Evaluation.h

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#pragma once
 
#include "Degree.h"
 
#include "../MultivariatePolynomial.h"
#include "../UnivariatePolynomial.h"
 
namespace carl {
 
template<typename Coefficient>
Coefficient evaluate(const Monomial& m, const std::map<Variable, Coefficient>& substitutions) {
    CARL_LOG_FUNC("carl.core.monomial", m << ", " << substitutions);
    Coefficient res = carl::constant_one<Coefficient>::get();
    for (const auto& ve : m) {
        auto it = substitutions.find(ve.first);
        assert(it != substitutions.end());
        res *= carl::pow(it->second, ve.second);
    }
    CARL_LOG_TRACE("carl.core.monomial", "Result: " << res);
    return res;
}
 
template<typename Coefficient>
Coefficient evaluate(const Term<Coefficient>& t, const std::map<Variable, Coefficient>& map) {
    if (t.monomial()) {
        return t.coeff() * evaluate(*t.monomial(), map);
    } else {
        return t.coeff();
    }
}
 
/**
 * Like substitute, but expects substitutions for all variables.
 * @return For a polynomial p, the function value p(x_1,...,x_n).
 */
template<typename C, typename O, typename P, typename SubstitutionType>
SubstitutionType evaluate(const MultivariatePolynomial<C,O,P>& p, const std::map<Variable, SubstitutionType>& substitutions) {
    if(carl::is_zero(p)) {
        return constant_zero<SubstitutionType>::get();
    } else {
        SubstitutionType result(evaluate(p[0], substitutions)); 
        for (unsigned i = 1; i < p.nr_terms(); ++i) {
            result += evaluate(p[i], substitutions);
        }
        return result;
    };
}
 
template<typename Coeff>
Coeff evaluate(const UnivariatePolynomial<Coeff>& p, const Coeff& value) {
    Coeff result(0);
    Coeff var(1);
    for (const Coeff& coeff : p.coefficients()) {
        result += (coeff * var);
        var *= value;
    }
    return result;
}
 
 
template<typename Coeff>
bool is_root_of(const UnivariatePolynomial<Coeff>& p, const Coeff& value) {
    return carl::sgn(carl::evaluate(p, value)) == Sign::ZERO;
}
 
}