Faster access than browser!
236 relations: Abelian integral, Abelian variety, Absolute geometry, Affine space, Affine variety, Alexander Grothendieck, Algebraic curve, Algebraic equation, Algebraic Geometry (book), Algebraic geometry and analytic geometry, Algebraic number field, Algebraic number theory, Algebraic space, Algebraic statistics, Algebraic surface, Algebraic variety, Algebraically closed field, Algorithm, Allen Tannenbaum, American Mathematical Society, Analytic function, Analytic geometry, André Weil, Apollonius of Perga, Arakelov theory, Archimedes, Arthur Cayley, Atomic formula, Éléments de géométrie algébrique, Barry Arthur Cipra, Bartel Leendert van der Waerden, Bézout's theorem, Bernhard Riemann, Bertrand Toën, Birational geometry, Blaise Pascal, Bruno Buchberger, Cambridge University Press, Carlos Simpson, Cassini oval, Category theory, Characteristic (algebra), Circle, Closure operator, Commutative algebra, Complement (set theory), Complex analysis, Complex geometry, Complex manifold, Complex number, ..., Complex-analytic variety, Computational complexity, Computational complexity theory, Computational phylogenetics, Computer algebra, Conic section, Continuous function, Control theory, Coordinate system, Critical point (mathematics), Cubic function, Cubic plane curve, Cusp (singularity), Cylindrical algebraic decomposition, Daniel Lazard, Degree of an algebraic variety, Deligne–Mumford stack, Derived algebraic geometry, Derived scheme, Differentiable manifold, Differential algebraic geometry, Differential geometry, Differential graded algebra, Dimension of an algebraic variety, Diophantine equation, Domain of a function, Doubling the cube, Dover, Dual (category theory), Econometrica, Edmond Laguerre, Elimination theory, Ellipse, Elliptic curve, Elliptic-curve cryptography, Equation solving, Equivalence of categories, Euclidean space, Faugère's F4 and F5 algorithms, Felix Klein, Fermat's Last Theorem, Field (mathematics), Field of fractions, First-order logic, Floating-point arithmetic, Formal scheme, François Viète, Francis Sowerby Macaulay, Function field of an algebraic variety, Galois connection, Game theory, Generic point, Geometric algebra, Geometric modeling, Geometry, George E. Collins, Gerolamo Cardano, Girard Desargues, Glossary of arithmetic and diophantine geometry, Glossary of classical algebraic geometry, Goppa code, Gottfried Wilhelm Leibniz, Graded ring, Gröbner basis, Grothendieck topology, Group (mathematics), Group action, Heisuke Hironaka, Hellenistic Greece, Higher category theory, Hilbert series and Hilbert polynomial, Hilbert's basis theorem, Hilbert's Nullstellensatz, Hilbert's sixteenth problem, Homogeneous coordinate ring, Homogeneous coordinates, Homogeneous polynomial, Homological algebra, Homological mirror symmetry, Hyperbola, Ibn al-Haytham, Ideal (ring theory), Image (mathematics), Ind-scheme, Inflection point, Integer programming, Integral domain, Intersection theory, Inverse function, Irreducible component, Isaac Newton, Italian school of algebraic geometry, Jacob Lurie, Jean-Pierre Serre, John Wiley & Sons, Joseph-Louis Lagrange, Klein geometry, Lemniscate of Bernoulli, Leonhard Euler, Line (geometry), Line at infinity, List of complex and algebraic surfaces, Marseille, Matching (graph theory), Mathematics, Mathematics in medieval Islam, Maxim Kontsevich, Maximal ideal, Menaechmus, Model category, Moduli space, Monomial order, Morphism, Morphism of algebraic varieties, N-sphere, Niccolò Fontana Tartaglia, Nikolai Durov, Nisnevich topology, Non-Euclidean geometry, Noncommutative algebraic geometry, Normal space, Number theory, Numerical algebraic geometry, Omar Khayyam, Ordered field, Oscar Zariski, Parabola, Persian people, Pierre de Fermat, Point at infinity, Polynomial, Prime ideal, Projective geometry, Projective plane, Projective space, Publications Mathématiques de l'IHÉS, Quadratic form, Quantifier elimination, Quasi-category, Radical of an ideal, Rational function, Rational mapping, Rational number, Rational variety, Real algebraic geometry, Real number, Reduced ring, Regular chain, Renaissance, René Descartes, Resolution of singularities, Resultant, Riemann surface, Riemann–Roch theorem, Ring homomorphism, Robotics, Scheme (mathematics), Sharaf al-Dīn al-Ṭūsī, Sheaf (mathematics), Singular point of a curve, Singular point of an algebraic variety, Singularity (mathematics), Singularity theory, Smooth completion, Smoothness, Software, Soliton, Solution set, Sphere, Springer Science+Business Media, Stack (mathematics), Synthetic geometry, System of polynomial equations, Tarski–Seidenberg theorem, Tietze extension theorem, Topological space, Topology, Tropical geometry, Tuple, Universal algebraic geometry, Valuation (algebra), Variety (universal algebra), Whitney conditions, Wiles's proof of Fermat's Last Theorem, Zariski topology, Zero of a function. Expand index (186 more) »
Abelian integral
In mathematics, an abelian integral, named after the Norwegian mathematician Niels Henrik Abel, is an integral in the complex plane of the form where R(x,w) is an arbitrary rational function of the two variables x and w, which are related by the equation where F(x,w) is an irreducible polynomial in w, whose coefficients \varphi_j(x), j.
New!!: Algebraic geometry and Abelian integral · See more »
Abelian variety
In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions.
New!!: Algebraic geometry and Abelian variety · See more »
Absolute geometry
Absolute geometry is a geometry based on an axiom system for Euclidean geometry with the parallel postulate removed and none of its alternatives used in place of it.
