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Quintic function

Index Quintic function

In algebra, a quintic function is a function of the form where,,,, and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero. [1]

64 relations: Abel–Ruffini theorem, Abraham de Moivre, Algebra, Algebraic expression, Angular velocity, Arthur Cayley, Évariste Galois, Bring radical, Carl David Tolmé Runge, Casus irreducibilis, Charles Hermite, Complex number, Cubic function, Daniel Lazard, Degree of a polynomial, Derivative, Earth, Elliptic function, Factorization, Felix Klein, Field (mathematics), Francesco Brioschi, Function (mathematics), Gaia (spacecraft), Galois group, Galois theory, Generalized hypergeometric function, George Jerrard, Golden ratio, Gravitational constant, Group theory, Icosahedron, Irreducible polynomial, J-invariant, Jörg Bewersdorff, Joseph-Louis Lagrange, Lagrangian point, Leopold Kronecker, Linear equation, Linear function, List of objects at Lagrangian points, Maxima and minima, Nested radical, Nth root, Polynomial, Quadratic equation, Quadratic function, Quartic function, Ragni Piene, Rational number, ..., Real number, Resolvent (Galois theory), Root of unity, Semi-major and semi-minor axes, Septic equation, Sextic equation, Solar and Heliospheric Observatory, Solvable group, Sun, Symmetric group, Theory of equations, Theta function, Trigonometric functions, Tschirnhaus transformation. Expand index (14 more) »

Abel–Ruffini theorem

In algebra, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no algebraic solution—that is, solution in radicals—to the general polynomial equations of degree five or higher with arbitrary coefficients.

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Abraham de Moivre

Abraham de Moivre (26 May 166727 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory.

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Algebra

Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

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Algebraic expression

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).

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Angular velocity

In physics, the angular velocity of a particle is the rate at which it rotates around a chosen center point: that is, the time rate of change of its angular displacement relative to the origin.

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Arthur Cayley

Arthur Cayley F.R.S. (16 August 1821 – 26 January 1895) was a British mathematician.

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Évariste Galois

Évariste Galois (25 October 1811 – 31 May 1832) was a French mathematician.

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Bring radical

In algebra, the Bring radical or ultraradical of a real number a is the unique real root of the polynomial The Bring radical of a complex number a is either any of the five roots of the above polynomial (it is thus multi-valued), or a specific root, which is usually chosen in order that the Bring radical is a function of a, which is real-valued when a is real, and is an analytic function in a neighborhood of the real line.

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Carl David Tolmé Runge

Carl David Tolmé Runge (30 August 1856 – 3 January 1927) was a German mathematician, physicist, and spectroscopist.

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Casus irreducibilis

In algebra, casus irreducibilis (Latin for "the irreducible case") is one of the cases that may arise in attempting to solve a cubic equation with integer coefficients with roots that are expressed with radicals.

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Charles Hermite

Prof Charles Hermite FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Cubic function

In algebra, a cubic function is a function of the form in which is nonzero.

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Daniel Lazard

Daniel Lazard (born December 10, 1941) is a French mathematician and computer scientist.

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Degree of a polynomial

The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.

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Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

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Earth

Earth is the third planet from the Sun and the only astronomical object known to harbor life.

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Elliptic function

In complex analysis, an elliptic function is a meromorphic function that is periodic in two directions.

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Factorization

In mathematics, factorization (also factorisation in some forms of British English) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

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Felix Klein

Christian Felix Klein (25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group theory.

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Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

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Francesco Brioschi

Francesco Brioschi (22 December 1824 – 13 December 1897) was an Italian mathematician.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Gaia (spacecraft)

Gaia is a space observatory of the European Space Agency (ESA) designed for astrometry: measuring the positions and distances of stars with unprecedented precision.

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Galois group

In mathematics, more specifically in the area of abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension.

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Galois theory

In the field of algebra within mathematics, Galois theory, provides a connection between field theory and group theory.

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Generalized hypergeometric function

In mathematics, a generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by analytic continuation.

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George Jerrard

George Birch Jerrard (25 November 1804 – 23 November 1863) was a British mathematician.

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Golden ratio

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

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Gravitational constant

The gravitational constant (also known as the "universal gravitational constant", the "Newtonian constant of gravitation", or the "Cavendish gravitational constant"), denoted by the letter, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general theory of relativity.

