Elementary number

Short description: Field extension of rational numbers

An elementary number is one formalization of the concept of a closed-form number. The elementary numbers form an algebraically closed field containing the roots of arbitrary expressions using field operations, exponentiation, and logarithms. The set of the elementary numbers is subdivided into the explicit elementary numbers and the implicit elementary numbers.

References

• Ritt, Joseph Fels (1948). Integration in finite terms. Liouville's theory of elementary methods. New York: Columbia University press. p. 60. 
• Lin, Ferng-Ching (1983). "Schanuel's conjecture implies Ritt's conjectures". Chin. J. Math. 11 (1): 41–50. 
• Chow, Timothy (1999). "What is a closed-form number". Amer. Math. Monthly 106 (5): 440–448. doi:10.1080/00029890.1999.12005066. 
• Richardson, Daniel (1997). "How to recognize zero". Journal of Symbolic Computation 24 (6): 627–645. doi:10.1006/jsco.1997.0157.