New!!: Algebraic geometry and Absolute geometry · See more »
Affine space
In mathematics, an affine space is a geometric structure that generalizes the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.
New!!: Algebraic geometry and Affine space · See more »
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.
New!!: Algebraic geometry and Affine variety · See more »
Alexander Grothendieck
Alexander Grothendieck (28 March 1928 – 13 November 2014) was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry.
New!!: Algebraic geometry and Alexander Grothendieck · See more »
Algebraic curve
In mathematics, a plane real algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables.
New!!: Algebraic geometry and Algebraic curve · See more »
Algebraic equation
In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers.
New!!: Algebraic geometry and Algebraic equation · See more »
Algebraic Geometry (book)
Algebraic Geometry is an influential, algebraic geometry textbook written by Robin Hartshorne and published by Springer-Verlag in 1977.
New!!: Algebraic geometry and Algebraic Geometry (book) · See more »
Algebraic geometry and analytic geometry
In mathematics, algebraic geometry and analytic geometry are two closely related subjects.
New!!: Algebraic geometry and Algebraic geometry and analytic geometry · See more »
Algebraic number field
In mathematics, an algebraic number field (or simply number field) F is a finite degree (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector space over Q. The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.
New!!: Algebraic geometry and Algebraic number field · See more »
Algebraic number theory
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations.
New!!: Algebraic geometry and Algebraic number theory · See more »
Algebraic space
In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by for use in deformation theory.
New!!: Algebraic geometry and Algebraic space · See more »
Algebraic statistics
Algebraic statistics is the use of algebra to advance statistics.
New!!: Algebraic geometry and Algebraic statistics · See more »
Algebraic surface
In mathematics, an algebraic surface is an algebraic variety of dimension two.
New!!: Algebraic geometry and Algebraic surface · See more »
Algebraic variety
Algebraic varieties are the central objects of study in algebraic geometry.
New!!: Algebraic geometry and Algebraic variety · See more »
Algebraically closed field
In abstract algebra, an algebraically closed field F contains a root for every non-constant polynomial in F, the ring of polynomials in the variable x with coefficients in F.
New!!: Algebraic geometry and Algebraically closed field · See more »
Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
New!!: Algebraic geometry and Algorithm · See more »
Allen Tannenbaum
Allen Robert Tannenbaum (born January 25, 1953) is an American/Israeli applied mathematician and presently Distinguished Professor of Computer Science and Applied Mathematics & Statistics at the State University of New York at Stony Brook.
New!!: Algebraic geometry and Allen Tannenbaum · See more »
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
New!!: Algebraic geometry and American Mathematical Society · See more »
Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
New!!: Algebraic geometry and Analytic function · See more »
Analytic geometry
In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.
New!!: Algebraic geometry and Analytic geometry · See more »
André Weil
André Weil (6 May 1906 – 6 August 1998) was an influential French mathematician of the 20th century, known for his foundational work in number theory, algebraic geometry.
New!!: Algebraic geometry and André Weil · See more »
Apollonius of Perga
Apollonius of Perga (Ἀπολλώνιος ὁ Περγαῖος; Apollonius Pergaeus; late 3rdearly 2nd centuries BC) was a Greek geometer and astronomer known for his theories on the topic of conic sections.
New!!: Algebraic geometry and Apollonius of Perga · See more »
Arakelov theory
In mathematics, Arakelov theory (or Arakelov geometry) is an approach to Diophantine geometry, named for Suren Arakelov.
New!!: Algebraic geometry and Arakelov theory · See more »
Archimedes
Archimedes of Syracuse (Ἀρχιμήδης) was a Greek mathematician, physicist, engineer, inventor, and astronomer.
New!!: Algebraic geometry and Archimedes · See more »
Arthur Cayley
Arthur Cayley F.R.S. (16 August 1821 – 26 January 1895) was a British mathematician.
New!!: Algebraic geometry and Arthur Cayley · See more »
Atomic formula
In mathematical logic, an atomic formula (also known simply as an atom) is a formula with no deeper propositional structure, that is, a formula that contains no logical connectives or equivalently a formula that has no strict subformulas.
New!!: Algebraic geometry and Atomic formula · See more »
Éléments de géométrie algébrique
The Éléments de géométrie algébrique ("Elements of Algebraic Geometry") by Alexander Grothendieck (assisted by Jean Dieudonné), or EGA for short, is a rigorous treatise, in French, on algebraic geometry that was published (in eight parts or fascicles) from 1960 through 1967 by the Institut des Hautes Études Scientifiques.
New!!: Algebraic geometry and Éléments de géométrie algébrique · See more »
Barry Arthur Cipra
Barry Arthur Cipra, an American mathematician and freelance writer, regularly contributes to ''Science'' magazine and SIAM News, a monthly publication of the Society for Industrial and Applied Mathematics.
New!!: Algebraic geometry and Barry Arthur Cipra · See more »
Bartel Leendert van der Waerden
Bartel Leendert van der Waerden (February 2, 1903 – January 12, 1996) was a Dutch mathematician and historian of mathematics.
New!!: Algebraic geometry and Bartel Leendert van der Waerden · See more »
Bézout's theorem
Bézout's theorem is a statement in algebraic geometry concerning the number of common points, or intersection points, of two plane algebraic curves which do not share a common component (that is, which do not have infinitely many common points).
New!!: Algebraic geometry and Bézout's theorem · See more »
Bernhard Riemann
Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry.
New!!: Algebraic geometry and Bernhard Riemann · See more »
Bertrand Toën
Bertrand Toën (born September 17, 1973 in Millau, France) is a mathematician who works as a director of research at the Centre national de la recherche scientifique (CNRS) at the Paul Sabatier University, Toulouse, France.
New!!: Algebraic geometry and Bertrand Toën · See more »
Birational geometry
In mathematics, birational geometry is a field of algebraic geometry the goal of which is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets.
