A new method for finding more symmetry relations of Feynman integrals

We introduce a new method for deriving Feynman integral symmetry relations. By solving the ansatz of momentum transformation in the field of rational functions rather than constants, this method can sometimes find more symmetry relations, compared to some state-of-the-art software. The new method may help to further decrease the number of unique sectors in an integral family. Well-chosen gauge conditions are implemented in this method for the efficient symmetry searching.