# The meaning of the 'toric' when making connections

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### Laura van de Weerd

Apr 28, 2015, 9:52:16 AM4/28/15
Hi all,

I want to make a 'connection' in DANA and I'm not sure wat exactly the meaning is of  'toric'. All the information that I can find in the handbook about toric is the following:
'It is possible to have toric connections by specifying toric=True when Connection is created'.
Does this only count for the boundary conditions or for the whole field? I have no idea what it means?

Hopefully someone can help me with this?

With kind regards,
Laura van de Weerd

### Nicolas P. Rougier

May 1, 2015, 2:05:25 AM5/1/15
Hi Laura,

Toric means there is no boundary when making connection. In 1d case, this means a group is considered as a ring and in 2d, a group is considered as a torus. Consider this small example:

>>> from dana import *
>>> G = np.zero(5)
>>> C = DenseConnection(G,G, np.ones(3), toric=False)
>>> print C.weights
[[ 1. 1. 0. 0. 0.]
[ 1. 1. 1. 0. 0.]
[ 0. 1. 1. 1. 0.]
[ 0. 0. 1. 1. 1.]
[ 0. 0. 0. 1. 1.]]
>>> C = DenseConnection(G,G, np.ones(3), toric=True)
>>> print C.weights
[[ 1. 1. 0. 0. 1.]
[ 1. 1. 1. 0. 0.]
[ 0. 1. 1. 1. 0.]
[ 0. 0. 1. 1. 1.]
[ 1. 0. 0. 1. 1.]]

You can see two extra 1 in the second case. The first correspond to the connection of G[0] with G[-1] and the second one to the connection of G[4] to G[5]. When toric is False, they are discarded since G[0] has not left neighbours and G[4] has no right neighbours. But in the toric case, they have.

The same is true for 2d but it is less convenient to write here.