Synonymer & Information om | Engelska ordet AFFINE

Exempel på hur man kan använda AFFINE i en mening

• the convex hull function from the power set of an affine space over the reals to itself is idempotent;.
• In Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles.
• As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement.
• In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher.
• In terms of 3-dimensional geometric vectors, these affine subspaces are all the "lines" or "planes" parallel to the subspace, which is a line or plane going through the origin.
• An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.
• A hyperboloid is the surface obtained from a hyperboloid of revolution by deforming it by means of directional scalings, or more generally, of an affine transformation.
• In the case of two variables and in the case of affine hypersurfaces, if multiplicities and points at infinity are not counted, this theorem provides only an upper bound of the number of points, which is almost always reached.
• There are five known ways to build a set of points on an Edwards curve: the set of affine points, the set of projective points, the set of inverted points, the set of extended points and the set of completed points.
• The first broad category of transformation models includes linear transformations, which include rotation, scaling, translation, and other affine transforms.
• Homogeneous dilation (homothety), the scalar multiplication operator on a vector space or affine space.
• This is one of the basic ideas of scheme theory, which allows one to build general algebraic varieties by gluing together affine varieties in a way similar to that in manifold theory, where manifolds are built by gluing together charts, which are open subsets of real affine spaces.
• In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance and angle.
• An indirect isometry is an affine transformation with an orthogonal matrix that has a determinant of −1.
• An affine variety over an algebraically closed field is conceptually the easiest type of variety to define, which will be done in this section.
• Some are intrinsic, as independent of any embedding of the variety into an affine or projective space, while other are related to such an embedding.
• An affine algebraic plane curve can be completed in a projective algebraic plane curve by homogenizing its defining polynomial.
• While there are many systems that could be called finite geometries, attention is mostly paid to the finite projective and affine spaces because of their regularity and simplicity.
• Other consistent axiom sets can yield other geometries, such as projective, elliptic, spherical or affine geometry.
• Iwahori–Matsumoto, Borel–Tits and Bruhat–Tits demonstrated that in analogy with Tits' construction of spherical buildings, affine buildings can also be constructed from certain groups, namely, reductive algebraic groups over a local non-Archimedean field.

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