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Discriminant

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 geometry.

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Overview

Origin

Definition

Low degrees

Properties

Real roots

Use in algebraic geometry

Generalizations

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Map overview Semantic statistics

Discriminant

Nodes165
Edges164
Triples69
Avg. degree1.99
Density0.012121
Components1

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Discriminant

Top relations

related to Use in algebraic geometry · 10
Discriminant → For, In, Let, The, This, Viewing, X-coordinates, X-discriminant, Y-axis, Y-discriminant
related to Low degrees · 8
Discriminant → A007878, For, If, OEIS, Sylvester, The, There, This
is a · 7
Discriminant → determinant, homogeneous polynomial in the coefficients, polynomial in a 0, polynomial in X whose roots are the X-coordinates of the singular points, product of a2 and the square of the difference of the roots.If a, product of the ai, square of a rational number
related to Fundamental discriminants · 5
Discriminant → An, Case, It, Not, The
related to Generalizations · 5
Discriminant → Discriminants, Most, The, There, This
related to Real quadric surfaces · 5
Discriminant → As, Both, Euclidean, Let, The
related to Real roots · 5
Discriminant → For, In, It, Low, More
related to Homogeneity · 4
Discriminant → In, Sylvester, The, This
related to Expression in terms of the roots · 3
Discriminant → If, In, When
related to Invariance under change of the variable · 3
Discriminant → As, Invariance, The

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Important terminology

polynomial displaystyle roots zero degree real coefficients quadratic two field number square may case positive homogeneous form root surface one

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Discriminantis apolynomial in a 00.90text
Discriminantis aproduct of a2 and the square of the difference of the roots.If a0.90text
Discriminantis asquare of a rational number0.90text
Discriminantis ahomogeneous polynomial in the coefficients0.90text
Discriminantis apolynomial in X whose roots are the X-coordinates of the singular points0.90text
Discriminantis aproduct of the ai0.90text
Discriminantis adeterminant0.90text
the functional equation of the Dedekind zeta function of Kinstance ofand occurs in several important analytic formulas0.80text
and the analytic class number formula for Kinstance ofand occurs in several important analytic formulas0.80text
Discriminantrelated to Degree 2The0.60section
Discriminantrelated to Degree 3The0.60section
Discriminantrelated to Degree 3In0.60section

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