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...

In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator...

In this case, the variety is said defined over k, and the points of the variety that belong to kn are said k-rational or rational over k. In the common...

Rationality is the quality of being guided by or based on reason. In this regard, a person acts rationally if they have a good reason for what they do...

a rational surface is a surface birationally equivalent to the projective plane, or in other words a rational variety of dimension two. Rational surfaces...

a rational point of an algebraic variety is a point whose coordinates belong to a given field. If the field is not mentioned, the field of rational numbers...

The rational choice model, also called rational choice theory refers to a set of guidelines that help understand economic and social behaviour. The theory...

two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational functions rather...

An affine variety is a rational variety if it is birationally equivalent to an affine space. This means that the variety admits a rational parameterization...

geometry, a rational map or rational mapping is a kind of partial function between algebraic varieties. This article uses the convention that varieties are irreducible...

expressed as a ratio of two integers Rational point of an algebraic variety, a point defined over the rational numbers Rational function, a function that may...

conversely, such a morphism as a rational function on X. On a normal variety (in particular, a smooth variety), a rational function is regular if and only...

occur as function fields of rational varieties. The problem of finding a rational parametrization of a rational variety is equivalent with the problem...

management process with a variety of features: The requirements database can be accessed with a web browser through Rational DOORS Web Access. Changes...

these basic examples for which rationality questions are often still tractable. Formally, a Fano variety is a complete variety X whose anticanonical bundle...

Rational emotive behavior therapy (REBT), previously called rational therapy and rational emotive therapy, is an active-directive, philosophically and...

mathematics, the rational normal curve is a smooth, rational curve C of degree n in projective n-space Pn. It is a simple example of a projective variety; formally...

IBM DevOps Code ClearCase (also known as IBM Rational ClearCase) is a family of computer software tools that supports software configuration management...

surface Rational surface Enriques surface K3 surface Hodge index theorem Elliptic surface Surface of general type Zariski surface Algebraic variety Hypersurface...

geometry, the function field of an algebraic variety V consists of objects that are interpreted as rational functions on V. In classical algebraic geometry...

birational invariants of an algebraic variety. In particular, the simplest way to prove that a variety is not rational (that is, not birational to projective...

Ecological rationality is a particular account of practical rationality, which in turn specifies the norms of rational action – what one ought to do in...

group is said to be rational if, viewed as a map from the group to the general linear group, it is a rational map of algebraic varieties. Finite direct sums...

for an abelian variety A {\displaystyle A} over a number field K {\displaystyle K} , the group A ( K ) {\displaystyle A(K)} of K-rational points of A {\displaystyle...

field k, much of the structure of an algebraic variety X over k is encoded in its set X(k) of k-rational points, which allows an elementary definition...

polynomial equations and computing the images of algebraic varieties under projections or rational maps. Gröbner basis computation can be seen as a multivariate...

sheaf of rational functions KX of a scheme X is the generalization to scheme theory of the notion of function field of an algebraic variety in classical...

a new invariant for varieties in characteristic p (the so-called p-rank when n = p {\displaystyle n=p} ). The group of k-rational points for a global...

ramification. A rational curve is a curve that is birationally equivalent to a projective line (see rational variety); its genus is 0. A rational normal curve...

Scientific skepticism or rational skepticism (also spelled scepticism), sometimes referred to as skeptical inquiry, is a position in which one questions...