New!!: Algebraic geometry and Birational geometry · See more »
Blaise Pascal
Blaise Pascal (19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, writer and Catholic theologian.
New!!: Algebraic geometry and Blaise Pascal · See more »
Bruno Buchberger
Bruno Buchberger (born October 22, 1942 in Innsbruck) is Professor of Computer Mathematics at Johannes Kepler University in Linz, Austria.
New!!: Algebraic geometry and Bruno Buchberger · See more »
Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
New!!: Algebraic geometry and Cambridge University Press · See more »
Carlos Simpson
Carlos Tschudi Simpson (born 30 June 1962) is an American mathematician, specializing in algebraic geometry.
New!!: Algebraic geometry and Carlos Simpson · See more »
Cassini oval
A Cassini oval is a quartic plane curve defined as the set (or locus) of points in the plane such that the product of the distances to two fixed points is constant.
New!!: Algebraic geometry and Cassini oval · See more »
Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
New!!: Algebraic geometry and Category theory · See more »
Characteristic (algebra)
In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0) if the sum does indeed eventually attain 0.
New!!: Algebraic geometry and Characteristic (algebra) · See more »
Circle
A circle is a simple closed shape.
New!!: Algebraic geometry and Circle · See more »
Closure operator
In mathematics, a closure operator on a set S is a function \operatorname: \mathcal(S)\rightarrow \mathcal(S) from the power set of S to itself which satisfies the following conditions for all sets X,Y\subseteq S |- | X \subseteq \operatorname(X) | (cl is extensive) |- | X\subseteq Y \Rightarrow \operatorname(X) \subseteq \operatorname(Y) | (cl is increasing) |- | \operatorname(\operatorname(X)).
New!!: Algebraic geometry and Closure operator · See more »
Commutative algebra
Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.
New!!: Algebraic geometry and Commutative algebra · See more »
Complement (set theory)
In set theory, the complement of a set refers to elements not in.
New!!: Algebraic geometry and Complement (set theory) · See more »
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.
New!!: Algebraic geometry and Complex analysis · See more »
Complex geometry
In mathematics, complex geometry is the study of complex manifolds and functions of several complex variables.
New!!: Algebraic geometry and Complex geometry · See more »
Complex manifold
In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic.
New!!: Algebraic geometry and Complex manifold · See more »
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.
New!!: Algebraic geometry and Complex number · See more »
Complex-analytic variety
In mathematics, specifically complex geometry, a complex-analytic variety is defined locally as the set of common zeros of finitely many analytic functions.
New!!: Algebraic geometry and Complex-analytic variety · See more »
Computational complexity
In computer science, the computational complexity, or simply complexity of an algorithm is the amount of resources required for running it.
New!!: Algebraic geometry and Computational complexity · See more »
Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
New!!: Algebraic geometry and Computational complexity theory · See more »
Computational phylogenetics
Computational phylogenetics is the application of computational algorithms, methods, and programs to phylogenetic analyses.
New!!: Algebraic geometry and Computational phylogenetics · See more »
Computer algebra
In computational mathematics, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects.
New!!: Algebraic geometry and Computer algebra · See more »
Conic section
In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.
New!!: Algebraic geometry and Conic section · See more »
Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
New!!: Algebraic geometry and Continuous function · See more »
Control theory
Control theory in control systems engineering deals with the control of continuously operating dynamical systems in engineered processes and machines.
New!!: Algebraic geometry and Control theory · See more »
Coordinate system
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
New!!: Algebraic geometry and Coordinate system · See more »
Critical point (mathematics)
In mathematics, a critical point or stationary point of a differentiable function of a real or complex variable is any value in its domain where its derivative is 0.
New!!: Algebraic geometry and Critical point (mathematics) · See more »
Cubic function
In algebra, a cubic function is a function of the form in which is nonzero.
New!!: Algebraic geometry and Cubic function · See more »
Cubic plane curve
In mathematics, a cubic plane curve is a plane algebraic curve C defined by a cubic equation applied to homogeneous coordinates for the projective plane; or the inhomogeneous version for the affine space determined by setting in such an equation.
New!!: Algebraic geometry and Cubic plane curve · See more »
Cusp (singularity)
In mathematics a cusp, sometimes called spinode in old texts, is a point on a curve where a moving point on the curve must start to move backward.
New!!: Algebraic geometry and Cusp (singularity) · See more »
Cylindrical algebraic decomposition
In mathematics, cylindrical algebraic decomposition (CAD) is a notion, and an algorithm to compute it, which are fundamental for computer algebra and real algebraic geometry.
New!!: Algebraic geometry and Cylindrical algebraic decomposition · See more »
Daniel Lazard
Daniel Lazard (born December 10, 1941) is a French mathematician and computer scientist.
New!!: Algebraic geometry and Daniel Lazard · See more »
Degree of an algebraic variety
In mathematics, the degree of an affine or projective variety of dimension is the number of intersection points of the variety with hyperplanes in general position (for an algebraic set, the intersection points must be counted with their intersection multiplicity) The degree is not an intrinsic property of the variety, as it depends on a specific embedding of the variety in an affine or projective space.
New!!: Algebraic geometry and Degree of an algebraic variety · See more »
Deligne–Mumford stack
In algebraic geometry, a Deligne–Mumford stack is a stack F such that.
New!!: Algebraic geometry and Deligne–Mumford stack · See more »
Derived algebraic geometry
Derived algebraic geometry (also called spectral algebraic geometry) is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local charts, are replaced by ring spectra in algebraic topology, whose higher homotopy accounts for the non-discreteness (e.g., Tor) of the structure sheaf.
New!!: Algebraic geometry and Derived algebraic geometry · See more »
Derived scheme
In algebraic geometry, a derived scheme is a pair (X, \mathcal) consisting of a topological space X and a sheaf \mathcal of commutative ring spectra on X such that (1) the pair (X, \pi_0 \mathcal) is a scheme and (2) \pi_k \mathcal is a quasi-coherent \pi_0 \mathcal-module.
