|
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
==> // 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
|
|