Singular Manual: Weyl

| ##### 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
    ==> // 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
    ==> // 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
See also: makeWeyl.

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