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Polynomial function of degree 4
derivative of a quartic function is a cubic function. Sometimes the term biquadratic is used instead of quartic, but, usually, biquadratic function refers to
Quartic_function
Polynomial equation of degree 4
In mathematics, a quartic equation is one which can be expressed as a quartic function equaling zero. The general form of a quartic equation is ax4+bx3+cx2+dx+e=0
Quartic_equation
Topics referred to by the same term
of the following: Quartic function, a polynomial function of degree 4 Quartic equation, a polynomial equation of degree 4 Quartic curve, an algebraic
Quartic
Compact Riemann surface of genus 3
simple group after the alternating group A5. The quartic was first described in (Klein 1878b). Klein's quartic occurs in many branches of mathematics, in contexts
Klein_quartic
straight line. Quadratic function: Second degree polynomial, graph is a parabola. Cubic function: Third degree polynomial. Quartic function: Fourth degree polynomial
List of mathematical functions
List_of_mathematical_functions
Plane algebraic curve defined by a 4th-degree polynomial
algebraic geometry, a plane quartic curve is a plane algebraic curve of the fourth degree. It can be defined by a bivariate quartic equation: A x 4 + B y 4
Plane_quartic_curve
Symbol representing a mathematical object
number, but has been used to denote an unassigned coefficient for quartic function and higher degree polynomials. Even the symbol 1 has been used to denote
Variable_(mathematics)
Extension of the factorial function
gamma function, denoted by Γ {\displaystyle \Gamma } (capital Greek letter gamma), is the most common extension of the factorial function to complex
Gamma_function
Polynomial equation of degree 5
and one additional local minimum. The derivative of a quintic function is a quartic function. Solving quintic equations in terms of radicals (nth roots)
Quintic_equation
Function used as a performance test problem for optimization algorithms
are roots of quartic polynomials, when written in terms of radicals, the expressions are somewhat complicated.[citation needed] The function is named after
Himmelblau's_function
Polynomial equation of degree 6
sextic function is a function defined by a sextic polynomial. Because they have an even degree, sextic functions appear similar to quartic functions when
Sextic_equation
Polynomial function: defined by evaluating a polynomial. Linear function; also affine function. Quadratic function Cubic function Quartic function Quintic
List_of_types_of_functions
Polynomial equation of degree 3
points of a quartic function are found by solving a cubic equation (the derivative set equal to zero). Inflection points of a quintic function are the solution
Cubic_equation
Polynomial equation of degree two
ex-tangential quadrilateral. Critical points of a cubic function and inflection points of a quartic function are found by solving a quadratic equation. In chemistry
Quadratic_equation
In mathematics, the Burkhardt quartic is a quartic threefold in 4-dimensional projective space studied by Burkhardt (1890, 1891, 1892), with the maximum
Burkhardt_quartic
Polynomial function of degree 3
related to Cubic functions. "Cardano formula", Encyclopedia of Mathematics, EMS Press, 2001 [1994] History of quadratic, cubic and quartic equations on MacTutor
Cubic_function
Mathematical relation consisting of a multi-variable function equal to zero
the multi-valued implicit function. While explicit solutions can be found for equations that are quadratic, cubic, and quartic in y, the same is not in
Implicit_function
Mathematical concept
"linear", "quadratic", "cubic", "quartic", and "quintic". (p. 107) King (2009) defines "quadratic", "cubic", "quartic", "quintic", "sextic", "septic",
Degree_of_a_polynomial
Type of mathematical expression
For higher degrees, the specific names are not commonly used, although quartic polynomial (for degree four) and quintic polynomial (for degree five) are
Polynomial
Polynomial equation of degree 7
symmetric functions of the sides of the pentagon. The same is true of the square of the area of a cyclic hexagon. Cubic function Quartic function Quintic
Septic_equation
Automorphism group of the Klein quartic
multiplication tables. The Klein quartic is the projective variety over the complex numbers C defined by the quartic polynomial x3y + y3z + z3x = 0. It
PSL(2,7)
Special functions of several complex variables
Nullwert function values from the cube root of the elliptic nome are obtained by contrasting the two real solutions of the corresponding quartic equations:
Theta_function
Quantum field theory with four-point interactions
quantum field theory, a quartic interaction or φ4 theory is a type of self-interaction of a scalar field. Other types of quartic interactions may be found
