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In algebraic geometry, a point with rational coordinates
In number theory and algebraic geometry, 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 is generally understood. If the field is the field of real numbers, a rational point is more commonly called a real point.
Understanding rational points is a central goal of number theory and Diophantine geometry. For example, Fermat's Last Theorem may be restated as: for n > 2, the Fermat curve of equation has no other rational points than (1, 0), (0, 1), and, if n is even, (–1, 0) and (0, –1).
a rationalpoint 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...
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...
rationalpoint is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational...
are said k-rational or rational over k. In the common case where k is the field of real numbers, a k-rationalpoint is called a real point. When the field...
rationalpoint (a/c, b/c), which, in the complex plane, is just a/c + ib/c, where i is the imaginary unit. Conversely, if (x, y) is a rationalpoint on...
the rational normal curve, where all these polynomials are monomials. Any conic section defined over F with a rationalpoint in F is a rational curve...
hypersurface at a single other point, which is rational if and only if the line is rational (that is, if the line is defined by rational parameters). This allows...
Rational choice theory refers to a set of guidelines that help understand economic and social behaviour. The theory originated in the eighteenth century...
establishes that each rationalpoint of the x-axis goes over to a rationalpoint of the unit circle. The converse, that every rationalpoint of the unit circle...
real numbers, is called a real point. A rationalpoint over Q {\displaystyle \mathbb {Q} } is called simply a rationalpoint. By clearing denominators, one...
Then the K-rational points of E are the points on E whose coordinates all lie in K, including the point at infinity. The set of K-rational points is denoted...
Gaussian rational number is a complex number of the form p + qi, where p and q are both rational numbers. The set of all Gaussian rationals forms the...
known rationalpoint, and then finding the other point of intersection of the tangent with the curve; that other point is a new rationalpoint. (Diophantus...
Archive for Rational Mechanics and Analysis rational thermodynamics This disambiguation page lists articles associated with the title Rational mechanics...
real point, which is defined over the rational numbers. It has no rationalpoint, but has many points that are rational over the Gaussian rationals. A projective...
Rational emotive behavior therapy (REBT), previously called rational therapy and rational emotive therapy, is an active-directive, philosophically and...
Bounded rationality is the idea that rationality is limited when individuals make decisions, and under these limitations, rational individuals will select...
function for rational points on an elliptic curve E. The context is of a hypothetical non-trivial rationalpoint on E. Doubling a point on E roughly doubles...
field of rational functions made by extracting the square root of a cubic. This does depend on having a K-rationalpoint, which serves as the point at infinity...
Focal Point was released in 1997. Focal Point was acquired by Telelogic on April 13, 2005. IBM Rational acquired Telelogic in April 2008., Focal Point was...
Rational expression may refer to: A mathematical expression that may be rewritten to a rational fraction, an algebraic fraction such that both the numerator...
Rational Synergy is a software tool that provides software configuration management (SCM) capabilities for all artifacts related to software development...
Rational egoism (also called rational selfishness) is the principle that an action is rational if and only if it maximizes one's self-interest. As such...
economic man, is the portrayal of humans as agents who are consistently rational and narrowly self-interested, and who pursue their subjectively defined...
preferences in decision theory that seem paradoxical from a traditional rationalpoint of view (e.g., preference reversals). Since the use of a quantum-theoretic...
Rational Rose was a development environment for Unified Modeling Language. It integrates with Microsoft Visual Studio .NET and Rational Application Developer...
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