# affine coordinates in a sentence

- In each
*affine coordinate*domain the coordinate vector fields form a web. - Therefore, barycentric and
*affine coordinates*are almost equivalent. - In most applications,
*affine coordinates*are preferred, as involving less coordinates that are independent. - There is a unique affine structure on this maximal spectrum that is compatible with the filtration on the
*affine coordinate*ring. - In
*affine coordinates*, which include Cartesian coordinates in Euclidean spaces, each output coordinate of an affine map is a translation. - It's difficult to find
*affine coordinates*in a sentence. - For defining a " polynomial function over the affine space ", one has to choose an
*affine coordinate*system. - A commonly used method for carrying out the embedding in this case involves expanding the set of
*affine coordinates*and working in a more general " algebra ". - Basis vectors that are the same at all points are "'global bases "', and can be associated only with linear or
*affine coordinate*systems. - I thought that may be the scalar represents the point in
*affine coordinates*, but what exactly does it mean to multiply and divide two points in the projective line? - The total degree defines also a graduation, but it depends on the choice of coordinates, as a change of
*affine coordinates*may map indeterminates on non-homogeneous polynomials. - In Euclidean geometry, Cartesian coordinates are
*affine coordinates*relative to an "'orthonormal frame "', that is an affine frame such that is an orthonormal basis. - As a change of
*affine coordinates*may be expressed by linear functions ( more precisely affine functions ) of the coordinates, this definition is independent of a particular choice of coordinates. - The most important case of
*affine coordinates*in Euclidean spaces is real-valued Cartesian coordinate system . rectangular, and others are referred to as "'oblique " '. - We may define the function field of " V " to be the field of fractions of the
*affine coordinate*ring of any open affine subset, since all such subsets are dense. - If T is linear the coordinate system Z ^ i will be called an "'
*affine coordinate*system "', otherwise Z ^ i is called a "'curvilinear coordinate system "'

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