Singular

LIB "brnoeth.lib";
int plevel=printlevel;
printlevel=-1;
ring s=2,(x,y),lp;
list C=Adj_div(x3y+y3+x);
==> The genus of the curve is 3
C=NSplaces(1..4,C);
// the first 3 Places in C[3] are of degree 1.
// we define the rational divisor G = 4*C[3][1]+4*C[3][3] (of degree 8):
intvec G=4,0,4;
def R=C[1][2];
setring R;
list LG=BrillNoether(G,C);
==> Vector basis successfully computed 
// here is the vector basis of L(G):
LG;
==> [1]:
==>    _[1]=1
==>    _[2]=1
==> [2]:
==>    _[1]=y
==>    _[2]=x
==> [3]:
==>    _[1]=z
==>    _[2]=x
==> [4]:
==>    _[1]=y2
==>    _[2]=x2
==> [5]:
==>    _[1]=xz2+y3
==>    _[2]=x3
==> [6]:
==>    _[1]=xyz2+y4
==>    _[2]=x4
printlevel=plevel;