New!!: Algebraic geometry and Derived scheme · See more »
Differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
New!!: Algebraic geometry and Differentiable manifold · See more »
Differential algebraic geometry
Differential algebraic geometry is an area of differential algebra that adapts concepts and methods from algebraic geometry and applies them to systems of differential equations/algebraic differential equations.
New!!: Algebraic geometry and Differential algebraic geometry · See more »
Differential geometry
Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.
New!!: Algebraic geometry and Differential geometry · See more »
Differential graded algebra
In mathematics, in particular abstract algebra and topology, a differential graded algebra is a graded algebra with an added chain complex structure that respects the algebra structure.
New!!: Algebraic geometry and Differential graded algebra · See more »
Dimension of an algebraic variety
In mathematics and specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent ways.
New!!: Algebraic geometry and Dimension of an algebraic variety · See more »
Diophantine equation
In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values).
New!!: Algebraic geometry and Diophantine equation · See more »
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.
New!!: Algebraic geometry and Domain of a function · See more »
Doubling the cube
Doubling the cube, also known as the Delian problem, is an ancient geometric problem.
New!!: Algebraic geometry and Doubling the cube · See more »
Dover
Dover is a town and major ferry port in the home county of Kent, in South East England.
New!!: Algebraic geometry and Dover · See more »
Dual (category theory)
In category theory, a branch of mathematics, duality is a correspondence between the properties of a category C and the dual properties of the opposite category Cop.
New!!: Algebraic geometry and Dual (category theory) · See more »
Econometrica
Econometrica is a peer-reviewed academic journal of economics, publishing articles in many areas of economics, especially econometrics.
New!!: Algebraic geometry and Econometrica · See more »
Edmond Laguerre
Edmond Nicolas Laguerre (9 April 1834, Bar-le-Duc – 14 August 1886, Bar-le-Duc) was a French mathematician and a member of the Académie française (1885).
New!!: Algebraic geometry and Edmond Laguerre · See more »
Elimination theory
In commutative algebra and algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating some variables between polynomials of several variables, in order to solve systems of polynomial equations.
New!!: Algebraic geometry and Elimination theory · See more »
Ellipse
In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.
New!!: Algebraic geometry and Ellipse · See more »
Elliptic curve
In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form which is non-singular; that is, the curve has no cusps or self-intersections.
New!!: Algebraic geometry and Elliptic curve · See more »
Elliptic-curve cryptography
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.
New!!: Algebraic geometry and Elliptic-curve cryptography · See more »
Equation solving
In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equality sign.
New!!: Algebraic geometry and Equation solving · See more »
Equivalence of categories
In category theory, an abstract branch of mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are "essentially the same".
New!!: Algebraic geometry and Equivalence of categories · See more »
Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
New!!: Algebraic geometry and Euclidean space · See more »
Faugère's F4 and F5 algorithms
In computer algebra, the Faugère F4 algorithm, by Jean-Charles Faugère, computes the Gröbner basis of an ideal of a multivariate polynomial ring.
New!!: Algebraic geometry and Faugère's F4 and F5 algorithms · See more »
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.
New!!: Algebraic geometry and Felix Klein · See more »
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers,, and satisfy the equation for any integer value of greater than 2.
New!!: Algebraic geometry and Fermat's Last Theorem · See more »
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.
New!!: Algebraic geometry and Field (mathematics) · See more »
Field of fractions
In abstract algebra, the field of fractions of an integral domain is the smallest field in which it can be embedded.
New!!: Algebraic geometry and Field of fractions · See more »
First-order logic
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
New!!: Algebraic geometry and First-order logic · See more »
Floating-point arithmetic
In computing, floating-point arithmetic is arithmetic using formulaic representation of real numbers as an approximation so as to support a trade-off between range and precision.
New!!: Algebraic geometry and Floating-point arithmetic · See more »
Formal scheme
In mathematics, specifically in algebraic geometry, a formal scheme is a type of space which includes data about its surroundings.
New!!: Algebraic geometry and Formal scheme · See more »
François Viète
François Viète (Franciscus Vieta; 1540 – 23 February 1603), Seigneur de la Bigotière, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to its innovative use of letters as parameters in equations.
New!!: Algebraic geometry and François Viète · See more »
Francis Sowerby Macaulay
Francis Sowerby Macaulay FRS (11 February 1862, Witney – 9 February 1937, Cambridge) was an English mathematician who made significant contributions to algebraic geometry.
New!!: Algebraic geometry and Francis Sowerby Macaulay · See more »
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.
New!!: Algebraic geometry and Function field of an algebraic variety · See more »
Galois connection
In mathematics, especially in order theory, a Galois connection is a particular correspondence (typically) between two partially ordered sets (posets).
New!!: Algebraic geometry and Galois connection · See more »
Game theory
Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers".
New!!: Algebraic geometry and Game theory · See more »
Generic point
In algebraic geometry, a generic point P of an algebraic variety X is, roughly speaking, a point at which all generic properties are true, a generic property being a property which is true for almost every point.
New!!: Algebraic geometry and Generic point · See more »
Geometric algebra
The geometric algebra (GA) of a vector space is an algebra over a field, noted for its multiplication operation called the geometric product on a space of elements called multivectors, which is a superset of both the scalars F and the vector space V. Mathematically, a geometric algebra may be defined as the Clifford algebra of a vector space with a quadratic form.
New!!: Algebraic geometry and Geometric algebra · See more »
Geometric modeling
Geometric modeling is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes.
New!!: Algebraic geometry and Geometric modeling · See more »
Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
New!!: Algebraic geometry and Geometry · See more »
George E. Collins
George E. Collins (January 10, 1928, Stuart, Iowa – November 21, 2017, Madison, Wisconsin) was an American mathematician and computer scientist.
