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7.5.20.0. Weyl
Procedure from library nctools.lib (see nctools_lib).
- Usage:
- Weyl()
- Return:
- ring
- Purpose:
- create a Weyl algebra structure on the basering
- Note:
- Activate this ring using the command
setring.
Assume the number of variables of a basering is 2k.
(if the number of variables is odd, an error message will be returned)
by default, the procedure treats first k variables as coordinates x_i and the last k as differentials d_i
if a non-zero optional argument is given, the procedure treats 2k variables of a basering as k pairs (x_i,d_i), i.e. variables with odd numbers are treated as coordinates and with even numbers as differentials
Example:
| | LIB "nctools.lib";
ring A1=0,(x(1..2),d(1..2)),dp;
def S=Weyl();
setring S; S;
==> // coefficients: QQ considered as a field
==> // number of vars : 4
==> // block 1 : ordering dp
==> // : names x(1) x(2) d(1) d(2)
==> // block 2 : ordering C
==> // noncommutative relations:
==> // d(1)x(1)=x(1)*d(1)+1
==> // d(2)x(2)=x(2)*d(2)+1
kill A1,S;
ring B1=0,(x1,d1,x2,d2),dp;
def S=Weyl(1);
setring S; S;
==> // coefficients: QQ considered as a field
==> // number of vars : 4
==> // block 1 : ordering dp
==> // : names x1 d1 x2 d2
==> // block 2 : ordering C
==> // noncommutative relations:
==> // d1x1=x1*d1+1
==> // d2x2=x2*d2+1
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See also:
makeWeyl.
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