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Then the discriminant is the product of the a i, which is well-defined as a class in K/(K ×) 2. Geometrically, the discriminant of a quadratic form in three variables is the equation of a quadratic projective curve. The discriminant is zero if and only if the curve is decomposed in lines (possibly over an algebraically closed extension of the ...
An integral basis is given by {1, α, α(α + 1)/2} and the discriminant of K is −503. [5] [6] Repeated discriminants: the discriminant of a quadratic field uniquely identifies it, but this is not true, in general, for higher-degree number fields. For example, there are two non-isomorphic cubic fields of discriminant 3969.
The symbolic representation of the discriminant is = where a and b are the symbols. The meaning of the expression (ab) 2 is as follows. First of all, (ab) is a shorthand form for the determinant of a matrix whose rows are a 1, a 2 and b 1, b 2, so
The following table shows some orders of small discriminant of quadratic fields. The maximal order of an algebraic number field is its ring of integers, and the discriminant of the maximal order is the discriminant of the field. The discriminant of a non-maximal order is the product of the discriminant of the corresponding maximal order by the ...
For this converse the field discriminant is needed. This is the Dedekind discriminant theorem. In the example above, the discriminant of the number field () with x 3 − x − 1 = 0 is −23, and as we have seen the 23-adic place ramifies. The Dedekind discriminant tells us it is the only ultrametric place that does.
Even as mortgage rates stay in the high-6% range, applications to purchase a new home rose 2% from a week earlier, snapping several weeks of declines, according to the Mortgage Bankers Association.
Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events.
Image credits: Old-time Photos To learn more about the fascinating world of photography from the past, we got in touch with Ed Padmore, founder of Vintage Photo Lab.Ed was kind enough to have a ...
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