Power.h

Go to the documentation of this file.

#pragma once
 
#include "../MultivariatePolynomial.h"
#include "../UnivariatePolynomial.h"
 
namespace carl {
 
/**
 * Calculates the given power of a monomial m.
 * @param m The monomial.
 * @param exp Exponent.
 * @return m to the power of exp.
 */
inline Monomial::Arg pow(const Monomial& m, uint exp) {
    if (exp == 0) {
        return nullptr;
    }
    Monomial::Content newExps;
    uint expsum = 0;
    for (const auto& it: m.exponents()) {
        newExps.emplace_back(it.first, uint(it.second * exp));
        expsum += newExps.back().second;
    }
    return createMonomial(std::move(newExps), expsum);
}
inline Monomial::Arg pow(const Monomial::Arg& m, uint exp) {
    if (m == nullptr) return nullptr;
    return pow(*m, exp);
}
 
template<typename Coeff>
Term<Coeff> pow(const Term<Coeff>& t, uint exp) {
    if (t.monomial()) {
        return Term<Coeff>(carl::pow(t.coeff(), exp), pow(*t.monomial(), exp));
    } else {
        return Term<Coeff>(carl::pow(t.coeff(), exp), nullptr);
    }
}
 
template<typename C, typename O, typename P>
MultivariatePolynomial<C,O,P> pow(const MultivariatePolynomial<C,O,P>& p, std::size_t exp) {
    //std::cout << "pw(" << *this << " ^ " << exp << ")" << std::endl;
    if (carl::is_zero(p)) return MultivariatePolynomial<C,O,P>(constant_zero<C>::get());
    if (exp == 0) return MultivariatePolynomial<C,O,P>(constant_one<C>::get());
    if (exp == 1) return MultivariatePolynomial<C,O,P>(p);
    if (exp == 2) return p*p;
    MultivariatePolynomial<C,O,P> res(constant_one<C>::get());
    MultivariatePolynomial<C,O,P> mult(p);
    while(exp > 0) {
        res *= mult;
        exp--;
    }
    return res;
}
 
template<typename C, typename O, typename P>
MultivariatePolynomial<C,O,P> pow_naive(const MultivariatePolynomial<C,O,P>& p, std::size_t exp) {
    if (exp == 0) {
        return MultivariatePolynomial(constant_one<C>::get());
    }
 
    CARL_LOG_INEFFICIENT();
    MultivariatePolynomial<C,O,P> res(p);
    for (std::size_t i = 1; i < exp; i++) {
        res *= p;
    }
    return res;
}
 
/**
 * Returns a polynomial to the given power.
 * @param p The polynomial.
 * @param exp Exponent.
 * @return The polynomial to the power of exp.
 */
template<typename Coeff>
UnivariatePolynomial<Coeff> pow(const UnivariatePolynomial<Coeff>& p, std::size_t exp) {
    if (exp == 0) return UnivariatePolynomial<Coeff>(p.main_var(), constant_one<Coeff>::get());
    if (carl::is_zero(p)) return UnivariatePolynomial<Coeff>(p.main_var());
    UnivariatePolynomial<Coeff> res(p.main_var(), constant_one<Coeff>::get());
    UnivariatePolynomial<Coeff> mult(p);
    while (exp > 0) {
        if ((exp & 1) != 0) res *= mult;
        exp /= 2;
        if(exp > 0) mult = mult * mult;
    }
    return res;
}
 
}