Height of a polynomial
Encyclopedia
In mathematics
, the height and length of a polynomial P with complex coefficients are measures of its "size".
For a polynomial
P given by
the height H(P) is defined to be the maximum of the magnitudes of its coefficients:
and the length L(P) is similarly defined as the sum of the magnitudes of the coefficients:
For a complex polynomial P of degree n, the height H(P), length L(P) and Mahler measure M(P) are related by the double inequalities
where
is the binomial coefficient
.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the height and length of a polynomial P with complex coefficients are measures of its "size".
For a polynomial
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
P given by
the height H(P) is defined to be the maximum of the magnitudes of its coefficients:
and the length L(P) is similarly defined as the sum of the magnitudes of the coefficients:
For a complex polynomial P of degree n, the height H(P), length L(P) and Mahler measure M(P) are related by the double inequalities
where
is the binomial coefficientBinomial coefficient
In mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem. They are indexed by two nonnegative integers; the binomial coefficient indexed by n and k is usually written \tbinom nk , and it is the coefficient of the x k term in...
.