# Singular

##### 7.7.11.0. makeQsl3
Procedure from library `ncalg.lib` (see ncalg_lib).

Usage:
makeQsl3([n]), n an optional int

Return:
ring

Purpose:
define the U_q(sl_3) as a factor-ring of a ring V_q(sl_3) modulo the ideal `Qideal`

Note:
the output consists of a ring, presenting V_q(sl_3) together with the ideal called `Qideal` in this ring
activate this ring with the `setring` command
in order to create the U_q(sl_3) from the output, execute the command like `qring Usl3q = Qideal;`
If n is specified, the quantum parameter q will be specialized at the n-th root of unity

Example:
 ```LIB "ncalg.lib"; def B = makeQsl3(5); setring B; qring Usl3q = Qideal; Usl3q; ==> // characteristic : 0 ==> // 1 parameter : q ==> // minpoly : (q^4+q^3+q^2+q+1) ==> // number of vars : 10 ==> // block 1 : ordering wp ==> // : names f12 f13 f23 k1 k2 l1 l2 e12 e13 e23 ==> // : weights 2 3 2 1 1 1 1 2 3 2 ==> // block 2 : ordering C ==> // noncommutative relations: ==> // f13f12=(q^3)*f12*f13 ==> // f23f12=(q^2)*f12*f23+(-q)*f13 ==> // k1f12=(q^3)*f12*k1 ==> // k2f12=(q)*f12*k2 ==> // l1f12=(q^2)*f12*l1 ==> // l2f12=(-q^3-q^2-q-1)*f12*l2 ==> // e12f12=f12*e12+(1/5*q^3-3/5*q^2-2/5*q-1/5)*k1^2+(-1/5*q^3+3/5*q^2+2\ /5*q+1/5)*l1^2 ==> // e13f12=f12*e13+(q^3+q^2+q+1)*l1^2*e23 ==> // f23f13=(q^3)*f13*f23 ==> // k1f13=(-q^3-q^2-q-1)*f13*k1 ==> // k2f13=(-q^3-q^2-q-1)*f13*k2 ==> // l1f13=(q)*f13*l1 ==> // l2f13=(q)*f13*l2 ==> // e12f13=f13*e12+(q)*f23*k1^2 ==> // e13f13=f13*e13+(-1/5*q^3+3/5*q^2+2/5*q+1/5)*k1^2*k2^2+(1/5*q^3-3/5*\ q^2-2/5*q-1/5)*l1^2*l2^2 ==> // e23f13=f13*e23+(q^3+q^2+q+1)*f12*l2^2 ==> // k1f23=(q)*f23*k1 ==> // k2f23=(q^3)*f23*k2 ==> // l1f23=(-q^3-q^2-q-1)*f23*l1 ==> // l2f23=(q^2)*f23*l2 ==> // e13f23=f23*e13+(q)*k2^2*e12 ==> // e23f23=f23*e23+(1/5*q^3-3/5*q^2-2/5*q-1/5)*k2^2+(-1/5*q^3+3/5*q^2+2\ /5*q+1/5)*l2^2 ==> // e12k1=(q^3)*k1*e12 ==> // e13k1=(-q^3-q^2-q-1)*k1*e13 ==> // e23k1=(q)*k1*e23 ==> // e12k2=(q)*k2*e12 ==> // e13k2=(-q^3-q^2-q-1)*k2*e13 ==> // e23k2=(q^3)*k2*e23 ==> // e12l1=(q^2)*l1*e12 ==> // e13l1=(q)*l1*e13 ==> // e23l1=(-q^3-q^2-q-1)*l1*e23 ==> // e12l2=(-q^3-q^2-q-1)*l2*e12 ==> // e13l2=(q)*l2*e13 ==> // e23l2=(q^2)*l2*e23 ==> // e13e12=(q^3)*e12*e13 ==> // e23e12=(q^2)*e12*e23+(-q)*e13 ==> // e23e13=(q^3)*e13*e23 ==> // quotient ring from ideal ==> _[1]=k2*l2-1 ==> _[2]=k1*l1-1 ```