Singular Manual: ring operations

| ### 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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