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4.16.3 ring operations

+

construct a new ring k[X,Y ] from k1[X] and k2[Y ] .

Concerning the ground fields k1 and k2 take the following guide lines into consideration:

  • Neither k1 nor k2 may be R or C .
  • If the characteristic of k1 and k2 differs, then one of them must be Q .
  • At most one of k1 and k2 may be have parameters.
  • If one of k1 and k2 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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