What's necessary for transformations to be commutative?

[nitroamos]

I'm trying to model D2 rotational symmetry in protein quaternary structure using my CoordTransformer code. A CoordTransformer is composed of a pre and post translation, and a quaternion rotation:

def transform(self,point):
   point -= self.pre
   self.rotate(point)
   point += self.post
   return point

D2 symmetry can be decomposed into two separate C2 operations. Starting from point A, I can use one of the C2 transformations to get to B, and the other to get to C, and both to get to D. The application of both transformations is commutative, such that A-->B-->D should produce the same result as A-->C-->D.

However, in my test case, the operators I'm fitting to the imperfect data are not commutative. So my question is what needs to be true of the relationship between the two C2 operators to get commutativity?

For example, in order for an operator to be C2, its rotation and translation directions need to be perpendicular, and the rotation to be 180 degrees. In order for the pair to compose a D2 operation, their rotation directions need to be perpendicular to each other. I'm enforcing these, but I'm still missing something I'm finding that order matters. Any ideas or references I can read?

 

[jvicens]

your first step in responding to this forum post would be to understand the problem and the goal of the individual. In this case, the individual is trying to model D2 rotational symmetry in protein quaternary structure using their CoordTransformer code. They have found that their operators are not commutative and are seeking advice on what needs to be true for them to achieve commutativity.

To provide a helpful response, you could start by asking for more information about the specific operators and their properties. This could help you understand why they are not commutative and what may be causing the issue. You could also suggest looking into the mathematical properties of D2 symmetry and how they may apply to this problem.

In addition, you could recommend some resources for the individual to read, such as scientific articles or textbooks on symmetry and protein structure. This could help them gain a better understanding of the concepts and potentially find a solution to their problem.

Finally, you could offer to collaborate with the individual to find a solution together. As scientists, collaboration and sharing of knowledge and ideas is key to solving complex problems. By working together, you may be able to identify the issue and find a way to achieve commutativity in the operators.