# Singular

##### 7.5.10.0. makeUsp2
Procedure from library ncalg.lib (see ncalg_lib).

Usage:
makeUsp2([p]); p an optional integer (field characteristic)

Return:
a ring, describing U(sp_2)

Note:
You have to activate this ring with the 'setring' command. The presentation of U(sp_2) is derived from the Chevalley representation of sp_2, positive resp. negative roots are denoted by x(i) resp. y(i); Cartan elements are denoted by h(i).

Example:
 LIB "ncalg.lib"; def ncAlgebra = makeUsp2(); setring ncAlgebra; ncAlgebra; ==> // coefficients: QQ ==> // number of vars : 10 ==> // block 1 : ordering dp ==> // : names X(1) X(2) X(3) X(4) Y(1) Y(2) Y(3) Y(4) H(\ 1) H(2) ==> // block 2 : ordering C ==> // noncommutative relations: ==> // X(2)X(1)=X(1)*X(2)+X(3) ==> // X(3)X(1)=X(1)*X(3)+2*X(4) ==> // Y(1)X(1)=X(1)*Y(1)-H(1) ==> // Y(3)X(1)=X(1)*Y(3)-2*Y(2) ==> // Y(4)X(1)=X(1)*Y(4)-Y(3) ==> // H(1)X(1)=X(1)*H(1)+2*X(1) ==> // H(2)X(1)=X(1)*H(2)-X(1) ==> // Y(2)X(2)=X(2)*Y(2)-H(2) ==> // Y(3)X(2)=X(2)*Y(3)+Y(1) ==> // H(1)X(2)=X(2)*H(1)-2*X(2) ==> // H(2)X(2)=X(2)*H(2)+2*X(2) ==> // Y(1)X(3)=X(3)*Y(1)-2*X(2) ==> // Y(2)X(3)=X(3)*Y(2)+X(1) ==> // Y(3)X(3)=X(3)*Y(3)-H(1)-2*H(2) ==> // Y(4)X(3)=X(3)*Y(4)+Y(1) ==> // H(2)X(3)=X(3)*H(2)+X(3) ==> // Y(1)X(4)=X(4)*Y(1)-X(3) ==> // Y(3)X(4)=X(4)*Y(3)+X(1) ==> // Y(4)X(4)=X(4)*Y(4)-H(1)-H(2) ==> // H(1)X(4)=X(4)*H(1)+2*X(4) ==> // Y(2)Y(1)=Y(1)*Y(2)-Y(3) ==> // Y(3)Y(1)=Y(1)*Y(3)-2*Y(4) ==> // H(1)Y(1)=Y(1)*H(1)-2*Y(1) ==> // H(2)Y(1)=Y(1)*H(2)+Y(1) ==> // H(1)Y(2)=Y(2)*H(1)+2*Y(2) ==> // H(2)Y(2)=Y(2)*H(2)-2*Y(2) ==> // H(2)Y(3)=Y(3)*H(2)-Y(3) ==> // H(1)Y(4)=Y(4)*H(1)-2*Y(4)