Dear PPL Developers,
Greetings. I have a few questions about affine image operations and some thing else. My understanding about affine transformation impelmentation in PPL is that we have only one-dimensional transformation operations. That is, any transformation is applied only to the specific variable x_k. I'm wondering how I can do affine transformations for all variables x_0,...,x_{n-1} at once. For example, let's think about the 2D transformation as follows.
x'' = a*x + b*y + c (1) y'' = d*x + e*y + f (2)
Please correct me if my understanding is ever wrong. I would think about doing this 2D transformation by applying 2 1D transformations (which are available in PPL) as:
x' = a*x + b*y + c y' = y
then x'' = x' y'' = d*x' + e*y' + f
. Surely, the results are, in general, not the same as I intended. Am I missing some basic concepts about affine transformations? Or is this just the limitation of PPL? What I'm now thinking to work around this, is, to first add 2 dimensions (x'' & y'') to the original 2D polyhedron (x & y), then add constraints for (1) and (2), then swap x''/y'' with x/y by a mapping function, then remove the higher 2 dimensions (now x & y). Is this a right and necessary approach? Your experienced comments would be greatly appreciated.
One more question is, I just skimmed through the new version, but I'm wondering if the C interface of the new version supports the powerset construction. If not, do you think it's quite difficult to add the support? Thanks in advance.
Best,
Hosung