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Places
- Zeros and poles of algebraic functions
- Valuation (zero, pole orders) of algebraic functions at places
- Residue class field at a place
- Evaluation of algebraic functions at places
- Decomposition of places of k(x) within F/k(x)
- Ramification index, inertia degree
- Bounds on the number of places of degree 1 (global field)
- All places of a prescribed degree (global field)
- Random place of a prescribed degree (global field)