Fundamental Theorem of Symmetric Functions

Any symmetric polynomial (respectively, symmetric rational function) can be expressed as a Polynomial (respectively,Rational Function) in the Elementary Symmetric Functions on those variables.

References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 2, 1959.

Herstein, I. N. Noncommutative Rings. Washington, DC: Math. Assoc. Amer., 1968.

• Fermat's Factorization Method
• Fermat's Last Theorem
• Fermat's Lesser Theorem
• Fermat's Little Theorem
• Fermat's Little Theorem Converse
• Fermat Spiral Inverse Curve
• Fermat's Polygonal Number Theorem
• Fermat's Primality Test
• Fermat's Problem
• Fermat's Right Triangle Theorem
• Fermat's Sigma Problem
• Fermat's Simple Theorem
• Fermat's Spiral
• Fermat's Theorem
• Fermat's Two-Square Theorem
• Fermat Sum Theorem
• Fermi-Dirac Distribution
• Fern
• Ferrari's Identity
• Ferrers Diagram
• Ferrers' Function
• Ferrier's Prime
• Feuerbach Circle
• Feuerbach Point
• Feuerbach's Conic Theorem