Quartic_interaction
Geometric relation between the roots of a polynomial and those of its derivative
formed by the zeros of P. For a fourth degree complex polynomial P (quartic function) with four distinct zeros forming a concave quadrilateral, one of the
Gauss–Lucas_theorem
function Homogeneous polynomial Polynomial SOS (sum of squares) Polynomial family Quadratic function Cubic function Quartic function Quintic function
List_of_polynomial_topics
Book by Jordan Ellenberg
other mathematical concepts, including the Null hypothesis and the Quartic function. He explains how underpowered statistical studies can lead to misleading
How_Not_to_Be_Wrong
Types of harmonic structures in music
In music, quartal harmony is the building of harmonic structures from the intervals of the perfect fourth, the augmented fourth, and the diminished fourth
Quartal_and_quintal_harmony
Mathematical functions
is a quartic analog of the (quadratic) π = {\displaystyle \pi =} 3.141592..., ratio of perimeter to diameter of a circle. As complex functions, sl and
Lemniscate_elliptic_functions
Integral of the Gaussian function, equal to sqrt(π)
convergence. For example, the solution to the integral of the exponential of a quartic polynomial is[citation needed] ∫ − ∞ ∞ e a x 4 + b x 3 + c x 2 + d x +
Gaussian_integral
Function of a polynomial's coefficients that gives information about its roots
degrees, it may become unwieldy. For example, the discriminant of a general quartic has 16 terms, that of a quintic has 59 terms, and that of a sextic has
Discriminant
Transformation of a polynomial induced by a transformation of its roots
examples of this, see Cubic function § Reduction to a depressed cubic or Quartic function § Converting to a depressed quartic. All preceding examples are
Polynomial_transformation
Concept in statistics
appropriate for the data. Several types of kernel functions are commonly used: uniform, triangle, Epanechnikov, quartic (biweight), tricube, triweight, Gaussian
Kernel_(statistics)
Italian theoretical physicist (1931–2014)
furniture manufacturer Gufram, for whom he "transformed a mathematical quartic function into a volume with intentionally ergonomic characteristics" to create
Tullio_Regge
Figure-eight-shaped curve
ribbons were made. Curves that have been called a lemniscate include three quartic plane curves: the hippopede or lemniscate of Booth, the lemniscate of Bernoulli
Lemniscate
Polynomial without nontrivial factorization
Factorization of polynomials over finite fields Quartic function § Reducible quartics Cubic function § Factorization Casus irreducibilis, the irreducible
Irreducible_polynomial
Algorithm for division of polynomials
it can be factored out to obtain a quartic (fourth degree) quotient; the explicit formula for the roots of a quartic polynomial can then be used to find
Polynomial_long_division
Modular function in mathematics
In mathematics, the j-invariant or j function is a modular function of weight zero for the special linear group SL ( 2 , Z ) {\displaystyle \operatorname
J-invariant
Mathematical formula involving a given set of operations
expressions in radicals for all solutions of cubic equations (degree 3) and quartic equations (degree 4). The size of these expressions increases significantly
Closed-form_expression
Number-theoretical function
In number theory, the sum of squares function is an arithmetic function that gives the number of representations for a given positive integer n {\displaystyle
Sum_of_squares_function
Special function defined by an integral
is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an exponential function and its argument
Exponential_integral
Number, approximately 3.14
positive number at which the cosine function equals 0. π is also the smallest positive number at which the sine function equals zero, and the difference between
Pi
Canadian-American mathematician (born 1974)
other situations. One major use of his results is the parametrization of quartic and quintic orders in number fields, thus allowing the study of the asymptotic
Manjul_Bhargava
Formula for solving a quadratic equation
This method can be generalized to give the roots of cubic polynomials and quartic polynomials, and leads to Galois theory, which allows one to understand
Quadratic_formula
Quartic potential in quantum mechanics
type of possible quartic potential is that of asymmetric shape of one of the first two named above. The double-well and other quartic potentials can be
Double-well_potential
Symbol representing the word "and" (&)
operator is exclusively used on Boolean types. Ampersand curve – Type of quartic plane curve And (disambiguation) Heta – Archaic letter in the Greek alphabet
Ampersand
Concept in mathematical invariant theory