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Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.

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Icosahedron

In geometry, an icosahedron is a polyhedron with 20 faces.

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Irreducible polynomial

In mathematics, an irreducible polynomial is, roughly speaking, a non-constant polynomial that cannot be factored into the product of two non-constant polynomials.

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J-invariant

In mathematics, Felix Klein's j-invariant or j function, regarded as a function of a complex variable τ, is a modular function of weight zero for defined on the upper half-plane of complex numbers.

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Jörg Bewersdorff

Jörg Bewersdorff (born 1 February 1958 in Neuwied) is a German mathematician who is working as mathematics writer and game designer.

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Joseph-Louis Lagrange

Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.

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Lagrangian point

In celestial mechanics, the Lagrangian points (also Lagrange points, L-points, or libration points) are positions in an orbital configuration of two large bodies, wherein a small object, affected only by the gravitational forces from the two larger objects, will maintain its position relative to them.

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Leopold Kronecker

Leopold Kronecker (7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, algebra and logic.

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Linear equation

In mathematics, a linear equation is an equation that may be put in the form where x_1, \ldots, x_n are the variables or unknowns, and c, a_1, \ldots, a_n are coefficients, which are often real numbers, but may be parameters, or even any expression that does not contain the unknowns.

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Linear function

In mathematics, the term linear function refers to two distinct but related notions.

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List of objects at Lagrangian points

This is a list of known objects which occupy, have occupied, or are planned to occupy any of the five Lagrangian points of two-body systems in space.

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Maxima and minima

In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).

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Nested radical

In algebra, a nested radical is a radical expression (one containing a square root sign, cube root sign, etc.) that contains (nests) another radical expression.

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Nth root

In mathematics, an nth root of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yields x: where n is the degree of the root.

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Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

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Quadratic equation

In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where represents an unknown, and,, and represent known numbers such that is not equal to.

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Quadratic function

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function in one or more variables in which the highest-degree term is of the second degree.

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Quartic function

In algebra, a quartic function is a function of the form where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.

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Ragni Piene

Ragni Piene (born 18 January 1947, Oslo) is a Norwegian mathematician, specializing in algebraic geometry, with particular interest in enumerative results and intersection theory.

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Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Resolvent (Galois theory)

In Galois theory, a discipline within the field of abstract algebra, a resolvent for a permutation group G is a polynomial whose coefficients depend polynomially on the coefficients of a given polynomial p and has, roughly speaking, a rational root if and only if the Galois group of p is included in G. More exactly, if the Galois group is included in G, then the resolvent has a rational root, and the converse is true if the rational root is a simple root.

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Root of unity

In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that gives 1 when raised to some positive integer power.

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Semi-major and semi-minor axes

In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the widest points of the perimeter.

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Septic equation

In algebra, a septic equation is an equation of the form where.

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Sextic equation

In algebra, a sextic polynomial is a polynomial of degree six.

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Solar and Heliospheric Observatory

The Solar and Heliospheric Observatory (SOHO) is a spacecraft built by a European industrial consortium led by Matra Marconi Space (now Astrium) that was launched on a Lockheed Martin Atlas II AS launch vehicle on December 2, 1995, to study the Sun, and has discovered over 3000 comets.

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Solvable group

In mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions.

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Sun

The Sun is the star at the center of the Solar System.

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Symmetric group

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.

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Theory of equations

In algebra, the theory of equations is the study of algebraic equations (also called “polynomial equations”), which are equations defined by a polynomial.

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Theta function

In mathematics, theta functions are special functions of several complex variables.

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Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

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Tschirnhaus transformation

In mathematics, a Tschirnhaus transformation, also known as Tschirnhausen transformation, is a type of mapping on polynomials developed by Ehrenfried Walther von Tschirnhaus in 1683.

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5th degree, 5th order, Bring-Gerrard normal form, De Moivre quintic, FIfth degree equation, Fifth-degree equation, General equation of the fifth degree, General quintic equation, Insolvability of the Quintic, Quintic, Quintic equation, Quintic functions, Quintic polynomial, Quintic polynomial equation, Solve quintic equation in general form, Y=ax5+bx4+cx3+dx2+ex+f, Y=ax^5+bx^4+cx^3+dx^2+ex+f.

References

[1] https://en.wikipedia.org/wiki/Quintic_function

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