To whom it may concern,
there is plural: http://www.singular.uni-kl.de/Manual/latest/sing_349.htm
which is shipped with SAGE (though, the interface hasn't been worked on)
sage: singular.lib('ncalg.lib')
sage: a = singular.makeUsl2()
sage: W = singular.ring(0,'(x,d)','dp')
sage: singular.Weyl()
`sage2`
sage: S = a + W
sage: singular.set_ring(S)
sage: 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=e*f-h
// he=e*h+2*e
// hf=f*h-2*f
// dx=x*d+1
or in terms of SINGULAR/PLURAL directly:
LIB "ncalg.lib";
def a = makeUsl2(); // 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
Martin
PS: I don't know much about non-commutative algebra, so I wouldn't know if
your favorite ring is supported by PLURAL.
--
name: Martin Albrecht
_pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99
_www: http://www.informatik.uni-bremen.de/~malb
_jab: [EMAIL PROTECTED]
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