[PPL-devel] Multi-dimensional affine transformation?

[Hosung Song]

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