-- -*- M2-comint -*- {* hash: -858428138 *}

i1 : gbTrace = 3

o1 = 3

i2 : R = ZZ[x,y,z];

   -- registering polynomial ring 4 at 0x8414510

i3 : f = matrix{{x^2-3, y^3-1, z^4-2}};

             1       3
o3 : Matrix R  <--- R

i4 : z = koszul(2,f)

o4 = {2} | -y3+1 -z4+2 0     |
     {3} | x2-3  0     -z4+2 |
     {4} | 0     x2-3  y3-1  |

             3       3
o4 : Matrix R  <--- R

i5 : g = forceGB(f, SyzygyMatrix=>z);

i6 : syz g -- no extra computation

o6 = {2} | -y3+1 -z4+2 0     |
     {3} | x2-3  0     -z4+2 |
     {4} | 0     x2-3  y3-1  |

             3       3
o6 : Matrix R  <--- R

i7 : syz f

   -- registering gb 1 at 0x912f260

   -- [gb]{2}(1)m{3}(1)m{4}(1)m{5}(1)z{6}(1)z{7}(1)z
   -- number of (nonminimal) gb elements = 3
   -- number of monomials                = 9
   -- ncalls = 0
   -- nloop = 0
   -- nsaved = 0
   -- 
o7 = {2} | -y3+1 -z4+2 0     |
     {3} | x2-3  0     -z4+2 |
     {4} | 0     x2-3  y3-1  |

             3       3
o7 : Matrix R  <--- R

i8 : kernel f

o8 = image {2} | -y3+1 -z4+2 0     |
           {3} | x2-3  0     -z4+2 |
           {4} | 0     x2-3  y3-1  |

                             3
o8 : R-module, submodule of R

i9 :