affine coordinate system in a sentence

1. For defining a " polynomial function over the affine space ", one has to choose an affine coordinate system.
2. Basis vectors that are the same at all points are "'global bases "', and can be associated only with linear or affine coordinate systems.
3. 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 "'
4. By the above definition, the choice of an affine coordinate system of an affine space \ mathbb A _ k ^ n allows to identify the polynomial functions on \ mathbb A _ k ^ n with polynomials in variables, the " i " th variable representing the function that maps a point to its " i " th coordinate.
5. It's difficult to find affine coordinate system in a sentence.