# Select elements in a list of tuples of quaternions that satisfy a condition

I defined 24 quaternions using the Quaternions package and i create the list of all possible 4-tuples using

ListQuad = Tuples[ListQuaternions, 4]


where ListQuaternions is the list of the 24 elements I defined. Now I would like to select all the 4-tuples such that the product of the four quaternions is equal to Quaternion[1, 0, 0, 0].

I tried to use this:

Select[ListQuad,{x_, y_, z_, w_} /; x ** y ** z ** w == Quaternion[1, 0, 0, 0] &]


but this gives me an empty list, which I'm sure it can't be true because I know that some 4-tuples satisfy that condition.

I don't understand what I'm doing wrong. Probably the condition I put in the Select command?

• You might want to use Select[ListQuad, (x ** y ** z ** w == Quaternion[1, 0, 0, 0]) &] instead. In general, you have to decide whether to use Select (function based selection) or Cases (pattern based selection). Oct 3, 2018 at 10:48
• I tried also the solution you wrote me but it still gives me an empty list. probably there is something wrong in the definition of the list. Thank you so much! Oct 3, 2018 at 15:10

Henrik has already mentioned Select[] and Cases[]. For this answer, I'll show how to use Pick[]:

<< Quaternions

ListQuaternions = UnitQuaternions;

The slightly complicated condition in Pick[] is necessitated by the fact that Equal (==) cannot handle quaternions; e.g. Quaternion[1, 0, 0, 0] == Quaternion[-1, 0, 0, 0] remains unevaluated.
• Thank you so much! I didn't know the Pick[] command, also the lengths of ListQuad and sel` coincide with the numbers I know I should get. Oct 3, 2018 at 15:11