 + 3465//256x² - 15015//128x⁴ + 45045//128x⁶ - 109395//256x⁸ + 46189//256x¹⁰

Here, I am using rational numbers to store the coefficients, you can change that to floats by replacing // with /.