Number of independent elastic tensors in trigonal and tetragonal lattice systems

[goodwilling]

Elastic is a very convenient tool for calculating elastic constants of crystals. Thanks a lot for the continuous development.

I would like to bring the following points into attention if not discussed yet.

In the Elastic code, the number of independent elastic tensors is taken as 6 for trigonal and tetragonal lattice systems.

On the other hand, it is stated that the number of independent elastic tensors can be either 6 or 7 for trigonal and tetragonal lattice systems due to different symmetries.

Elasticity measurements on minerals: A review European Journal of Mineralogy 21(3), June 2009 DOI: https://doi.org/10.1127/0935-1221/2009/0021-1925 https://web.gps.caltech.edu/~jackson/pdf/Angel2009_EJM.pdf

also: https://github.com/libAtoms/matscipy/blob/master/matscipy/elasticity.py

'trigonal_high': np.array([[1, 7, 8, 9, 10, 0], [7, 1, 8, 0,-9, 0], [8, 8, 3, 0, 0, 0], [9, -9, 0, 4, 0, 0], [10, 0, 0, 0, 4, 0], [0, 0, 0, 0, 0, 6]]),

'trigonal_low': np.array([[1, 7, 8, 9, 10, 0 ], [7, 1, 8, -9, -10, 0 ], [8, 8, 3, 0, 0, 0 ], [9, -9, 0, 4, 0, -10], [10,-10, 0, 0, 4, 9 ], [0, 0, 0, -10 , 9, 6 ]]),

'tetragonal_high': np.array([[1, 7, 8, 0, 0, 0], [7, 1, 8, 0, 0, 0], [8, 8, 3, 0, 0, 0], [0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 4, 0], [0, 0, 0, 0, 0, 6]]),

'tetragonal_low': np.array([[1, 7, 8, 0, 0, 11], [7, 1, 8, 0, 0, -11], [8, 8, 3, 0, 0, 0], [0, 0, 0, 4, 0, 0], [0, 0, 0, 0, 4, 0], [11, -11, 0, 0, 0, 6]])