bit::polynomial — Random Polynomials
Factory method to construct a fixed degree bit-polynomial whose coefficients come from independent random draws from a Bernoulli distribution
static bit::polynomial random(std::size_t n, double prob_one = 0.5);This method returns a polynomial of degree \(n\) with \(n+1\) coefficients.
If \(n > 0\) then \(p_n = 1\) and all the other coefficients in the polynomial are 1 with probability prob_one. If \(n = 0\) then the single coefficient \(p_0\) is 1 with probability prob_one.
The default probability value is 0.5, so n coefficient values are determined by tossing a fair coin.
At the extremes, if this parameter is 1.0, the coefficients will all be 1; if it is 0.0, the elements will all be 0.
This method throws a std::invalid_argument exception if the prob_one argument is not in the valid range \([0, 1]\).
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Example
#include <bit/bit.h>
int main()
{
// lambda: Turns the degree of a polynomial into a string.
auto deg = [](auto& p) { return p.degree() == bit::polynomial<>::ndeg ? "NONE" : std::format("{}", p.degree()); };
auto p0 = bit::polynomial<>::random(0);
std::cout << std::format("p0(x) = {} has degree: {}.\n", p0, deg(p0));
auto p1 = bit::polynomial<>::random(7);
std::cout << std::format("p0(x) = {} has degree: {}.\n", p1, deg(p1));
auto p2 = bit::polynomial<>::random(7, 0.9);
std::cout << std::format("p0(x) = {} has degree: {}.\n", p2, deg(p2));
}Output (will vary from run to run)
p0(x) = 0 has degree: NONE.
p0(x) = x^1 + x^3 + x^5 + x^7 has degree: 7.
p0(x) = 1 + x^1 + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 has degree: 7.