polynomial
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 
.
[cite:;taken from @tao_analysis_2 definition 3.8.1]
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 .[cite:;taken from @tao_analysis_2 definition 3.8.1]
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: 
.
[cite:;taken from @complexity_jukna_2012 chapter 2.1 boolean functions as polynomials]
, 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: .[cite:;taken from @complexity_jukna_2012 chapter 2.1 boolean functions as polynomials]