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In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a polynomial function of the coefficients of the original polynomial. The discriminant is widely used in polynomial factoring, number theory, and algebraic ...
Each coordinate of the intersection points of two conic sections is a solution of a quartic equation. The same is true for the intersection of a line and a torus.It follows that quartic equations often arise in computational geometry and all related fields such as computer graphics, computer-aided design, computer-aided manufacturing and optics.
The discriminant of a polynomial is a quantity that depends on the coefficients and determines various properties of the roots. Discriminant may also refer to its various generalizations: Mathematics
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.
The discriminant of K is 49 = 7 2. Accordingly, the volume of the fundamental domain is 7 and K is only ramified at 7. In mathematics, the discriminant of an algebraic number field is a numerical invariant that, loosely speaking, measures the size of the (ring of integers of the) algebraic number field.
The Vietnamese Wikipedia initially went online in November 2002, with a front page and an article about the Internet Society.The project received little attention and did not begin to receive significant contributions until it was "restarted" in October 2003 [3] and the newer, Unicode-capable MediaWiki software was installed soon after.
Sóc Trăng (362,029 people, constituting 30.18% of the province's population and 27.43% of all Khmer in Vietnam), Trà Vinh (318,231 people, constituting 31.53% of the province's population and 24.11% of all Khmer in Vietnam), Kiên Giang (211,282 people, constituting 12.26% of the province's population and 16.01% of all Khmer in Vietnam), An ...
Linear discriminant analysis (LDA), normal discriminant analysis (NDA), canonical variates analysis (CVA), 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 ...