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7.2.7.2 ring operations (plural)

+
construct a tensor product 195#195of two 190#190-algebras 191#191 and 196#196 over the ground field. Let, e.g.,

197#197 198#198, and 199#199 200#200

be two 190#190-algebras, then 78#78 is defined to be the algebra

201#201 202#202, 203#203, 204#204.

Concerning the ground fields 98#98 resp. 99#99 of 191#191 resp. 196#196, take the following guidelines for 205#205 into consideration:

  • Neither 98#98 nor 99#99 may be 53#53 or 78#78.
  • If the characteristic of 98#98 and 99#99 differs, then one of them must be 3#3.
  • At most one of 98#98 and 99#99 may have parameters.
  • If one of 98#98 and 99#99 is an algebraic extension of 22#22 it may not be defined by a charstr of type (p^n,a).
One can create a ring using ring(list), see also ringlist.

Example:
 
LIB "ncalg.lib";
def a = makeUsl2();       // U(sl_2) in e,f,h presentation
ring W0 = 0,(x,d),dp;
def W = Weyl();              // 1st Weyl algebra in x,d
def S = a+W;
setring S;
S;
==> // coefficients: QQ considered as a field
==> // number of vars : 5
==> //        block   1 : ordering dp
==> //                  : names    e f h
==> //        block   2 : ordering dp
==> //                  : names    x d
==> //        block   3 : ordering C
==> // noncommutative relations:
==> //    fe=ef-h
==> //    he=eh+2e
==> //    hf=fh-2f
==> //    dx=xd+1


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