KnowraRational functionLinked fromLinked fromThe 21 pages that link to Rational function, each with the reason it gives.All 21Broader topic 4Related 6Narrower topic 4Compared with 7PolynomialCompared with: Unlike a polynomial, it may have variables in a denominator.Domain of a functionBroader topic: Its real domain excludes zeros of the denominator polynomial.Polynomial interpolationCompared with: Rational interpolants can represent some poles and sharp changes that polynomial interpolants handle poorly.Meromorphic functionBroader topic: Rational functions are the basic examples, with poles at uncancelled denominator zeros.CoefficientRelated: Coefficients determine both polynomials and can affect poles, zeros, and simplification.Entire functionCompared with: A rational function is entire only when its denominator's apparent poles cancel, leaving a polynomial.Polynomial degreeCompared with: Its numerator and denominator have degrees, but the quotient is not generally a polynomial.Polynomial functionCompared with: Unlike a polynomial function, a rational function can be undefined at inputs that make its denominator zero.Algebraic identityBroader topic: Rational identities require excluding inputs that make a denominator zero.Padé approximantNarrower topic: A Padé approximant belongs to this broader class rather than the class of polynomials.Removable singularityRelated: Common factors can create apparent singularities that disappear after cancellation.Riemann sphereRelated: Every rational function extends to a map of the sphere when poles map to infinity.Partial fraction decompositionNarrower topic: Partial fraction decomposition applies to rational functions and rewrites them as sums.Mittag-Leffler theoremBroader topic: Finite pole prescriptions reduce to rational-function constructions with a polynomial ambiguity.Quadratic functionCompared with: Rational functions can have asymptotes and excluded inputs absent from ordinary quadratic polynomials.Runge's theoremNarrower topic: Runge's approximants are rational functions whose poles lie outside the compact set.Algebraic functionRelated: Its coefficients in an algebraic function’s defining equation may depend rationally on the input.Division by zeroRelated: Its domain excludes denominator zeros even when cancellation makes a finite limiting value possible.Bhāskara INarrower topic: The approximation’s quotient structure makes sine values computable with arithmetic operations.Cubic functionCompared with: Rational functions may have poles, whereas cubic functions are defined for every real input.Lüroth's theoremRelated: The generator f expresses every intermediate field as k(f).
KnowraRational functionLinked fromLinked fromThe 21 pages that link to Rational function, each with the reason it gives.All 21Broader topic 4Related 6Narrower topic 4Compared with 7PolynomialCompared with: Unlike a polynomial, it may have variables in a denominator.Domain of a functionBroader topic: Its real domain excludes zeros of the denominator polynomial.Polynomial interpolationCompared with: Rational interpolants can represent some poles and sharp changes that polynomial interpolants handle poorly.Meromorphic functionBroader topic: Rational functions are the basic examples, with poles at uncancelled denominator zeros.CoefficientRelated: Coefficients determine both polynomials and can affect poles, zeros, and simplification.Entire functionCompared with: A rational function is entire only when its denominator's apparent poles cancel, leaving a polynomial.Polynomial degreeCompared with: Its numerator and denominator have degrees, but the quotient is not generally a polynomial.Polynomial functionCompared with: Unlike a polynomial function, a rational function can be undefined at inputs that make its denominator zero.Algebraic identityBroader topic: Rational identities require excluding inputs that make a denominator zero.Padé approximantNarrower topic: A Padé approximant belongs to this broader class rather than the class of polynomials.Removable singularityRelated: Common factors can create apparent singularities that disappear after cancellation.Riemann sphereRelated: Every rational function extends to a map of the sphere when poles map to infinity.Partial fraction decompositionNarrower topic: Partial fraction decomposition applies to rational functions and rewrites them as sums.Mittag-Leffler theoremBroader topic: Finite pole prescriptions reduce to rational-function constructions with a polynomial ambiguity.Quadratic functionCompared with: Rational functions can have asymptotes and excluded inputs absent from ordinary quadratic polynomials.Runge's theoremNarrower topic: Runge's approximants are rational functions whose poles lie outside the compact set.Algebraic functionRelated: Its coefficients in an algebraic function’s defining equation may depend rationally on the input.Division by zeroRelated: Its domain excludes denominator zeros even when cancellation makes a finite limiting value possible.Bhāskara INarrower topic: The approximation’s quotient structure makes sine values computable with arithmetic operations.Cubic functionCompared with: Rational functions may have poles, whereas cubic functions are defined for every real input.Lüroth's theoremRelated: The generator f expresses every intermediate field as k(f).