Before revision:  in the former the shape of flux is constrained completely by deformed toric ideal constraints, and in the latter, it is shown the deformed toric ideal constrains the  parameters of flux at least partially  .
After revision:  in the former the shape of flux is constrained completely by deformed toric ideal constraints, and in the latter, it is shown the deformed toric ideal constrains the linear combination parameters of flux at least partially .