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63 relations: Abstract algebra, Affine variety, Algebraic element, Algebraic fraction, Approximation, Archimedean property, Automorphism, Codomain, Coefficient, Complex analysis, Complex number, Computer algebra system, Constant function, Constant term, Covering space, Degree of a polynomial, Domain of a function, Elementary algebra, Equivalence class, Field (mathematics), Field extension, Field of fractions, Fraction (mathematics), Function (mathematics), Function field of an algebraic variety, Generating function, Geometric series, Group (mathematics), Henri Padé, Imaginary unit, Impulse response, Infinite impulse response, Interpolation, Irreducible fraction, Laplace transform, Like terms, Linear time-invariant theory, Mathematics, Möbius transformation, Meromorphic function, Monic polynomial, Numerical analysis, Padé approximant, Partial fraction decomposition, Polynomial, Polynomial greatest common divisor, Polynomial ring, Projective line, Rational number, Real number, ..., Recurrence relation, Removable singularity, Riemann sphere, Ring (mathematics), Ring theory, Signal processing, Software, Taylor series, Unique factorization domain, Value (mathematics), Variable (mathematics), Z-transform, Zeros and poles. Expand index (13 more) »
Abstract algebra
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
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Affine variety
In algebraic geometry, an affine variety over an algebraically closed field k is the zero-locus in the affine ''n''-space k^n of some finite family of polynomials of n variables with coefficients in k that generate a prime ideal.
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Algebraic element
In mathematics, if is a field extension of, then an element of is called an algebraic element over, or just algebraic over, if there exists some non-zero polynomial with coefficients in such that.
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Algebraic fraction
In algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraic expressions.
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Approximation
An approximation is anything that is similar but not exactly equal to something else.
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Archimedean property
In abstract algebra and analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, is a property held by some algebraic structures, such as ordered or normed groups, and fields.
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Automorphism
In mathematics, an automorphism is an isomorphism from a mathematical object to itself.
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Codomain
In mathematics, the codomain or target set of a function is the set into which all of the output of the function is constrained to fall.
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Coefficient
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but may be any expression.
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Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
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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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Computer algebra system
A computer algebra system (CAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists.
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Constant function
In mathematics, a constant function is a function whose (output) value is the same for every input value.
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Constant term
In mathematics, a constant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables.
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Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.
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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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Domain of a function
In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.
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Elementary algebra
Elementary algebra encompasses some of the basic concepts of algebra, one of the main branches of mathematics.
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Equivalence class
In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.
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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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Field extension
In mathematics, and in particular, algebra, a field E is an extension field of a field F if E contains F and the operations of F are those of E restricted to F. Equivalently, F is a subfield of E. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers.
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Field of fractions
In abstract algebra, the field of fractions of an integral domain is the smallest field in which it can be embedded.
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Fraction (mathematics)
A fraction (from Latin fractus, "broken") represents a part of a whole or, more generally, any number of equal parts.
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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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Function field of an algebraic variety
In algebraic geometry, the function field of an algebraic variety V consists of objects which are interpreted as rational functions on V. In classical algebraic geometry they are ratios of polynomials; in complex algebraic geometry these are meromorphic functions and their higher-dimensional analogues; in modern algebraic geometry they are elements of some quotient ring's field of fractions.
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Generating function
In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.
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Geometric series
In mathematics, a geometric series is a series with a constant ratio between successive terms.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Henri Padé
Henri Eugène Padé (December 17, 1863 – July 9, 1953) was a French mathematician, who is now remembered mainly for his development of Padé approximation techniques for functions using rational functions.
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Imaginary unit
The imaginary unit or unit imaginary number is a solution to the quadratic equation.
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Impulse response
In signal processing, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse.
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Infinite impulse response
Infinite impulse response (IIR) is a property applying to many linear time-invariant systems.
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Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.
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Irreducible fraction
An irreducible fraction (or fraction in lowest terms or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and -1, when negative numbers are considered).
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Laplace transform
In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.
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Like terms
In algebra, like terms are terms that have the same variables and powers.
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Linear time-invariant theory
Linear time-invariant theory, commonly known as LTI system theory, comes from applied mathematics and has direct applications in NMR spectroscopy, seismology, circuits, signal processing, control theory, and other technical areas.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Möbius transformation
In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0.
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Meromorphic function
In the mathematical field of complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all of D except for a discrete set of isolated points, which are poles of the function.
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Monic polynomial
In algebra, a monic polynomial is a single-variable polynomial (that is, a univariate polynomial) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1.
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Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
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Padé approximant
In mathematics a Padé approximant is the 'best' approximation of a function by a rational function of given order – under this technique, the approximant's power series agrees with the power series of the function it is approximating.
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Partial fraction decomposition
In algebra, the partial fraction decomposition or partial fraction expansion of a rational function (that is, a fraction such that the numerator and the denominator are both polynomials) is the operation that consists in expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.
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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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Polynomial greatest common divisor
In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials.
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Polynomial ring
In mathematics, especially in the field of abstract algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field.
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Projective line
In mathematics, a projective line is, roughly speaking, the extension of a usual line by a point called a point at infinity.
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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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Recurrence relation
In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.
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Removable singularity
In complex analysis, a removable singularity of a holomorphic function is a point at which the function is undefined, but it is possible to redefine the function at that point in such a way that the resulting function is regular in a neighbourhood of that point.
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Riemann sphere
In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity.
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Ring (mathematics)
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
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Ring theory
In algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers.
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Signal processing
Signal processing concerns the analysis, synthesis, and modification of signals, which are broadly defined as functions conveying "information about the behavior or attributes of some phenomenon", such as sound, images, and biological measurements.
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Software
Computer software, or simply software, is a generic term that refers to a collection of data or computer instructions that tell the computer how to work, in contrast to the physical hardware from which the system is built, that actually performs the work.
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Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.
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Unique factorization domain
In mathematics, a unique factorization domain (UFD) is an integral domain (a non-zero commutative ring in which the product of non-zero elements is non-zero) in which every non-zero non-unit element can be written as a product of prime elements (or irreducible elements), uniquely up to order and units, analogous to the fundamental theorem of arithmetic for the integers.
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Value (mathematics)
In mathematics, value may refer to several, strongly related notions.
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Variable (mathematics)
In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.
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Z-transform
In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency domain representation.
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Zeros and poles
In mathematics, a zero of a function is a value such that.
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Redirects here:
Fractional-rational function, Irrational function, Proper rational function, Rational Functions, Rational formula, Rational fraction, Rational function field, Rational functions.
References
[1] https://en.wikipedia.org/wiki/Rational_function
