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4.19.4 ring operations

construct a new ring $k[X,Y]$ from $k_1[X]$ and $k_2[Y]$. (The sets of variables must be distinct).
compare two rings

Note: Concerning the ground fields $k_1$ and $k_2$ take the following guide lines into consideration:

  • Neither $k_1$ nor $k_2$ may be $R$ or $C$.
  • If the characteristic of $k_1$ and $k_2$ differs, then one of them must be $Q$.
  • At most one of $k_1$ and $k_2$ may have parameters.
  • If one of $k_1$ and $k_2$ is an algebraic extension of $Z/p$ it may not be defined by a charstr of type (p^n,a).


  ring R1=0,(x,y),dp;
  ring R2=32003,(a,b),dp;
  def R=R1+R2;
==> // 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