New!!: Algebraic geometry and George E. Collins · See more »
Gerolamo Cardano
Gerolamo (or Girolamo, or Geronimo) Cardano (Jérôme Cardan; Hieronymus Cardanus; 24 September 1501 – 21 September 1576) was an Italian polymath, whose interests and proficiencies ranged from being a mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, writer, and gambler.
New!!: Algebraic geometry and Gerolamo Cardano · See more »
Girard Desargues
Girard Desargues (21 February 1591 – September 1661) was a French mathematician and engineer, who is considered one of the founders of projective geometry.
New!!: Algebraic geometry and Girard Desargues · See more »
Glossary of arithmetic and diophantine geometry
This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry.
New!!: Algebraic geometry and Glossary of arithmetic and diophantine geometry · See more »
Glossary of classical algebraic geometry
The terminology of algebraic geometry changed drastically during the twentieth century, with the introduction of the general methods, initiated by David Hilbert and the Italian school of algebraic geometry in the beginning of the century, and later formalized by André Weil, Jean-Pierre Serre and Alexander Grothendieck.
New!!: Algebraic geometry and Glossary of classical algebraic geometry · See more »
Goppa code
In mathematics, an algebraic geometric code (AG-code), otherwise known as a Goppa code, is a general type of linear code constructed by using an algebraic curve X over a finite field \mathbb_q.
New!!: Algebraic geometry and Goppa code · See more »
Gottfried Wilhelm Leibniz
Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.
New!!: Algebraic geometry and Gottfried Wilhelm Leibniz · See more »
Graded ring
In mathematics, in particular abstract algebra, a graded ring is a ring that is a direct sum of abelian groups R_i such that R_i R_j \subseteq R_.
New!!: Algebraic geometry and Graded ring · See more »
Gröbner basis
In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring over a field.
New!!: Algebraic geometry and Gröbner basis · See more »
Grothendieck topology
In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space.
New!!: Algebraic geometry and Grothendieck topology · See more »
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.
New!!: Algebraic geometry and Group (mathematics) · See more »
Group action
In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.
New!!: Algebraic geometry and Group action · See more »
Heisuke Hironaka
is a Japanese mathematician.
New!!: Algebraic geometry and Heisuke Hironaka · See more »
Hellenistic Greece
In the context of ancient Greek art, architecture, and culture, Hellenistic Greece corresponds to the period between the death of Alexander the Great in 323 BC and the annexation of the classical Greek heartlands by the Roman Republic.
New!!: Algebraic geometry and Hellenistic Greece · See more »
Higher category theory
In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities.
New!!: Algebraic geometry and Higher category theory · See more »
Hilbert series and Hilbert polynomial
In commutative algebra, the Hilbert function, the Hilbert polynomial, and the Hilbert series of a graded commutative algebra finitely generated over a field are three strongly related notions which measure the growth of the dimension of the homogeneous components of the algebra.
New!!: Algebraic geometry and Hilbert series and Hilbert polynomial · See more »
Hilbert's basis theorem
In mathematics, specifically commutative algebra, Hilbert's basis theorem says that a polynomial ring over a Noetherian ring is Noetherian.
New!!: Algebraic geometry and Hilbert's basis theorem · See more »
Hilbert's Nullstellensatz
Hilbert's Nullstellensatz (German for "theorem of zeros," or more literally, "zero-locus-theorem"—see Satz) is a theorem that establishes a fundamental relationship between geometry and algebra.
New!!: Algebraic geometry and Hilbert's Nullstellensatz · See more »
Hilbert's sixteenth problem
Hilbert's 16th problem was posed by David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900, as part of his list of 23 problems in mathematics.
New!!: Algebraic geometry and Hilbert's sixteenth problem · See more »
Homogeneous coordinate ring
In algebraic geometry, the homogeneous coordinate ring R of an algebraic variety V given as a subvariety of projective space of a given dimension N is by definition the quotient ring where I is the homogeneous ideal defining V, K is the algebraically closed field over which V is defined, and is the polynomial ring in N + 1 variables Xi.
New!!: Algebraic geometry and Homogeneous coordinate ring · See more »
Homogeneous coordinates
In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry.
New!!: Algebraic geometry and Homogeneous coordinates · See more »
Homogeneous polynomial
In mathematics, a homogeneous polynomial is a polynomial whose nonzero terms all have the same degree.
New!!: Algebraic geometry and Homogeneous polynomial · See more »
Homological algebra
Homological algebra is the branch of mathematics that studies homology in a general algebraic setting.
New!!: Algebraic geometry and Homological algebra · See more »
Homological mirror symmetry
Homological mirror symmetry is a mathematical conjecture made by Maxim Kontsevich.
New!!: Algebraic geometry and Homological mirror symmetry · See more »
Hyperbola
In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.
New!!: Algebraic geometry and Hyperbola · See more »
Ibn al-Haytham
Hasan Ibn al-Haytham (Latinized Alhazen; full name أبو علي، الحسن بن الحسن بن الهيثم) was an Arab mathematician, astronomer, and physicist of the Islamic Golden Age.
New!!: Algebraic geometry and Ibn al-Haytham · See more »
Ideal (ring theory)
In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring.
New!!: Algebraic geometry and Ideal (ring theory) · See more »
Image (mathematics)
In mathematics, an image is the subset of a function's codomain which is the output of the function from a subset of its domain.
New!!: Algebraic geometry and Image (mathematics) · See more »
Ind-scheme
In algebraic geometry, an ind-scheme is a set-valued functor that can be written (represented) as a direct limit (i.e., inductive limit) of closed embedding of schemes.
New!!: Algebraic geometry and Ind-scheme · See more »
Inflection point
In differential calculus, an inflection point, point of inflection, flex, or inflection (British English: inflexion) is a point on a continuously differentiable plane curve at which the curve crosses its tangent, that is, the curve changes from being concave (concave downward) to convex (concave upward), or vice versa.
