symmetric polynomial

symmetric polynomial (plural symmetric polynomials)

1. (algebra) A polynomial which remains unchanged if its variables are permuted

   ${\displaystyle x+y+z}$

   ${\displaystyle xyz}$

   ${\displaystyle 2x^{2}+2y^{2}+2z^{2}}$, etc.

   An example of a non-symmetric polynomial is ${\displaystyle x+2y}$: if we interchange ${\displaystyle x}$ and ${\displaystyle y}$, this polynomial changes to ${\displaystyle 2x+y}$.

• elementary symmetric polynomial