Singular

7.7.16.0. makeWeyl

Usage:

makeWeyl(n,[p]); n an integer, n>0; p an optional integer (field characteristic)

Return:

ring

Purpose:

create the n-th Weyl algebra over the rationals Q or F_p

Note:

activate this ring with the "setring" command.
The presentation of an n-th Weyl algebra is classical: D(i)x(i)=x(i)D(i)+1,
where x(i) correspond to coordinates and D(i) to partial differentiations, i=1,...,n.
If p is not prime, the next larger prime number will be used.

LIB "nctools.lib";
def a = makeWeyl(3);
setring a;
a;
==> // coefficients: QQ
==> // number of vars : 6
==> //        block   1 : ordering dp
==> //                  : names    x(1) x(2) x(3) D(1) D(2) D(3)
==> //        block   2 : ordering C
==> // noncommutative relations:
==> //    D(1)x(1)=x(1)*D(1)+1
==> //    D(2)x(2)=x(2)*D(2)+1
==> //    D(3)x(3)=x(3)*D(3)+1