> ring r=2,(x,y,z),dp;
> ideal I = xy-z2,x+y+z,z2+y;


> facstd (I);   // the result looks still complicated, since ...
[1]:
   _[1]=y
   _[2]=x+y+z
   _[3]=z2+y
[2]:
   _[1]=y+z+1
   _[2]=x+y+z
   _[3]=z2+y

> option();      // the option redSB is not enabled
//options: redTail redThrough redefine loadLib usage prompt notWarnSB
> option(redSB);  / computed a reduced Groebner basis

> facstd (I);   // now the result is clear
[1]:
   _[1]=z
   _[2]=y
   _[3]=x
[2]:
   _[1]=y+z+1
   _[2]=x+1
   _[3]=z2+z+1

solve(I)

[1]:
    x = 0;
    y = 0;
    z = 0;
...

> ring r=2,(x,y,z),dp;
> ideal I = xy-z2,x+y+z,z2+y;
> option(redSB);
> int TeXwidth =0;
> option(redSB);
> list L = facstd(I);
> texobj("",L[1]);
$$
\begin{array}{*{5}{c}cr}
  &  &   &  & z & = & 0 \\
  &  & y &  &   & = & 0 \\
x &  &   &  &   & = & 0
\end{array}$$
> texobj("",L[2]);
$$
\begin{array}{rcl}
y+z & = & 1 \\
x & = & 1 \\
z^{2}+z & = & 1
\end{array}
$$

// ** loaded /u/gorzelc/.../latex2e.lib 1.0
> texfacstd("",I);
$\{ z=y=x=0 \} \cup \{ y+z+1=x+1=z^{2}+z+1=0 \}$

solve(I)

[1]: 0
[2]: 1
[3]: 0
...

proc gf2solver(string fnm, ideal I)
// writes the solutions in GF(2)^n to stdout resp. writes to file fnm
{
int i,j;
option(redSB);
list L = facstd(I);
ideal J;
string S;

for(i=1;i<=size(L);i++)
{
  if (deg(L[i])==1)  // solutions in GF(2), no field extension is needed
  {
   J= L[i];
   S = newline + S + "["+string(i)+"]" +newline;
   for (j=1;j<=ncols(J);j++)
   {
     S = S + string(J[j]-jet(J[j],0)) + " = "+ string(jet(J[j],0)) + ";"
           + newline;
   }
    S = S + newline;
  }
  else
  {
    "ignoring solution";
    L[i];
  }
}
if (fnm=="") {return(S);}
else {write(fnm,S);}
}

> ring r=2,(x,y,z),dp;
> ideal I = xy-z2,x+y+z,z2+y;

> facstd(I*(x+1));
[1]:
   _[1]=x+1
[2]:
   _[1]=z
   _[2]=y
   _[3]=x
[3]:
   _[1]=x+y+z
   _[2]=z2+y
   _[3]=y2+y+1

> gf2solver("",I*(x+1));
ignoring solution
_[1]=x+y+z
_[2]=z2+y
_[3]=y2+y+1


[1]
x = 1;

[2]
z = 0;
y = 0;
x = 0;