New!!: Algebraic geometry and Inflection point · See more »
Integer programming
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers.
New!!: Algebraic geometry and Integer programming · See more »
Integral domain
In mathematics, and specifically in abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero.
New!!: Algebraic geometry and Integral domain · See more »
Intersection theory
In mathematics, intersection theory is a branch of algebraic geometry, where subvarieties are intersected on an algebraic variety, and of algebraic topology, where intersections are computed within the cohomology ring.
New!!: Algebraic geometry and Intersection theory · See more »
Inverse function
In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.
New!!: Algebraic geometry and Inverse function · See more »
Irreducible component
In mathematics, and specifically in algebraic geometry, the concept of irreducible component is used to make formal the idea that a set such as defined by the equation is the union of the two lines and Thus an algebraic set is irreducible if it is not the union of two proper algebraic subsets.
New!!: Algebraic geometry and Irreducible component · See more »
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.
New!!: Algebraic geometry and Isaac Newton · See more »
Italian school of algebraic geometry
In relation with the history of mathematics, the Italian school of algebraic geometry refers to the work over half a century or more (flourishing roughly 1885–1935) done internationally in birational geometry, particularly on algebraic surfaces.
New!!: Algebraic geometry and Italian school of algebraic geometry · See more »
Jacob Lurie
Jacob Alexander Lurie (born December 7, 1977) is an American mathematician who is a professor at Harvard University.
New!!: Algebraic geometry and Jacob Lurie · See more »
Jean-Pierre Serre
Jean-Pierre Serre (born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory.
New!!: Algebraic geometry and Jean-Pierre Serre · See more »
John Wiley & Sons
John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.
New!!: Algebraic geometry and John Wiley & Sons · See more »
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.
New!!: Algebraic geometry and Joseph-Louis Lagrange · See more »
Klein geometry
In mathematics, a Klein geometry is a type of geometry motivated by Felix Klein in his influential Erlangen program.
New!!: Algebraic geometry and Klein geometry · See more »
Lemniscate of Bernoulli
In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points F1 and F2, known as foci, at distance 2a from each other as the locus of points P so that PF1·PF2.
New!!: Algebraic geometry and Lemniscate of Bernoulli · See more »
Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
New!!: Algebraic geometry and Leonhard Euler · See more »
Line (geometry)
The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.
New!!: Algebraic geometry and Line (geometry) · See more »
Line at infinity
In geometry and topology, the line at infinity is a projective line that is added to the real (affine) plane in order to give closure to, and remove the exceptional cases from, the incidence properties of the resulting projective plane.
New!!: Algebraic geometry and Line at infinity · See more »
List of complex and algebraic surfaces
This is a list of named algebraic surfaces, compact complex surfaces, and families thereof, sorted according to the Enriques–Kodaira classification.
New!!: Algebraic geometry and List of complex and algebraic surfaces · See more »
Marseille
Marseille (Provençal: Marselha), is the second-largest city of France and the largest city of the Provence historical region.
New!!: Algebraic geometry and Marseille · See more »
Matching (graph theory)
In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices.
New!!: Algebraic geometry and Matching (graph theory) · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Algebraic geometry and Mathematics · See more »
Mathematics in medieval Islam
Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta).
New!!: Algebraic geometry and Mathematics in medieval Islam · See more »
Maxim Kontsevich
Maxim Lvovich Kontsevich (Макси́м Льво́вич Конце́вич;; born 25 August 1964) is a Russian and French mathematician.
New!!: Algebraic geometry and Maxim Kontsevich · See more »
Maximal ideal
In mathematics, more specifically in ring theory, a maximal ideal is an ideal that is maximal (with respect to set inclusion) amongst all proper ideals.
New!!: Algebraic geometry and Maximal ideal · See more »
Menaechmus
Menaechmus (Μέναιχμος, 380–320 BC) was an ancient Greek mathematician and geometer born in Alopeconnesus in the Thracian Chersonese, who was known for his friendship with the renowned philosopher Plato and for his apparent discovery of conic sections and his solution to the then-long-standing problem of doubling the cube using the parabola and hyperbola.
New!!: Algebraic geometry and Menaechmus · See more »
Model category
In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences', 'fibrations' and 'cofibrations'.
New!!: Algebraic geometry and Model category · See more »
Moduli space
In algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects.
New!!: Algebraic geometry and Moduli space · See more »
Monomial order
In mathematics, a monomial order (sometimes called a term order or an admissible order) is a total order on the set of all (monic) monomials in a given polynomial ring, satisfying the property of respecting multiplication, i.e.,.
New!!: Algebraic geometry and Monomial order · See more »
Morphism
In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.
New!!: Algebraic geometry and Morphism · See more »
Morphism of algebraic varieties
In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials.
New!!: Algebraic geometry and Morphism of algebraic varieties · See more »
N-sphere
In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.
New!!: Algebraic geometry and N-sphere · See more »
Niccolò Fontana Tartaglia
Niccolò Fontana Tartaglia (1499/1500, Brescia – 13 December 1557, Venice) was a Venetian mathematician, engineer (designing fortifications), a surveyor (of topography, seeking the best means of defense or offense) and a bookkeeper from the then-Republic of Venice (now part of Italy).
New!!: Algebraic geometry and Niccolò Fontana Tartaglia · See more »
Nikolai Durov
Nikolai Valeryevich Durov (Никола́й Вале́рьевич Ду́ров; born 21 November 1980) is a Russian programmer and mathematician.
New!!: Algebraic geometry and Nikolai Durov · See more »
Nisnevich topology
In algebraic geometry, the Nisnevich topology, sometimes called the completely decomposed topology, is a Grothendieck topology on the category of schemes which has been used in algebraic K-theory, A¹ homotopy theory, and the theory of motives.
