`bit::polynomial` — Multiplication by \(x^n\)

We have methods that multiply a polynomial by \(x^n\) where \(n\) defaults to 1.

constexpr polynomial&
1times_x(std::size_t n = 1);

constexpr polynomial
2times_x(const polynomial& p, std::size_t n = 1);

1: This multiplies this polynomial by \(x^n\) in place.
2: This returns a new polynomial that is this one multiplied by \(x^n\).

These methods are faster than using the multiplication operator.

Example

#include <bit/bit.h>
int main()
{
    auto x3 = bit::polynomial<>::power(3);
    bit::polynomial p{6};
    p.set();

    std::cout << std::format("p(x)            = {}\n", p);
    std::cout << std::format("x^3 * p(x)      = {}\n", x3 * p);
    std::cout << std::format("p(x).times_x(3) = {}\n", p.times_x(3));
}

Output

p(x)            = 1 + x^1 + x^2 + x^3 + x^4 + x^5
x^3 * p(x)      = x^3 + x^4 + x^5 + x^6 + x^7 + x^8
p(x).times_x(3) = x^3 + x^4 + x^5 + x^6 + x^7 + x^8

See Also