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2.7.2 ring operations
+
- construct an algebra
for two
-algebras.
Let
,
and

be two G-algebras, then C is defined to be the algebra
,
,
.
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 charstr of type (p^n,a) .
Example:
| LIB "ncalg.lib";
def a = sl2(); // U(sl_2) in e,f,h presentation
ring W = 0,(x,d),dp;
Weyl(); // 1st Weyl algebra in x,d
def S = a+W;
setring S;
S;
==> // characteristic : 0
==> // 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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