- 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. 用affine coordinates造句挺难的
- 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 "'