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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 ...
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. More specifically, it is proportional to the squared volume of the fundamental domain of the ring of integers , and it regulates which primes are ramified .
The character ∂ (Unicode: U+2202) is a stylized cursive d mainly used as a mathematical symbol, usually to denote a partial derivative such as / (read as "the partial derivative of z with respect to x").
The discriminant of a polynomial equation, especially the quadratic equation: [7] [8] =. The area of a triangle = . The symmetric difference of two sets. A macroscopic change in the value of a variable in mathematics or science.
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
By definition, the different ideal δ K is the inverse fractional ideal I −1: it is an ideal of O K. The ideal norm of δ K is equal to the ideal of Z generated by the field discriminant D K of K. The different of an element α of K with minimal polynomial f is defined to be δ(α) = f′(α) if α generates the field K (and zero otherwise ...
Let D be the discriminant of the field, n be the degree of K over , and = be the number of complex embeddings where is the number of real embeddings.Then every class in the ideal class group of K contains an integral ideal of norm not exceeding Minkowski's bound
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.