User:CRGreathouse/Functions
Type | Properties | Closure | Examples | Limitations |
---|---|---|---|---|
Polynomial function
|
Addition, subtraction, multiplication, composition | x^2 - 3x + 1 | ||
Rational function | field operations, composition | (3x^2 + 1)/(2x - 1) | Division by zero | |
Algebraic function | Meromorphic, decidable | field operations | sqrt(x), Bring radical | Abel–Ruffini theorem |
High-school identities | 2^x | Tarski's high school algebra problem | ||
Real + exponential | e^x - 1 | Tarski's exponential function problem | ||
Elementary function | Continuous | Field operations, composition, derivative | |sin(sin(x))|, e^cosh(x) | Richardson's theorem |
Liouvillian function | Field operations, composition, derivative, integral | li (x)
|