Hamilton's equations have another advantage over Lagrange's equations: if a system has a symmetry, so that some coordinate q i does not occur in the Hamiltonian (i.e. a cyclic coordinate), the corresponding momentum coordinate p i is conserved along each trajectory, and that coordinate can be reduced to a constant in the other equations of the set. This effectively reduces the problem from n coordinates to (n − 1) coordinates: this is the basis of symplectic reduction in geometry. In the Lagrangian framework, the conservation of momentum also follows immediately, however all the generalized velocities q ˙ ˙ i still occur in the Lagrangian, and a system of equations in n coordinates still has to be solved.