Hi,
I'm a bit confused, maybe because I never think carefully enough about use of duality in PPL. I can tell you what we do in the implementation: do you help me to decide what we need?
Several function in the PPL are used both to work on constraints and generators without any difference (look, for example, at conversion.cc) and we justify this with duality. In other words we treat lines like equalities and rays like inequalities. I think this is allowed for double representation and duality, but I can't put these things together. Can you help me?
The concept of "dual" has a generic meaning and of course, there is a kind of duality between the two representations. But, in LP, the term "dual" has a very specific meaning converting between a max and a min computation. This does not seem to correspond exactly to the implicit duality observed in the DD method. I think it only corresponds when we have a polytope that includes the origin. I think I have read that somewhere. (Also, it is clear that a polytope always has a finite max and a min but a cone does not.)
In the paper by Fukuda and Prodin you sent me, page 2, (A,R) is a DD pair iff (R^T,A^T) is a DD pair. So, of course, the same algorithms can be used to go from A to R and from R^T to A^T.
However, if (A,R) is a DD pair, this is not saying that P(A) is a dual of P(R).
- first I have not clear the meaning of "feels up" (sorry!)
- moreover I don't understand what does it means that a ray is stable (even
it seems to be very easy! ;-))
Sorry, I should be more careful in using colloquial expressions... "feels up to" means (approximately) "is able to" but it also implies that the task is hard and you may not want to... I am sure it is hard - but maybe one of you young mathematicians can show us an easy way to understand this - just in the context of polyhedra.
Well, in italian we say:"Posso parlare solo per me stessa"... in english maybe:"I'm sure I'm not able to..., but maybe the others guys do!".
Esattamente ;)
If you have an idea of how it can be done, please let me know it. I will think about it and I will try to improve the documentation.
I will check the actual documentation and see if I can be of more direct help.
ciao, Pat