symmetric polynomial
التعريفات والمعاني
== English ==
=== Noun ===
symmetric polynomial (plural symmetric polynomials)
(algebra) A polynomial which remains unchanged if its variables are permuted
x
+
y
+
z
{\displaystyle x+y+z}
x
y
z
{\displaystyle xyz}
2
x
2
+
2
y
2
+
2
z
2
{\displaystyle 2x^{2}+2y^{2}+2z^{2}}
, etc.
An example of a non-symmetric polynomial is
x
+
2
y
{\displaystyle x+2y}
: if we interchange
x
{\displaystyle x}
and
y
{\displaystyle y}
, this polynomial changes to
2
x
+
y
{\displaystyle 2x+y}
.
==== Hyponyms ====
elementary symmetric polynomial