Affine arithmetic (AA) is a model for self-validated numerical analysis. In AA, the quantities of interest are represented as affine combinations (affine...

§ Arithmetic.) More sophisticated methods of dealing with uncertain values include interval arithmetic and affine arithmetic. Interval arithmetic describes...

geometric tools. Arakelov theory overcomes this obstacle by compactifying affine arithmetic schemes, adding points at infinity corresponding to valuations. If...

REC (International Workshop on Reliable Engineering Computing). Affine arithmetic INTLAB (Interval Laboratory) Automatic differentiation Multigrid method...

irreducible affine algebraic set is also called an affine variety.: 3  (Some authors use the phrase affine variety to refer to any affine algebraic set...

In mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or a family of abelian varieties. It goes...

The affine cipher is a type of monoalphabetic substitution cipher, where each letter in an alphabet is mapped to its numeric equivalent, encrypted using...

see Floating-point arithmetic § Infinities and IEEE floating point Some authors use Affinely extended real number system and Affinely extended real number...

based on a wide range of published theories, from simple complex-number arithmetic to group theory and number theory. The best-known FFT algorithms depend...

the positive definiteness of a given matrix) root-finding algorithm Affine arithmetic Solving ODEs rigorously (This feature includes external tools such...

In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance...

an affine variety to A1, we can define regular maps from one affine variety to another. First we will define a regular map from a variety into affine space:...

committed by doing only a finite numbers of steps Well-posed problem Affine arithmetic Unrestricted algorithm Summation: Kahan summation algorithm Pairwise...

ISBN 978-1107167483, MR 3729270 Milne, J. S., Affine Group Schemes; Lie Algebras; Lie Groups; Reductive Groups; Arithmetic Subgroups Mumford, David (1970), Abelian...

shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works...

triangles for rendering and affine mapping is used on them. The reason this technique works is that the distortion of affine mapping becomes much less noticeable...

is an affine Weyl group, the Coxeter complex is a subdivision of the affine plane and one speaks of affine, or Euclidean, buildings. An affine building...

Arithmetic dynamics is a field that amalgamates two areas of mathematics, dynamical systems and number theory. Part of the inspiration comes from complex...

Choose an open affine subset U = Spec A of X. The ring A is an Fp-algebra, so it admits a Frobenius endomorphism. If V is an open affine subset of U, then...

such as when H is closed in G and both are affine. The multiplicative group Gm has the punctured affine line as its underlying scheme, and as a functor...

distinguishing such a linear function from the other concept, the term affine function is often used. In linear algebra, mathematical analysis, and functional...

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

This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass...

dividend (numerator). The usual definition of the quotient in elementary arithmetic is the number which yields the dividend when multiplied by the divisor...

space as a three-dimensional affine space E ( 3 ) {\displaystyle E(3)} over the real numbers. This is unique up to affine isomorphism. It is sometimes...

mathematical spaces have additional arithmetical structure associated with their points. A vector plane is an affine plane whose points, called vectors...

finite geometries, attention is mostly paid to the finite projective and affine spaces because of their regularity and simplicity. Other significant types...

faithfully is an affine space group. Combining these results shows that classifying space groups in n dimensions up to conjugation by affine transformations...

of a line, thereby reducing geometry to arithmetic. Three-dimensional Euclidean space is defined to be an affine space whose associated vector space of...

when the complex plane is transformed by translation or dilation (by an affine transformation), corresponding to the intuitive notion of shape, and describing...