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4.18.4 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).
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; ==> // characteristic : 32003 ==> // number of vars : 4 ==> // block 1 : ordering dp ==> // : names x y ==> // block 2 : ordering dp ==> // : names a b ==> // block 3 : ordering C |