Singular Manual: ring operations

| ### 4.20.4 ring operations `+` construct a new ring 95#95 from 96#96 and 97#97. (The sets of variables must be distinct). `==`,`<>` compare two rings Note: Concerning the ground fields 98#98 and 99#99 take the following guide lines into consideration: Neither 98#98 nor 99#99 may be 53#53 or 78#78. If the characteristic of 98#98 and 99#99 differs, then one of them must be 3#3. At most one of 98#98 and 99#99 may have parameters. If one of 98#98 and 99#99 is an algebraic extension of 22#22 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
    ==> // 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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