Complex sentence: These monomial symmetric polynomials form a vector space basis: every symmetric polynomial "P" can be written as a linear combination of the monomial symmetric polynomials; to do this it suffices to separate the different types of monomials occurring in "P".
Split into simpler sentences: These monomial symmetric polynomials form a vector space basis: every symmetric polynomial "P" can be written as a linear combination of the monomial symmetric polynomials. To do this it suffices to separate the different types of monomial occurring in "P".