Singular

LIB "nctools.lib";
/////////////////////////////////////////////////////////////////////
ring R = 0,(x(1..4)),dp; // commutative
if(IsSCA())
{ "Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; }
else
{ "Not a super-commutative algebra!!!"; }
==> Not a super-commutative algebra!!!
kill R;
/////////////////////////////////////////////////////////////////////
ring R = 0,(x(1..4)),dp;
def S = nc_algebra(1, 0); setring S; S; // still commutative!
==> // coefficients: QQ
==> // number of vars : 4
==> //        block   1 : ordering dp
==> //                  : names    x(1) x(2) x(3) x(4)
==> //        block   2 : ordering C
==> // noncommutative relations:
if(IsSCA())
{ "Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; }
else
{ "Not a super-commutative algebra!!!"; }
==> Not a super-commutative algebra!!!
kill R, S;
/////////////////////////////////////////////////////////////////////
ring R = 0,(x(1..4)),dp;
list CurrRing = ringlist(R);
def ER = ring(CurrRing);
setring ER; // R;
matrix E = UpOneMatrix(nvars(R));
int i, j; int b = 2; int e = 3;
for ( i = b; i < e; i++ )
{
for ( j = i+1; j <= e; j++ )
{
E[i, j] = -1;
}
}
def S = nc_algebra(E,0); setring S; S;
==> // coefficients: QQ
==> // number of vars : 4
==> //        block   1 : ordering dp
==> //                  : names    x(1) x(2) x(3) x(4)
==> //        block   2 : ordering C
==> // noncommutative relations:
==> //    x(3)x(2)=-x(2)*x(3)
if(IsSCA())
{ "Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; }
else
{ "Not a super-commutative algebra!!!"; }
==> Not a super-commutative algebra!!!
kill R, ER, S;
/////////////////////////////////////////////////////////////////////
ring R = 0,(x(1..4)),dp;
def ER = superCommutative(2); // (b = 2, e = N)
setring ER; ER;
==> // coefficients: QQ
==> // number of vars : 4
==> //        block   1 : ordering dp
==> //                  : names    x(1) x(2) x(3) x(4)
==> //        block   2 : ordering C
==> // noncommutative relations:
==> //    x(3)x(2)=-x(2)*x(3)
==> //    x(4)x(2)=-x(2)*x(4)
==> //    x(4)x(3)=-x(3)*x(4)
==> // quotient ring from ideal
==> _[1]=x(4)^2
==> _[2]=x(3)^2
==> _[3]=x(2)^2
if(IsSCA())
{ "This is a SCA! Alternating variables: [", AltVarStart(), ",", AltVarEnd(), "]."; }
==> This is a SCA! Alternating variables: [ 2 , 4 ].
else
{ "Not a super-commutative algebra!!!"; }
kill R, ER;