New!!: Algebraic geometry and Nisnevich topology · See more »
Non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.
New!!: Algebraic geometry and Non-Euclidean geometry · See more »
Noncommutative algebraic geometry
Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutative geometry, that studies the geometric properties of formal duals of non-commutative algebraic objects such as rings as well as geometric objects derived from them (e.g. by gluing along localizations or taking noncommutative stack quotients).
New!!: Algebraic geometry and Noncommutative algebraic geometry · See more »
Normal space
In topology and related branches of mathematics, a normal space is a topological space X that satisfies Axiom T4: every two disjoint closed sets of X have disjoint open neighborhoods.
New!!: Algebraic geometry and Normal space · See more »
Number theory
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
New!!: Algebraic geometry and Number theory · See more »
Numerical algebraic geometry
Numerical algebraic geometry is a field of computational mathematics, particularly computational algebraic geometry, which uses methods from numerical analysis to study and manipulate algebraic varieties on a computer.
New!!: Algebraic geometry and Numerical algebraic geometry · See more »
Omar Khayyam
Omar Khayyam (عمر خیّام; 18 May 1048 – 4 December 1131) was a Persian mathematician, astronomer, and poet.
New!!: Algebraic geometry and Omar Khayyam · See more »
Ordered field
In mathematics, an ordered field is a field together with a total ordering of its elements that is compatible with the field operations.
New!!: Algebraic geometry and Ordered field · See more »
Oscar Zariski
Oscar Zariski (born Oscher Zaritsky (О́скар Зари́сский; April 24, 1899 – July 4, 1986) was a Russian-born American mathematician and one of the most influential algebraic geometers of the 20th century.
New!!: Algebraic geometry and Oscar Zariski · See more »
Parabola
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
New!!: Algebraic geometry and Parabola · See more »
Persian people
The Persians--> are an Iranian ethnic group that make up over half the population of Iran.
New!!: Algebraic geometry and Persian people · See more »
Pierre de Fermat
Pierre de Fermat (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.
New!!: Algebraic geometry and Pierre de Fermat · See more »
Point at infinity
In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.
New!!: Algebraic geometry and Point at infinity · See more »
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.
New!!: Algebraic geometry and Polynomial · See more »
Prime ideal
In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers.
New!!: Algebraic geometry and Prime ideal · See more »
Projective geometry
Projective geometry is a topic in mathematics.
New!!: Algebraic geometry and Projective geometry · See more »
Projective plane
In mathematics, a projective plane is a geometric structure that extends the concept of a plane.
New!!: Algebraic geometry and Projective plane · See more »
Projective space
In mathematics, a projective space can be thought of as the set of lines through the origin of a vector space V. The cases when and are the real projective line and the real projective plane, respectively, where R denotes the field of real numbers, R2 denotes ordered pairs of real numbers, and R3 denotes ordered triplets of real numbers.
New!!: Algebraic geometry and Projective space · See more »
Publications Mathématiques de l'IHÉS
Publications Mathématiques de l'IHÉS is a mathematical journal.
New!!: Algebraic geometry and Publications Mathématiques de l'IHÉS · See more »
Quadratic form
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.
New!!: Algebraic geometry and Quadratic form · See more »
Quantifier elimination
Quantifier elimination is a concept of simplification used in mathematical logic, model theory, and theoretical computer science.
New!!: Algebraic geometry and Quantifier elimination · See more »
Quasi-category
In mathematics, more specifically category theory, a quasi-category (also called quasicategory, weak Kan complex, inner Kan complex, infinity category, ∞-category, Boardman complex, quategory) is a generalization of the notion of a category.
New!!: Algebraic geometry and Quasi-category · See more »
Radical of an ideal
In commutative ring theory, a branch of mathematics, the radical of an ideal I is an ideal such that an element x is in the radical if some power of x is in I. A radical ideal (or semiprime ideal) is an ideal that is its own radical (this can be phrased as being a fixed point of an operation on ideals called 'radicalization').
New!!: Algebraic geometry and Radical of an ideal · See more »
Rational function
In mathematics, a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials.
New!!: Algebraic geometry and Rational function · See more »
Rational mapping
In mathematics, in particular the subfield of algebraic geometry, a rational map is a kind of partial function between algebraic varieties.
New!!: Algebraic geometry and Rational mapping · See more »
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.
New!!: Algebraic geometry and Rational number · See more »
Rational variety
In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to a projective space of some dimension over K. This means that its function field is isomorphic to the field of all rational functions for some set \ of indeterminates, where d is the dimension of the variety.
New!!: Algebraic geometry and Rational variety · See more »
Real algebraic geometry
In mathematics, real algebraic geometry is the study of real algebraic sets, i.e. real-number solutions to algebraic equations with real-number coefficients, and mappings between them (in particular real polynomial mappings).
New!!: Algebraic geometry and Real algebraic geometry · See more »
Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
New!!: Algebraic geometry and Real number · See more »
Reduced ring
In ring theory, a ring R is called a reduced ring if it has no non-zero nilpotent elements.
New!!: Algebraic geometry and Reduced ring · See more »
Regular chain
In computer algebra, a regular chain is a particular kind of triangular set in a multivariate polynomial ring over a field.
New!!: Algebraic geometry and Regular chain · See more »
Renaissance
The Renaissance is a period in European history, covering the span between the 14th and 17th centuries.
New!!: Algebraic geometry and Renaissance · See more »
René Descartes
René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.
New!!: Algebraic geometry and René Descartes · See more »
Resolution of singularities
In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, a non-singular variety W with a proper birational map W→V.
New!!: Algebraic geometry and Resolution of singularities · See more »
Resultant
In mathematics, the resultant of two polynomials is a polynomial expression of their coefficients, which is equal to zero if and only if the polynomials have a common root (possibly in a field extension), or, equivalently, a common factor (over their field of coefficients).
