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7.5.19.0. makeHeisenberg
Procedure from library nctools.lib (see nctools_lib).
- Usage:
- makeHeisenberg(n, [p,d]); int n (setting 2n+1 variables), optional int p (field characteristic), optional int d (power of h in the commutator)
- Return:
- ring
- Purpose:
- create the n-th Heisenberg algebra in the variables x(1),y(1),...,x(n),y(n),h over the rationals Q or F_p with the relations
\forall\;i\in\{1,2,\ldots,n\}\;\;y(j)x(i) = x(i)y(j)+h^d.
- Note:
- activate this ring with the
setring command
If p is not prime, the next larger prime number will be used.
Example:
| | LIB "nctools.lib";
def a = makeHeisenberg(2);
setring a; a;
==> // coefficients: QQ
==> // number of vars : 5
==> // block 1 : ordering lp
==> // : names x(1) x(2) y(1) y(2) h
==> // block 2 : ordering C
==> // noncommutative relations:
==> // y(1)x(1)=x(1)*y(1)+h
==> // y(2)x(2)=x(2)*y(2)+h
def H3 = makeHeisenberg(3, 7, 2);
setring H3; H3;
==> // coefficients: ZZ/7
==> // number of vars : 7
==> // block 1 : ordering lp
==> // : names x(1) x(2) x(3) y(1) y(2) y(3) h
==> // block 2 : ordering C
==> // noncommutative relations:
==> // y(1)x(1)=x(1)*y(1)+h^2
==> // y(2)x(2)=x(2)*y(2)+h^2
==> // y(3)x(3)=x(3)*y(3)+h^2
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See also:
makeWeyl.
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