In general, symmetry reduction is not helpful for SDSOS nor DSOS, since these cones are basis-dependent. In contrast to SOS cone or SDP cone, symmetry-adapted bases change the scaled diagonally dominant and diagonally dominant cones. So many people use symmetry reduction for SDSOS while not being aware the answer is different from the answer before symmetry reduction. This is exactly my point of research. I’ve partially characterized the effect of symmetry reduction on these problems. That is why I want to use your package for SDSOS or scaled diagonally dominant optimization problems with different symmetries.
Thanks for your help