syz(Matrix) returns nonminimal syzygies

[aalmousa]

This is related to the example that produced the bug in #3017. In the documentation for syz(Matrix), the output is "the matrix of minimal or trimmed generators for the syzygies among the columns of h". However, this is not true:

i1 : R = QQ[x]

o1 = R

o1 : PolynomialRing

i2 : h = transpose matrix{{x^3+1},{x^2+1}}

o2 = {-3} | x3+1 x2+1 |

             1      2
o2 : Matrix R  <-- R

i3 : syz h

o3 = | x2+1  x3+x2+x+1  |
     | -x3-1 -x4-x3-x-1 |

             2      2
o3 : Matrix R  <-- R

i4 : mingens image oo

o4 = | -x2-1 |
     | x3+1  |

             2      1
o4 : Matrix R  <-- R

I am not sure if the solution here is to fix the code, or to fix the documentation -- the documentation for syz(GroebnerBasis) reiterates that the output might include nonminimal syzygies, but the documentation for syz(Matrix) is misleading.