Singular Manual: makeHeisenberg

| ##### 7.5.20.0. 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
See also: makeWeyl.

User manual for Singular version 4.3.2, 2023, generated by texi2html.