Singular Manual: makeUgl

7.7.11.0. makeUgl

Procedure from library ncalg.lib (see ncalg_lib).

Usage:: makeUgl(n,[p]); n an int, n>1; p an optional int (field characteristic)
Return:: ring
Purpose:: set up the U(gl_n) in the (e_ij (1<i,j<n)) presentation (where e_ij corresponds to a matrix with 1 at i,j only) over the field of char p
Note:: activate this ring with the setring command
the variables are ordered as e_12,e_13,...,e_1n,e_21,...,e_nn.

Example:

LIB "ncalg.lib";
def a=makeUgl(3);
setring a; a;
==> //   characteristic : 0
==> //   number of vars : 9
==> //        block   1 : ordering dp
==> //                  : names    e_1_1 e_1_2 e_1_3 e_2_1 e_2_2 e_2_3 e_3_1 \
   e_3_2 e_3_3
==> //        block   2 : ordering C
==> //   noncommutative relations:
==> //    e_1_2e_1_1=e_1_1*e_1_2-e_1_2
==> //    e_1_3e_1_1=e_1_1*e_1_3-e_1_3
==> //    e_2_1e_1_1=e_1_1*e_2_1+e_2_1
==> //    e_3_1e_1_1=e_1_1*e_3_1+e_3_1
==> //    e_2_1e_1_2=e_1_2*e_2_1-e_1_1+e_2_2
==> //    e_2_2e_1_2=e_1_2*e_2_2-e_1_2
==> //    e_2_3e_1_2=e_1_2*e_2_3-e_1_3
==> //    e_3_1e_1_2=e_1_2*e_3_1+e_3_2
==> //    e_2_1e_1_3=e_1_3*e_2_1+e_2_3
==> //    e_3_1e_1_3=e_1_3*e_3_1-e_1_1+e_3_3
==> //    e_3_2e_1_3=e_1_3*e_3_2-e_1_2
==> //    e_3_3e_1_3=e_1_3*e_3_3-e_1_3
==> //    e_2_2e_2_1=e_2_1*e_2_2+e_2_1
==> //    e_3_2e_2_1=e_2_1*e_3_2+e_3_1
==> //    e_2_3e_2_2=e_2_2*e_2_3-e_2_3
==> //    e_3_2e_2_2=e_2_2*e_3_2+e_3_2
==> //    e_3_1e_2_3=e_2_3*e_3_1-e_2_1
==> //    e_3_2e_2_3=e_2_3*e_3_2-e_2_2+e_3_3
==> //    e_3_3e_2_3=e_2_3*e_3_3-e_2_3
==> //    e_3_3e_3_1=e_3_1*e_3_3+e_3_1
==> //    e_3_3e_3_2=e_3_2*e_3_3+e_3_2