See the following example. According to your suggestion, I got three different results:
In[111]:= mat=tbasSGAK227Left1
%//HermiteDecomposition
Map[Transpose, Reverse[HermiteDecomposition[Transpose[mat]]]]
mat//Transpose//HermiteDecomposition
Out[111]= {{1/2, 0, 0}, {0, 1/2, -(1/2)}, {1/2, 1/2, 1/2}}
Out[112]= {{{1, 0, 0}, {-1, 0, 1}, {-1, -1, 1}}, {{1/2, 0, 0}, {0, 1/
2, 1/2}, {0, 0, 1}}}
Out[113]= {{{1/2, 0, 0}, {0, 1/2, 0}, {1/2, 1/2, 1}}, {{1, 0, 0}, {0,
1, 1}, {0, 0, 1}}}
Out[114]= {{{1, 0, 0}, {0, 1, 0}, {0, 1, 1}}, {{1/2, 0, 1/2}, {0, 1/2,
1/2}, {0, 0, 1}}}
However, I still haven't seen any clue.
Regards,
Zhao
