polynomial

Elementary algebra - Linear equations. The simplest equations to solve are linear equations. They contain only constant numbers and a single variable without an exponent. For example: The central technique is add, subtract, multiply, or divide both sides of the equation by the same thing in such a way to eventually arrive at the value of the unknown variable. If we subtract 4 from both sides in the equation above we get: and if we then divide both sides by 2, we get our solution E ...

See also:

Elementary algebra, Elementary algebra - Laws of elementary algebra, Elementary algebra - Examples, Elementary algebra - Linear equations, Elementary algebra - Quadratic equations, Elementary algebra - System of linear equations

Read more here: » Elementary algebra: Encyclopedia II - Elementary algebra - Examples

In mathematics, the complex conjugate of a complex number is given by changing the sign of the imaginary part. Thus, the conjugate of the complex number z = a + ib (where a and b are real numbers) is defined to be z * = a − ib. The complex conjugate of a number z can be denoted by: or The symbol can also denote the conjugate transpose of a matrix A so care must be taken not to confuse notations. If a complex number i ...

Including:

• Complex conjugate - Properties
• Complex conjugate - Generalizations

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In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation obeys the commutative law. This means that if a and b are any elements of the ring, then a×b=b×a. The study of commutative rings is called commutative algebra. Commutative ring - Examples. The most important example is the ring of integers with the two operations of addition and multiplication. Ordinary multiplication of inte ...

Including:

• Commutative ring - Examples
• Commutative ring - Constructing new commutative rings from given ones
• Commutative ring - General discussion

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In complex analysis, a zero of a holomorphic function f is a complex number a such that f(a) = 0. Zero complex analysis - Multiplicity of a zero. A complex number a is a simple zero of f, or a zero of multiplicity 1 of f, if f can be written as where g is a holomorphic function g such that g(a) is not zero. Generally, the multiplicity of the zero of f at ...

Including:

• Zero complex analysis - Multiplicity of a zero
• Zero complex analysis - Existence of zeroes

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In mathematics, a complex number is an expression of the form a + bi, where a and b are real numbers, and i stands for the square root of minus one (−1), which cannot be represented by any real number. For example, 3 + 2i is a complex number, where 3 is called the real part and 2 the imaginary part. Since a complex number a + bi is uniquely specified by an ordered pair (a, b) of real numbers, the complex numbers are in one-to-one corresponde ...

Including:

• Complex number - Definition
• Complex number - The complex number field
• Complex number - The complex plane
• Complex number - Absolute value conjugation and distance
• Complex number - Complex number division
• Complex number - Matrix representation of complex numbers
• Complex number - Geometric interpretation of the operations on complex numbers
• Complex number - Some properties
• Complex number - Real vector space
• Complex number - Solutions of polynomial equations
• Complex number - Algebraic characterization
• Complex number - Characterization as a topological field
• Complex number - Complex analysis
• Complex number - Applications
• Complex number - Control theory
• Complex number - Signal analysis
• Complex number - Improper integrals
• Complex number - Quantum mechanics
• Complex number - Relativity
• Complex number - Applied mathematics
• Complex number - Fluid dynamics
• Complex number - Fractals
• Complex number - History

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In mathematics, a coefficient is a constant multiplicative factor of a certain object such as a variable (for example, the coefficients of a polynomial), a basis vector, a basis function and so on. Usually, the objects and the coefficients are indexed in the same way, leading to expressions such as a1x1 + a2x2 + a3x3 + … where an is the coefficient of the variable xn for each n = 1, 2, 3, … For example, the coeffi ...

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In mathematics a constant function is a function whose values do not vary and thus are constant. For example, if we have the function f(x) = 4, then f is constant since f maps any value to 4. More formally, a function f : A → B, is a constant function if f(x) = f(y) for all x and y in A. Notice that every empty function, that is, any function whose domain equals the empty set, is included in the above definition vacuously, sin ...

