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...

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...

rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational...

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...

rational point (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 rational point on...

are said k-rational or rational over k. In the common case where k is the field of real numbers, a k-rational point is called a real point. When the field...

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...

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...

real numbers, is called a real point. A rational point over Q {\displaystyle \mathbb {Q} } is called simply a rational point. By clearing denominators, one...

the rational normal curve, where all these polynomials are monomials. Any conic section defined over F with a rational point in F is a rational curve...

establishes that each rational point of the x-axis goes over to a rational point of the unit circle. The converse, that every rational point of the unit circle...

if r is rational there is no non-trivial rational point (x, y) on this curve (that is, no point for which both x and y are non-zero rational numbers)...

function for rational points on an elliptic curve E. The context is of a hypothetical non-trivial rational point on E. Doubling a point on E roughly doubles...

result that a smooth quadric over a field k is rational over k if and only if X has a k-rational point. That is, if there is a solution of the equation...

at the point s = 1. In particular if the elliptic curve has (analytic) rank 1, then the Heegner points can be used to construct a rational point on the...

} This is an elliptic curve with a rational point at v1 = −⁠31/467⁠. From this initial rational point, one can compute an infinite collection of...

} If P = ( x , y ) {\displaystyle P=(x,y)} is a rational point of finite order on E, for the elliptic curve group law, then: x and...

In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example...

that is continuous at every rational point, but discontinuous at every irrational point. The indicator function of the rationals, also known as the Dirichlet...

(often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem...

Non-singular point Normal point Parshin point Periodic point Pinch point Point (geometry) Point source Rational point Recurrent point Regular point, Regular...

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

Rational choice modeling refers to the use of decision theory (the theory of rational choice) as a set of guidelines to help understand economic and social...

that is no restriction for F of characteristic zero). If X has an F-rational point, then it is isomorphic to G/P for some parabolic subgroup P of G. A...

field of rational functions made by extracting the square root of a cubic. This does depend on having a K-rational point, which serves as the point at infinity...

rational points. For each rational number p / q {\displaystyle p/q} , expressed in lowest terms, there is a Ford circle whose center is at the point (...

isomorphism Cl(P1) ≅ Z. For any smooth projective curve X with a k-rational point, the degree homomorphism is surjective, and the kernel is isomorphic...

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...

way that the algebra splits over K if and only if the variety has a rational point over K. Francesco Severi (1932) studied these varieties, and they are...

Bounded rationality is the idea that rationality is limited when individuals make decisions, and under these limitations, rational individuals will select...