# Singular

##### 7.7.11.0. makeQsl2
Procedure from library `ncalg.lib` (see ncalg_lib).

Usage:
makeQsl2([n]), n an optional int

Return:
ring

Purpose:
define the U_q(sl_2) as a factor-ring of a ring V_q(sl_2) modulo the ideal `Qideal`

Note:
the output consists of a ring, presenting V_q(sl_2) together with the ideal called `Qideal` in this ring
activate this ring with the `setring` command
in order to create the U_q(sl_2) from the output, execute the command like `qring Usl2q = Qideal;`
If n is specified, the quantum parameter q will be specialized at the n-th root of unity

Example:
 ```LIB "ncalg.lib"; def A = makeQsl2(3); setring A; Qideal; ==> Qideal[1]=Ke*Kf-1 qring Usl2q = Qideal; Usl2q; ==> // characteristic : 0 ==> // 1 parameter : q ==> // minpoly : (q^2+q+1) ==> // number of vars : 4 ==> // block 1 : ordering dp ==> // : names E F Ke Kf ==> // block 2 : ordering C ==> // noncommutative relations: ==> // FE=E*F+(2/3*q+1/3)*Ke+(-2/3*q-1/3)*Kf ==> // KeE=(-q-1)*E*Ke ==> // KfE=(q)*E*Kf ==> // KeF=(q)*F*Ke ==> // KfF=(-q-1)*F*Kf ==> // quotient ring from ideal ==> _[1]=Ke*Kf-1 ```