Including:

• Constant function - Properties

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Curve fitting is finding a curve which matches a series of data points and possibly other constraints. This section is an introduction to both interpolation (where an exact fit to constraints is expected) and curve fitting/regression analysis (where an approximate fit is permitted). Curve fitting - Fitting data points to lines and polynomial curves. Let's start with a first degree polynomial equation: This is a line with slope a (as opposed to the usual slope m for ...

Including:

• Curve fitting - Fitting data points to lines and polynomial curves
• Curve fitting - Fitting data points to other curves
• Curve fitting - Application to surfaces

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VAX is a 32-bit computing architecture that supports an orthogonal instruction set (machine language) and virtual addressing (i.e. demand paged virtual memory). It was developed in the mid-1970s by Digital Equipment Corporation (DEC). DEC was later purchased by Compaq, which in turn was purchased by Hewlett-Packard. The VAX has been perceived as the quintessential CISC processing architecture, with its very large number of addressing modes and machine instructions, including instructions for such complex operations as queue ins ...

Including:

• VAX - The name
• VAX - Operating systems
• VAX - History
• VAX - VAX models

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In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. They are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to positive and negative values and even to comp ...

Including:

• Trigonometric function - List of trigonometric functions
• Trigonometric function - History
• Trigonometric function - Right triangle definitions
• Trigonometric function - Mnemonics
• Trigonometric function - Slope definitions
• Trigonometric function - Unit-circle definitions
• Trigonometric function - Series definitions
• Trigonometric function - Relationship to exponential function
• Trigonometric function - Definitions via differential equations
• Trigonometric function - The significance of radians
• Trigonometric function - Other definitions
• Trigonometric function - Computation
• Trigonometric function - Inverse functions
• Trigonometric function - Identities
• Trigonometric function - Properties and applications
• Trigonometric function - Law of sines
• Trigonometric function - Law of cosines
• Trigonometric function - Law of tangents

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Carl Friedrich Gauss (Gauß) (April 30, 1777 – February 23, 1855) was a German mathematician and scientist of profound genius who contributed significantly to many fields, including number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. Sometimes known as "the prince of mathematicians", Gauss had a remarkable influence in many fields of mathematics and science and is ranked beside Euler, Newton ...

Including:

• Carl Friedrich Gauss - Biography
• Carl Friedrich Gauss - Early years
• Carl Friedrich Gauss - Middle years
• Carl Friedrich Gauss - Later years death and afterwards
• Carl Friedrich Gauss - Family
• Carl Friedrich Gauss - Personality
• Carl Friedrich Gauss - Commemorations

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In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. This is in contrast to a variable, which is not fixed. Constant - Unspecified constants. The most widely mentioned sort of constant is a fixed, but possibly unspecified, number. Usually the term constant is used in connection with mathematical functions of one or more variable arguments. These arguments, or other variables, are often called x, y, or z, using lower-case let ...

Including:

• Constant - Unspecified constants
• Constant - Specified constants
• Constant - Constant term
• Constant - Constants vs variables

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In mathematics, particularly in combinatorics, the binomial coefficient of the natural number n and the integer k is defined to be the natural number and where m! denotes the factorial of m. According to Nicholas J. Higham, the notation was introduced by Albert von Ettinghausen in 1826, although these numbers ha ...

Including:

• Binomial coefficient - Example
• Binomial coefficient - Derivation from binomial expansion
• Binomial coefficient - Pascal's triangle
• Binomial coefficient - Combinatorics and statistics
• Binomial coefficient - Formulas involving binomial coefficients
• Binomial coefficient - Divisors of binomial coefficients
• Binomial coefficient - Bounds for binomial coefficients
• Binomial coefficient - Generalization to multinomials
• Binomial coefficient - Generalization to real and complex argument
• Binomial coefficient - Newton's binomial series
• Binomial coefficient - Generalization to q-series

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In mathematics, an algebraic number relative to a field F is any element x of a given field K containing F such that x is a solution of a polynomial equation of the form: anxn + an−1xn−1 + ··· + a1x + a0 = 0 wh ...

