Binary Grassmann-Pliicker relations

First, an alternating, nontrivial (i.e. not constantly zero) function x from ri to +,-,0 fulfilling the binary Grassmann-Pliicker relations (defined below) is called a chirotope (of rank 4) over n= 0,..., n -1, according to Definition 3.5.3 in... 

As orientations are signs of determinants, it follows that the orientation function of any conformation fulfills the binary Grassmann Pliicker relations, introduced below (Herrmann Grassmann, German mathematician, 1809-1877, Julius Pliicker, German mathematician and physicist, 1801-1868). 

Note that different binary Grassmann-Pliicker relations may lead to the seune condition. For example, the one corresponding to (2,3,0,1) and (6,5,1,0) leads to the same condition as the one discussed above. Test 4 checks all such criteria obtained by binary Grassmann Pliicker relations ... 

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