let be an interval. a polynomial on is a function of the form , where is an integer and are real numbers. if , then is called the degree of .
fix a field , and let be variables taking values in this field. a (multilinear) monomial is a product of variables, where ; we assume that . the degree of this monomial is the cardinality of . a multilinear polynomial of variables is a function that can be written as for some coefficients . the degree of is the degree of its largest monomial: .