affine coordinate造句

• 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.
• 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 "'
• The choice of a system of affine coordinates for an affine space \ mathbb A _ k ^ n of dimension over a field induces an affine isomorphism between \ mathbb A _ k ^ n and the affine coordinate space.
• The choice of a system of affine coordinates for an affine space \ mathbb A _ k ^ n of dimension over a field induces an affine isomorphism between \ mathbb A _ k ^ n and the affine coordinate space.
• The theorem can be refined to include a chain of ideals of " R " ( equivalently, closed subsets of " X " ) that are finite over the affine coordinate subspaces of the appropriate dimensions.
• Taking their conjugates, we see that z is a weighted sum with positive coefficients that sum to one, or the barycenter on affine coordinates, of the complex numbers a _ i ( with different mass assigned on each root whose weights collectively sum to 1 ).
• For the Riemann sphere, above, the notion of a polynomial is not defined globally, but simply with respect to an affine coordinate ring of " U ", and that a rational function on all of " V " consists of such local data which agree on the intersections of open affines.