} The catalecticant of a quartic form is the resultant of its second partial derivatives. For binary quartics the catalecticant vanishes when the
Catalecticant
Italian furniture company
theoretical physicist Tullio Regge, who "transformed a mathematical quartic function into a volume with intentionally ergonomic characteristics" for the
Gufram
Function of propagation delay and Doppler frequency
Maio, Bo Jiang, and Shuzhong Zhang. "Ambiguity function shaping for cognitive radar via complex quartic optimization." IEEE Transactions on Signal Processing
Ambiguity_function
Natural number, composite number
nine others only tile the plane alongside irregular polygons. The Klein quartic is a compact Riemann surface of genus 3 that has the largest possible automorphism
14_(number)
28 lines which touch a general quartic plane curve in two places
explicit quartic with twenty-eight real bitangents was first given by Plücker (1839). As Plücker showed, the number of real bitangents of any quartic must
Bitangents_of_a_quartic
Statistic which divides data into four same-sized parts for analysis
function QUARTILE.INC(array, quart) provides the desired quartile value for a given array of data, using Method 3 from above. The QUARTILE function is
Quartile
Irreducible nodal surface
on a quartic is 16, and in this case they are all simple nodes (to show that p {\displaystyle p} is simple project from another node). A quartic which
Kummer_surface
Algorithm to smooth data points
central coefficient. Smoothing of a function leaves the area under the function unchanged. Convolution of a symmetric function with even-derivative coefficients
Savitzky–Golay_filter
Mathematical function
In mathematics, the prime zeta function is an analogue of the Riemann zeta function, studied by Glaisher (1891). It is defined as the following infinite
Prime_zeta_function
_{n}}{2n}}.} The quartic n = 4 {\displaystyle n=4} case results in a square lattice in the complex plane, related to the lemniscate elliptic functions. The Dixon
Dixon_elliptic_functions
Fortified gate in València, Spain
torn down in 1865, but Torres de Quart, along with another gate, the Torres de Serranos, survived thanks to their functions as prisons. Additional cannon
Torres_de_Quart
Real root of the polynomial x^5+x+a
{\displaystyle \tau } ) of (*) is a solution of the quartic but not every solution of the quartic is a solution of (*). The roots of the Bring–Jerrard
Bring_radical
Type of plane curve
the first one. See diagram.) For a curve given in polar coordinates by a function r(φ) the following connection to Cartesian coordinates hold: x(φ)=r(φ)cosφ
Cardioid
Solution in radicals of a polynomial equation
ax^{2}+bx+c=0.} There exist algebraic solutions for cubic equations and quartic equations, which are more complicated than the quadratic formula. The Abel–Ruffini
Solution_in_radicals
Function whose composition with the logarithm is convex
of positive matrices. Quart. J. Math. Oxford (2) 12,283-284. Montel 1928. NiculescuPersson 2006, p. 70. John B. Conway. Functions of One Complex Variable
Logarithmically convex function
Logarithmically_convex_function
Concept in statistics
density estimation is implemented using five different kernel functions – normal, uniform, quartic, negative exponential, and triangular. Both single- and dual-kernel
Kernel_density_estimation
Algebraic variety
60 isomorphic to A5 and PSL(2, 5). The modular curve X(7) is the Klein quartic of genus 3 with 24 cusps. It can be interpreted as a surface with three
Modular_curve
Mathematical concept
if they are non-singular, elliptic curves. Those of degree 4 are called quartic plane curves. Numerous examples of plane curves are shown in Gallery of
Plane_curve
Swiss mathematician (1707–1783)
theory of higher transcendental functions by introducing the gamma function and introduced a new method for solving quartic equations. He found a way to
Leonhard_Euler
1552 novel by François Rabelais
Le Quart Livre (The Fourth Book in English) is a novel by François Rabelais and published in its final version in 1552. The author was confronted with
Le_Quart_Livre
Coupling constant divergence at high energies
such as quantum electrodynamics (QED) or φ4 theory—a scalar field with a quartic interaction—such as ones that may describe the Higgs boson. In these theories
Landau_pole
Boson with spin equal to zero
scalar bosons, e.g. the alpha particle and scalar mesons. The φ4-theory or quartic interaction is a popular "toy model" quantum field theory that uses scalar
Scalar_boson
British-American mathematician
Equations, Report of the British Association. 1914: (dissertation) The Quartic Curve and its Inscribed Configurations, American Journal of Mathematics
Harry_Bateman
Algebraic curve
quartic Fermat curve x 4 + y 4 = 1 {\displaystyle x^{4}+y^{4}=1} , the hyperbolic lemniscate sine is analogous to the trigonometric tangent function.
