Symmetric Expression
Field
-variable polynomial ring on
Field of polynomial ring remainders
Symmetric group using 
For
, the mapping is defined as
is an automorphism mapping in 
.If
for 
, then the set formed by 
is a symmetric rational expression, constituting the fixed field 
.
is a normal extension of 
.
The following symmetric expressions are defined:
In this case, we have:
.
is a decomposition field of the polynomial 
in 
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