4.16.3 ring operations
----------------------
+
construct a new ring 
$k[X,Y]$
 from 
$k_1[X]$
  and 
$k_2[Y]$
.

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 be 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).


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

See also:
ring_lib.

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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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