New!!: Algebraic geometry and Resultant · See more »
Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.
New!!: Algebraic geometry and Riemann surface · See more »
Riemann–Roch theorem
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles.
New!!: Algebraic geometry and Riemann–Roch theorem · See more »
Ring homomorphism
In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the structure.
New!!: Algebraic geometry and Ring homomorphism · See more »
Robotics
Robotics is an interdisciplinary branch of engineering and science that includes mechanical engineering, electronics engineering, computer science, and others.
New!!: Algebraic geometry and Robotics · See more »
Scheme (mathematics)
In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x.
New!!: Algebraic geometry and Scheme (mathematics) · See more »
Sharaf al-Dīn al-Ṭūsī
(c. 1135 – c. 1213) was an Iranian mathematician and astronomer of the Islamic Golden Age (during the Middle Ages).
New!!: Algebraic geometry and Sharaf al-Dīn al-Ṭūsī · See more »
Sheaf (mathematics)
In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.
New!!: Algebraic geometry and Sheaf (mathematics) · See more »
Singular point of a curve
In geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter.
New!!: Algebraic geometry and Singular point of a curve · See more »
Singular point of an algebraic variety
In the mathematical field of algebraic geometry, a singular point of an algebraic variety V is a point P that is 'special' (so, singular), in the geometric sense that at this point the tangent space at the variety may not be regularly defined.
New!!: Algebraic geometry and Singular point of an algebraic variety · See more »
Singularity (mathematics)
In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability.
New!!: Algebraic geometry and Singularity (mathematics) · See more »
Singularity theory
In mathematics, singularity theory studies spaces that are almost manifolds, but not quite.
New!!: Algebraic geometry and Singularity theory · See more »
Smooth completion
In algebraic geometry, the smooth completion (or smooth compactification) of a smooth affine algebraic curve X is a complete smooth algebraic curve which contains X as an open subset.
New!!: Algebraic geometry and Smooth completion · See more »
Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
New!!: Algebraic geometry and Smoothness · See more »
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.
New!!: Algebraic geometry and Software · See more »
Soliton
In mathematics and physics, a soliton is a self-reinforcing solitary wave packet that maintains its shape while it propagates at a constant velocity.
New!!: Algebraic geometry and Soliton · See more »
Solution set
In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities.
New!!: Algebraic geometry and Solution set · See more »
Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
New!!: Algebraic geometry and Sphere · See more »
Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
New!!: Algebraic geometry and Springer Science+Business Media · See more »
Stack (mathematics)
In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets.
New!!: Algebraic geometry and Stack (mathematics) · See more »
Synthetic geometry
Synthetic geometry (sometimes referred to as axiomatic or even pure geometry) is the study of geometry without the use of coordinates or formulas.
New!!: Algebraic geometry and Synthetic geometry · See more »
System of polynomial equations
A system of polynomial equations is a set of simultaneous equations f1.
New!!: Algebraic geometry and System of polynomial equations · See more »
Tarski–Seidenberg theorem
In mathematics, the Tarski–Seidenberg theorem states that a set in (n + 1)-dimensional space defined by polynomial equations and inequalities can be projected down onto n-dimensional space, and the resulting set is still definable in terms of polynomial identities and inequalities.
New!!: Algebraic geometry and Tarski–Seidenberg theorem · See more »
Tietze extension theorem
In topology, the Tietze extension theorem (also known as the Tietze–Urysohn–Brouwer extension theorem) states that continuous functions on a closed subset of a normal topological space can be extended to the entire space, preserving boundedness if necessary.
New!!: Algebraic geometry and Tietze extension theorem · See more »
Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
New!!: Algebraic geometry and Topological space · See more »
Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
New!!: Algebraic geometry and Topology · See more »
Tropical geometry
Tropical geometry is a relatively new area in mathematics, which might loosely be described as a piece-wise linear or skeletonized version of algebraic geometry.
New!!: Algebraic geometry and Tropical geometry · See more »
Tuple
In mathematics, a tuple is a finite ordered list (sequence) of elements.
New!!: Algebraic geometry and Tuple · See more »
Universal algebraic geometry
In algebraic geometry, universal algebraic geometry is generalized from the geometry of rings to geometry of arbitrary varieties of algebras, so that every variety of algebra has its own algebraic geometry.
New!!: Algebraic geometry and Universal algebraic geometry · See more »
Valuation (algebra)
In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of size or multiplicity of elements of the field.
New!!: Algebraic geometry and Valuation (algebra) · See more »
Variety (universal algebra)
In the mathematical subject of universal algebra, a variety of algebras is the class of all algebraic structures of a given signature satisfying a given set of identities.
New!!: Algebraic geometry and Variety (universal algebra) · See more »
Whitney conditions
In differential topology, a branch of mathematics, the Whitney conditions are conditions on a pair of submanifolds of a manifold introduced by Hassler Whitney in 1965.
New!!: Algebraic geometry and Whitney conditions · See more »
Wiles's proof of Fermat's Last Theorem
Wiles's proof of Fermat's Last Theorem is a proof by British mathematician Andrew Wiles of a special case of the modularity theorem for elliptic curves.
New!!: Algebraic geometry and Wiles's proof of Fermat's Last Theorem · See more »
Zariski topology
In algebraic geometry and commutative algebra, the Zariski topology is a topology on algebraic varieties, introduced primarily by Oscar Zariski and later generalized for making the set of prime ideals of a commutative ring a topological space, called the spectrum of the ring.
New!!: Algebraic geometry and Zariski topology · See more »
Zero of a function
In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).
New!!: Algebraic geometry and Zero of a function · See more »
Redirects here:
Algebraic Geometry, Applications of algebraic geometry, Complex algebraic geometry, Computational algebraic geometry, History of algebraic geometry.
References
[1] https://en.wikipedia.org/wiki/Algebraic_geometry
