Syzygies Probing Scattering Amplitudes

Understand

We propose a new efficient algorithm to obtain the locally minimal generating set of the syzygies for an ideal, i.e.

• a generating set whose proper subsets cannot be generating sets.
• Syzygy is a concept widely used in the current study of scattering amplitudes.
• This new algorithm can deal with more syzygies effectively because a new generation of syzygies is obtained in each step and the irreducibility of this generation is also verified in the process.