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One of the reasons Gauss's composition law is so important is that it provides information about quadratic number fields.
Artin's early work centred on the analytical and arithmetic theory of quadratic number fields.
In particular, one can use the geometry of numbers to show that, for discriminant with absolute value less than X, there are approximately X quadratic number fields.
A number field is built by extending the rational numbers to include non-rational roots of a polynomial; if the polynomial is quadratic, then one obtains a quadratic number field.
If one has a quadratic polynomial, counting the number of integer lattice points in a certain region of 3-dimensional space provides information about the associated quadratic number field.
For instance, if patterns to memorize contain many zeros, it is possible to store nearly a quadratic number [11].
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And since the discriminant of the polynomial (yz^{2}-2(f^{2}-g^{2} z+yinmathbb{Z}[z]) is equal to (-16f^{2}g^{2}), we see that α is a quadratic algebraic number, α and (alpha^{-1}) are its whole conjugate numbers.
The size of signing key in the proposed schemes is quadratic in number of attributes.
A diploid individual requires two sets of latent states (one for each haplotype), and, consequently, fitting a two-layer model is quadratic in number of haplotype clusters (Guan 2014).
We included nine variables in the Assessment of Different NEoplasias in the adneXa (ADNEX) model: age, serum CA-125 level (log transformed), type of centre, maximum diameter of the lesion (log transformed), proportion of solid tissue (with quadratic term), number of papillary projections, more than 10 cyst locules, acoustic shadows, and ascites.
Ped-IBD shows a time complexity pattern linear to marker numbers and quadratic to the number of typed individuals.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com