mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations...

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...

cylindrical algebraic decomposition (CAD) is a notion, along with an algorithm to compute it, that is fundamental for computer algebra and real algebraic geometry...

real algebraic geometry which is the appropriate framework for algebraic geometry over the real numbers. Let F {\displaystyle \mathbb {F} } be a real...

who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations. Nash and fellow...

are purely algebraic and rely on commutative algebra. Some are restricted to algebraic varieties while others apply also to any algebraic set. Some are...

numbers, the projection of an algebraic set may be non-algebraic. Thus the existence of real algebraic sets with non-algebraic projections does not rely on...

methods—differential geometry, algebraic geometry, computational geometry, algebraic topology, discrete geometry (also known as combinatorial geometry), etc.—or...

In real algebraic geometry, a Nash function on an open semialgebraic subset U ⊂ Rn is an analytic function f: U → R satisfying a nontrivial polynomial...

plays a similar role in real algebraic geometry that the radical of an ideal plays in algebraic geometry over an algebraically closed field. More specifically...

geometrical theory of dynamical systems, algebra, catastrophe theory, topology, real algebraic geometry, symplectic geometry, differential equations, classical...

Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as...

are called algebraic numbers. There are also real numbers which are not, such as π = 3.1415...; these are called transcendental numbers. Real numbers can...

and optimization problems. Real algebra is the part of algebra which is relevant to real algebraic (and semialgebraic) geometry. It is mostly concerned with...

arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around...

Harnack's curve theorem for a classical result. Real algebraic geometry Ragsdale conjecture "Plane real algebraic curve", Encyclopedia of Mathematics, EMS Press...

the coefficients, which may be real or complex numbers, rational numbers, or integers. In linear algebra, analytic geometry, and in the majority of applications...

purposes, for example for algorithms of real algebraic geometry that involve infinitesimals. For isolating the real roots, one starts from an interval (...

Some examples are the field of real numbers, the field of real algebraic numbers, and the field of hyperreal numbers. A real closed field is a field F in...

Études Sci. Publ. Math. (1988), no. 67, 5–42. MR0972342 Real Algebraic and Analytic Geometry Preprint Server This article incorporates material from Subanalytic...

squares on real algebraic surfaces". Manuscripta Math. 119 (2006), no. 4, 395–410. Dressler, Mareike; Murray, Riley (2022-12-31). "Algebraic Perspectives...

In mathematics, especially in real algebraic geometry, a semialgebraic space is a space which is locally isomorphic to a semialgebraic set. Let U be an...

This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory...

In real algebraic geometry, Gudkov's conjecture, also called Gudkov’s congruence, (named after Dmitry Gudkov) was a conjecture, and is now a theorem,...

of general type Zariski surface Algebraic variety Hypersurface Quadric (algebraic geometry) Dimension of an algebraic variety Hilbert's Nullstellensatz...

Rational geometry Real algebra the study of the part of algebra relevant to real algebraic geometry. Real algebraic geometry the part of algebraic geometry that...

manifolds or projective complex algebraic varieties. Complex geometry is different in flavour to what might be called real geometry, the study of spaces based...

mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became...

In the theory of algebraic plane curves, a general quartic plane curve has 28 bitangent lines, lines that are tangent to the curve in two places. These...

mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has...