Singular

LIB "brnoeth.lib";
ring s=2,(x,y),lp;
// this is just the affine plane over F_4 :
ideal I=x4+x,y4+y;
list L=closed_points(I);
// and here you have all the points :
L;
==> [1]:
==>    _[1]=y
==>    _[2]=x
==> [2]:
==>    _[1]=y
==>    _[2]=x+1
==> [3]:
==>    _[1]=y
==>    _[2]=x2+x+1
==> [4]:
==>    _[1]=y+1
==>    _[2]=x
==> [5]:
==>    _[1]=y+1
==>    _[2]=x+1
==> [6]:
==>    _[1]=y+1
==>    _[2]=x2+x+1
==> [7]:
==>    _[1]=y2+y+1
==>    _[2]=x+y
==> [8]:
==>    _[1]=y2+y+1
==>    _[2]=x+y+1
==> [9]:
==>    _[1]=y2+y+1
==>    _[2]=x+1
==> [10]:
==>    _[1]=y2+y+1
==>    _[2]=x