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Function Fields (1849 words) |
 | The function field of the curve is the corresponding field of fractions. |
| This is a vector subspace of the function field of a curve. |
| Since function fields are realised by completely separate code, one cannot automatically expect rational functions written in terms of the generators of the coordinate ring of the curve to be elements of the function field. |
| Function Fields (2592 words) |
| The function field of the curve is the corresponding field of fractions in the affine case and the homogeneous degree 0 part of this in projective cases. |
| As with schemes generally, a function field is attached to projective curves and the same object represents the function field of all of its affine patchs. |
| Return the function f in the function field of a scheme as a function in projective coordinates (as an element in the field of fractions of the coordinate ring of the projective scheme having function field the parent of f). |
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