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- X1, X2, ..., Xn,
is a function F that satisfies some non-trivial equation
- P(F, X1, X2, ..., Xn) = 0,
- F(X) = √(X2 + 1).
The class of algebraic functions contains all rational functions, but is larger. In fact in terms of abstract algebra it is the algebraic closure of the field of rational functions, for any fixed set of indeterminates. (NB: when K is a finite field it is inaccurate to equate polynomials with functions, rather than symbolic expressions; however the term algebraic function is used nonetheless).
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