Fermat_curve
Curve used in computer graphics and related fields
point to the end point. A quadratic Bézier curve is the path traced by the function B(t), given points P0, P1, and P2, B ( t ) = ( 1 − t ) [ ( 1 − t ) P 0
Bézier_curve
Class of quartic plane curves
In geometry, a Cassini oval is a quartic plane curve defined as the locus of points in the plane such that the product of the distances to two fixed points
Cassini_oval
Optimization algorithm
multivariate function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current
Gradient_descent
Sum in algebraic number theory
sums can be used to prove quadratic reciprocity, cubic reciprocity, and quartic reciprocity. Gauss sums can be used to calculate the number of solutions
Gauss_sum
One-dimensional complex manifold
surface, with order 48. For genus 3 the order is maximized by the Klein quartic, with order 168; this is the first Hurwitz surface, and its automorphism
Riemann_surface
Trident curve Trisectrix of Maclaurin Tschirnhausen cubic Witch of Agnesi Quartic plane curves include Ampersand curve Bean curve Bicorn Bow curve Bullet-nose
List_of_curves
Polynomial equation, generally univariate
quasi-palindromic (e = a, d = b). Some cubic and quartic equations can be solved using trigonometry or hyperbolic functions. Évariste Galois and Niels Henrik Abel
Algebraic_equation
Mathematical puzzle
reduced to the quartic equation x3(x − c) − 1 = 0, which can be solved by approximation methods, as suggested by Gardner, or the quartic may be solved
Crossed_ladders_problem
British mathematician (1854–1930)
Company. Alfred B. Basset (1901). An elementary treatise on cubic and quartic curves. Deighton, Bell and Company. Alfred B. Basset (1910). A treatise
Alfred_Barnard_Basset
Indian mathematician (1887–1920)
equations in 1902. He would later develop his own method to solve the quartic. In 1903, he tried to solve the quintic, not knowing that it was impossible
Srinivasa_Ramanujan
2011 edition of the C++ programming language standard
0> { // ''N == 0'' condition of termination. enum { VALUE = 1 }; }; int quartic_of_three = Power<3, 4>::VALUE; Many algorithms can operate on different
C++11
Town and municipality in Valencian Community, Spain
Quart de Poblet, in Valencian (Spanish and unofficially: Cuart de Poblet), or simply Quart (Spanish: Cuart), is a municipality in the comarca of Horta
Quart_de_Poblet
Cubic polynomials defined from a monic polynomial of degree four
some cases, the concept of resolvent cubic is defined only when P(x) is a quartic in depressed form—that is, when a3 = 0. Note that the fourth and fifth
Resolvent_cubic
Counterintuitive mathematical object
in the 16th century in order to find the roots of cubic and quartic polynomial functions. Some number fields have rings of integers that do not form a
Pathological_(mathematics)
Three notes in intervals of a third
scale to which it corresponds, primarily determine its function. Secondarily, a triad's function is determined by its quality: major, minor, diminished
Triad_(music)
Square root of a non-positive real number
and zeta function applications. Horwood. p. 1. ISBN 978-1-904275-25-1. Corry, Leo (2026-04-24). "Cardano and the solving of cubic and quartic equations"
Imaginary_number
Probability distribution
3 and β = 2, median = 0.6142724318676105..., the real solution to the quartic equation 1 − 8x3 + 6x4 = 0, which lies in [0,1]. For α = 2 and β = 3, median
Beta_distribution
Mathematical function defined piecewise by polynomials
In mathematics, a spline is a function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial
Spline_(mathematics)
Mathematical test in control system theory
means that w(+∞)−w(−∞)=2 (the degree of f). By the properties of the function w, this is the same as w(+∞)=2 and w(−∞)=0. Thus, a,b and c must
Routh–Hurwitz stability criterion
Routh–Hurwitz_stability_criterion
Physical substance of the human organism
Physiology focuses on the systems and organs of the human body and their functions. Many systems and mechanisms interact in order to maintain homeostasis
Human_body
Medical condition caused by receiving too little or too many nutrients
micronutrient deficiencies. It adversely affects physical and mental functioning, and causes changes in body composition and body cell mass. Undernutrition
Malnutrition
Country in Europe
two countries resulting in Atlanticism. Germany's development policy functions as a distinct sector within its foreign policy framework. It is formulated
Germany
Topics referred to by the same term
Quadratic reciprocity, a theorem about modular arithmetic Cubic reciprocity Quartic reciprocity Artin reciprocity Weil reciprocity for algebraic curves Frobenius
Reciprocity_theorem
Plane algebraic curve
Because the curve is of genus zero, it can be parametrized by rational functions; one means of doing that is x = t 2 − 1 t 2 + 1 , y = 2 t ( t 2 − 1
Lemniscate_of_Gerono
Number with a real and an imaginary part
in the 16th century when algebraic solutions for the roots of cubic and quartic polynomials were discovered by Italian mathematicians (Niccolò Fontana
Complex_number
Plane algebraic curve
Solved for y 2 {\displaystyle \textstyle y^{2}} as a function of x {\displaystyle x} : y 2 = ( 8 x 2 + a 2 − a ) a 2 − x 2 {\displaystyle
Lemniscate_of_Bernoulli
Function in number theory
n}{p}}\right)}}.} Using certain elliptic functions instead of the sine function, Eisenstein was able to prove cubic and quartic reciprocity as well. The Jacobi
Legendre_symbol
Energy difference between ground state and lightest excited state(s)
to gauge freedom. Quantization preserves this gauge freedom property. A quartic massless scalar field theory develops a mass gap already at classical level[clarification
Mass_gap
Wigner distribution function in physics as opposed to in signal processing
The Wigner quasiprobability distribution, also called the Wigner function or the Wigner–Ville distribution, after Eugene Wigner and Jean-André Ville, is
Wigner quasiprobability distribution
Wigner_quasiprobability_distribution
Mathematical formula expressing equality
parabolas, ellipses, hyperbolas, cubic curves like elliptic curves and quartic curves like lemniscates, and Cassini ovals. A point of the plane belongs
Equation
Sporadic simple group
generation. M24 can be constructed starting from the symmetries of the Klein quartic (the symmetries of a tessellation of the genus three surface), which is
Mathieu_group_M24
travel, tourism, insurance
QUARTIC FUNCTION
QUARTIC FUNCTION
Biblical
fourth
Female
Chinese
blue glitter, or blue quartz.
