Singular Manual: makeQsl3

7.5.10.0. 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;
==> // coefficients: QQ[q]/(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