Angela,
There are still something not clear. I tried to give redundancy definition independently from saturation rule and independence rule. I found the definition for equalities in G. B Dantzig - Linear programming and extensions - Princeton University Press, New Jersey 1963 pages 71 and I tried to give a meaningful definitions for inequalities, lines, vertices and rays: can you check them?
The page documentation starts on page 178: can you give a look and let me know if I used some notion before define it?
Starting with page 180, the definition of redundant, I find this hard to follow. In the context of a polyhedra, we have already extreme rays and we know these are not redundant. (But a ray which is defined by just a point, is only unique up to a positive multiple.)
Any other ray that is not extreme nor in the lineality space is redundant in the sense that it is the positive combination of extreme rays and lines.
In the lineality space of dimension t, we have t lines generating it. But there is no unique set of generating lines. How do we decide which are redundant?
As for vertices, I think these are by definition never redundant as they cannot be the multiple of other vertices. On page 3, of the user-manual, we give that as the definition.
Can you help me with the underlying ideas that you are defining? Maybe I can help then better.
On page 182, the independence rule for 2 and 4 again is in trouble for the same reasons. Note that in Wilde, these are only defined for a library where there is a specific set of rays and lines stored. I assume that the redundant idea is meant to remove any rays/lines that are (positive) linear combinations of other rays/lines in the given set.
The "redundant rule" on page 182 -redefines- a redundant inequality/ray etc. I can try and help reformulate these definitions, but I have to go now.
I can only assume that there is a sort of connection between "minimize" and "redundant". I will check Wilde again here.
I'll think about this further and see if I can help more.
ciao, Pat