Monomial_Create.cpp

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#include <cassert>
 
#include <carl-arith/poly/umvpoly/Monomial.h>
#include <carl-arith/poly/umvpoly/MonomialPool.h>
 
int main() {
    /*
     * A carl::Monomial object represents a monomial, being the product of
     * multiple variables. Our representation consists of a list of (unique)
     * carl::Variable objects, each associated with an exponent.
     *
     * Internally, a carl::Monomial stores the actual monomial as 
     * std::vector<std::pair<carl::Variable,unsigned>>
     * and, for caching purposes, the following data:
     * - the total degree, that is the sum of all exponents,
     * - the id, a unique identifier managed by the carl::MonomialPool and
     * - the hash of the monomial.
     */
    carl::Variable x = carl::fresh_real_variable("x");
    carl::Variable y = carl::fresh_real_variable("y");
 
    /*
     * However, carl::Monomial objects are managed by a carl::MonomialPool,
     * though the carl::MonomialPool seldomly accessed directly.
     * This means, that there is only a single instance of every monomial and
     * all objects that use this monomial have a std::shared_ptr of this 
     * instance. To obtain this std::shared_ptr, use carl::createMonomial
     * instead of the normal constructor.
     * The type of the std::shared_ptr is defined by carl::Monomial::Arg.
     */
    
    auto a = carl::createMonomial(x, (carl::exponent)2);
    auto b = carl::createMonomial(std::initializer_list<std::pair<carl::Variable, carl::exponent>>({std::make_pair(x,(carl::exponent)3), std::make_pair(y, (carl::exponent)2)}), (carl::exponent)5);
 
    assert(a == x*x);
    assert(b == x*x*x * y*y);
 
    /*
     * As you see, the creation of monomials with multiple variables is somewhat
     * clumsy, but in the above assertions a simpler way is already used.
     * Two variables can be multiplied, resulting in a monomial. Monomials can 
     * also be multiplied, resulting in a new monomial.
     */
    auto c = x*x*y;
    auto d = x*y;
    auto e = c*d;
 
    assert(e == b);
}