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Construction of the bezoutian matrix. Uses a hash table and sort the monomials in X and Y by insertion. In this matrix, the rows are indexed by monomials in X and columns by monomial in Y. The entry corresponding to a given the row $X^a$ and column $Y^b$ is the coefficient of $X^{a} Y^{b}$ in the Bezoutian polynomial.

We do not know apriori the number of monomials in $X$ and $Y$. so that we use sorted lists of monomials. Finding the coefficient of a monomial in $X$ in the bezoutian is performed through a hashtable, the key beeing the monomial in $X$ and the value is the term in $Y$. The hashing functions is computed in the method Monome::Hash. This allows quick insertion and acces to coefficients.