Sparse polynomial

rdf:langString Sparse polynomial

rdf:langString In mathematics, a sparse polynomial (also lacunary polynomial or fewnomial) is a polynomial that has far fewer terms than its degree and number of variables would suggest. Examples include * monomials, polynomials with only one term, * binomials, polynomials with only two terms, and * trinomials, polynomials with only three terms. Research on sparse polynomials has included work on algorithms whose running time grows as a function of the number of terms rather than on the degree, for problems including polynomial multiplication, root-finding algorithms, and polynomial greatest common divisors. Sparse polynomials have also been used in pure mathematics, especially in the study of Galois groups, because it has been easier to determine the Galois groups of certain families of sparse polynomials than it is for other polynomials. The algebraic varieties determined by sparse polynomials have a simple structure, which is also reflected in the structure of the solutions of certain related differential equations.