Height of a polynomial
From Infogalactic: the planetary knowledge core
In mathematics, the height and length of a polynomial P with complex coefficients are measures of its "size".
For a polynomial P of degree n given by
the height H(P) is defined to be the maximum of the magnitudes of its coefficients:
- Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): H(P) = \underset{i}{\max} \,|a_i| \,
and the length L(P) is similarly defined as the sum of the magnitudes of the coefficients:
The Mahler measure M(P) of P is also a measure of the size of P. The three functions H(P), L(P) and M(P) are related by the inequalities
- Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \binom{n}{\lfloor n/2 \rfloor}^{-1} H(P) \le M(P) \le H(P) \sqrt{n+1} ;
where Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \scriptstyle \binom{n}{\lfloor n/2 \rfloor}
is the binomial coefficient.
References
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External links
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