examples/make_polynomial.cpp

How to build your own sequence of known polynomials, here Abel polynomials

#include <iostream>
#include "../src/aerobus.h"
 
 
// let's build Abel polynomials from scratch using Aerobus
// note : it's now integrated in the main library, but still serves as an example
 
template<typename I = aerobus::i64>
struct AbelHelper {
 private:
    using P = aerobus::polynomial<I>;
 
 public:
    // to keep recursion working, we need to operate on a*n and not just a
    template<size_t deg, I::inner_type an>
    struct Inner {
        // abel(n, a) = (x-an) * abel(n-1, a)
        using type = typename aerobus::mul_t<
            typename Inner<deg-1, an>::type,
            typename aerobus::sub_t<typename P::X, typename P::template inject_constant_t<an>>
        >;
    };
 
    // abel(0, a) = 1
    template<I::inner_type an>
    struct Inner<0, an> {
        using type = P::one;
    };
 
    // abel(1, a) = X
    template<I::inner_type an>
    struct Inner<1, an> {
        using type = P::X;
    };
};
 
template<size_t n, auto a, typename I = aerobus::i64>
using AbelPolynomials = typename AbelHelper<I>::template Inner<n, a*n>::type;
 
using A2_3 = AbelPolynomials<3, 2>;
 
int main() {
    std::cout << "expected = x^3 - 12 x^2 + 36 x" << std::endl;
    std::cout << "aerobus  = " << A2_3::to_string() << std::endl;
    return 0;
}