### 4.20.4 ring operations

`+`
  construct a new ring from and . (The sets of variables must be distinct).
`==`,`<>`
  compare two rings

Note: Concerning the ground fields and take the following guide lines into consideration:

- Neither nor may be or .
- If the characteristic of and differs, then one of them must be .
- At most one of and may have parameters.
- If one of and is an algebraic extension of it may not be defined by a `charstr` of type `(p^n,a)`.

Example:

      ring R1=0,(x,y),dp;
      ring R2=32003,(a,b),dp;
      def R=R1+R2;
      R;
    ==> // coefficients: ZZ/32003 considered as a field
    ==> // number of vars : 4
    ==> //        block   1 : ordering dp
    ==> //                  : names    x y
    ==> //        block   2 : ordering dp
    ==> //                  : names    a b
    ==> //        block   3 : ordering C

ring_lib

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