Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Resultant

In mathematics, the resultant of two polynomials is a polynomial expression of their coefficients that is equal to zero if and only if the polynomials have a common root (possibly in a field extension), or, equivalently, a common factor (possibly in a field extension as well). In some older texts, the resultant is also called the eliminant.

Applications, Properties & Other applications

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Resultant. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Notation

Definition

Properties

Computation

Application to polynomial systems

Other applications

Homogeneous resultant

Macaulay's resultant

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Resultant

Nodes123
Edges122
Triples101
Avg. degree1.98
Density0.01626
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Resultant

Top relations

is a · 10
Resultant → determinant of the matrix over the monomial basis of the linear map, fundamental tool in computer algebra, greatest common divisor which becomes 1, polynomial in the coefficients of these n homogeneous polynomials that vanishes if and only if the polynomials have a common non-zero solution in an algebraically closed field c…, polynomial of very high degree, power of the minimal polynomial of β, result of the, resultant of the n polynomials P 1, symmetric function of the roots of each polynomial, unique function of the coefficients of two polynomials that satisfies these properties.If R is a subring of another ring S
related to Definition · 10
Resultant → AP, BQ, For, If, In, Let, More, Sylvester, The, This
related to Homogeneous resultant · 7
Resultant → AP, BQ, Given, In, Res, That, The
related to Macaulay's resultant · 7
Resultant → Francis Sowerby Macaulay, Gröbner, However, It, Like, Macaulay's, The
related to Zeros · 7
Resultant → AP, BQ, Bézout's, In, The, There, This
related to Computation · 6
Resultant → As, Bézout, However, Sylvester, Theoretically, This
related to Characterizing properties · 5
Resultant → AB, If, Similarly, That, The
related to Generic properties · 5
Resultant → If, In, It, Let, The
related to Homogeneity · 5
Resultant → If, It, More, Notation, The
related to U-resultant · 5
Resultant → Given, Macaulay, Macaulay's, Notation, U-resultant

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

displaystyle polynomials res degree polynomial operatorname homogeneous coefficients two zero degrees ldots common field may one indeterminates number macaulay defined

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Resultantis aunique function of the coefficients of two polynomials that satisfies these properties.If R is a subring of another ring S0.90text
Resultantis asymmetric function of the roots of each polynomial0.90text
Resultantis apower of the minimal polynomial of β0.90text
Resultantis afundamental tool in computer algebra0.90text
Resultantis adeterminant of the matrix over the monomial basis of the linear map0.90text
Resultantis apolynomial in the coefficients of these n homogeneous polynomials that vanishes if and only if the polynomials have a common non-zero solution in an algebraically closed field c…0.90text
Resultantis agreatest common divisor which becomes 10.90text
Resultantis apolynomial of very high degree0.90text
Resultantis aresult of the0.90text
Resultantis aresultant of the n polynomials P 10.90text
Resultantrelated to Algebraic geometryGiven0.60section
Resultantrelated to Algebraic geometryMore0.60section

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.