Including:

• Algebraic number - The field of algebraic numbers
• Algebraic number - Numbers defined by radicals
• Algebraic number - Algebraic integers
• Algebraic number - Special classes of algebraic number

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In mathematics, an algebraic function of indeterminates X1, X2, ..., Xn, is a function F that satisfies some non-trivial equation P(F, X1, X2, ..., Xn) = 0, with P a polynomial in n + 1 variables over a given field K. That is, F is an implicit function that solves an algebraic equation. A simple example would be < ...

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The mathematical constant π is a real number which may be defined as the ratio of a circle's circumference (Greek περιφέρεια, periphery) to its diameter in Euclidean geometry, and which is in common use in mathematics, physics, and engineering. The name of the Greek letter π is pi (pronounced pie in English), and this spelling can be used in typographical contexts where the Greek letter is not available. π is also known as Archimedes' constant (not to be confused with Archime ...

Including:

• Pi - Properties
• Pi - Formulae involving π
• Pi - Geometry
• Pi - Analysis
• Pi - Continued fractions
• Pi - Number theory
• Pi - Dynamical systems and ergodic theory
• Pi - Physics
• Pi - Probability and statistics
• Pi - History of π
• Pi - Numerical approximations of π
• Pi - Miscellaneous formulae
• Pi - Less accurate approximations
• Pi - Open questions
• Pi - The nature of π
• Pi - Fictional references
• Pi - π culture

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0 1 2 3 4 5 6 7 8 9 >> List of numbers -- Integers 0 10 20 30 40 50 60 70 80 90 >> quinque-/quinqu-/quint- (from Latin) 5 (five) is a number, numeral, and glyph. It is the natural number following 4 and preceding 6. The SI prefix for 10005 is peta (P), and for its reciprocal femto (f). 5 number - In mathematics. Five is the third smallest prime number, after 2 and 3, and before 7. Because it can b ...

Including:

• 5 number - In mathematics
• 5 number - In numbering systems
• 5 number - The Arabic glyph
• 5 number - In science
• 5 number - In astronomy
• 5 number - In various cultures
• 5 number - In music
• 5 number - In sports
• 5 number - In technology
• 5 number - In other fields
• 5 number - Years

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In mathematics, an algebraic variety is essentially a set of common zeroes of a set of polynomials. Algebraic varieties are one of the central objects of study in classical (and to some extent, modern) algebraic geometry. Historically, the fundamental theorem of algebra established a link between algebra and geometry by saying that a polynomial in one variable over the complex numbers is determined by the set of its roots, which is an inherently geometric object. Building on this result, Hilbert's Nullstellensatz provides a fun ...

Including:

• Algebraic variety - Formal definitions
• Algebraic variety - Affine varieties
• Algebraic variety - Projective varieties
• Algebraic variety - Basic results
• Algebraic variety - Discussion and generalizations

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In mathematics, a field F is said to be algebraically closed if every polynomial in one variable of degree at least 1, with coefficients in F, has a zero (root) in F. As an example, the field of real numbers is not algebraically closed, because the polynomial equation ...

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In mathematics, a smooth function is one that is infinitely (indefinitely) differentiable, i.e., has derivatives of all finite orders. A function is called C or more commonly C0 if it is a continuous function. A function is C1 if it has a derivative that is continuous; such functions are also called continuously differentiable. A function is called Cn for n ≥ 1 if it can be differentiated n times, with a continuous n-th derivative. The sm ...

Including:

• Smooth function - Constructing smooth functions to specifications
• Smooth function - Relation to analytic function theory
• Smooth function - Smooth partitions of unity
• Smooth function - Smooth maps of manifolds
• Smooth function - Advanced definitions

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