|  |  4.19.4 ring operations 
 
+construct a new ring 
![$k[X,Y]$](sing_94.png) from ![$k_1[X]$](sing_95.png) and ![$k_2[Y]$](sing_96.png) .
(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 charstrof 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
 |