Male
Hebrew
Variant spelling of Hebrew Yamiyn, YAMIN means "the right hand," "the right side," or "the right quarter."
Boy/Male
Latin Biblical
Born fourth.
Girl/Female
Assamese, Greek, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu, Traditional
Polite; Born in the First Quarter of the Day
Male
Hebrew
(יָמִין) Hebrew name YAMIYN means "the right hand," "the right side," or "the right quarter." In the bible, this is the name of several characters, including a son of Simeon. The English form is Jamin.
Girl/Female
Muslim
Quarter Moon
Girl/Female
Arabic, Hindu, Indian, Muslim
Quarter Moon
Female
English
English name derived from Latin candida, CANDIDA means "clear and white,"Â like pure quartz rather than the whiteness of milk. George Bernard Shaw used this name for his 1895 play of the same name.
Boy/Male
Spanish
Born fourth.
Girl/Female
Hindu
The Goddess who is quarter of the world
Girl/Female
Bengali, Hindu, Indian, Tamil
Peaceful; Born in the First Quarter of an Astrological Day
Male
English
Anglicized form of Hebrew Yamiyn, JAMIN means "the right hand," "the right side," or "the right quarter." In the bible, this is the name of several characters, including a son of Simeon.
Girl/Female
Tamil
The Goddess who is quarter of the world
Surname or Lastname
English (West Midlands)
English (West Midlands) : patronymic from Firkin, a metonymic occupational name for a maker of casks and barrels, or a nickname for a stout man or a heavy drinker, from Middle English fer(de)kyn ‘small cask’ (probably from a Middle Dutch diminutive of vierde ‘fourth (part)’; as a measure of capacity a firkin was reckoned as a quarter of a barrel).
Boy/Male
Scottish
Proud.
Male
English
 English form of Spanish Gaspar, JASPER means "treasure bearer." Early Christians assigned names to the three Magi ("wise men from the east") who visited the baby Jesus. They are mentioned but not named in the bible; Jasper is one of them, the other two are Balthasar and Melchior. Jasper is also the name of an opaque cryptocrystalline variety of quartz that may be red, yellow or brown in color. Also spelled Casper and Kasper.
Girl/Female
Biblical
Fourth.
Surname or Lastname
English (mainly East Anglia)
English (mainly East Anglia) : metonymic occupational name for someone who dealt in weights and measures, for example a grain factor, from Middle English pekke ‘peck’ (an old measure of dry goods equivalent to eight quarts or a quarter of a bushel).English : variant of Peak 1.Irish : variant of Peak 2.South German : variant of Beck.North German and Dutch : metonymic occupational name for someone who prepared or sold pitch, from Middle Low German pek, Middle Dutch pec, pic.Dutch : from Middle Dutch pec, pick ‘desperate straits’, hence a nickname for a person in difficult circumstances or perhaps for someone with a gloomy disposition.
Surname or Lastname
English
English : variant of Sale 1.English : metonymic occupational name for a maker of seals or signet rings, from Middle English, Old French seel ‘seal’ (Latin sigillum).English : metonymic occupational name for a maker of saddles, from Old French seele ‘saddle’.English : nickname for a plump or ungainly person, from Middle English sele ‘seal’ (the aquatic mammal).Americanized form (translation) of Jewish Siegel.
QUARTIC FUNCTION
QUARTIC FUNCTION
QUARTIC FUNCTION
QUARTIC FUNCTION
QUARTIC FUNCTION
QUARTIC FUNCTION
QUARTIC FUNCTION
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