In various places in the source files, we have assertions requiring that matrices (of constraints and generators) have a number of columns <> 1. These assertions can be violated by the following code, that should be considered legal, since it builds the simplest form of an always-flase constraint:
LinExpression e0 = LinExpression(0); LinExpression e1 = LinExpression(1); Constraint c0(e0 == e1); // Built the always-false 0-dim constraint c0, that is 0 = 1. ConSys cs; cs.insert(c0); Polyhedron ph(cs);
error6: ../../ppl/src/Polyhedron.cc:155: Parma_Polyhedra_Library::Polyhedron::Polyhedron (Parma_Polyhedra_Library::ConSys &): Assertion `cs.num_columns() != 1' failed.
There are three ways to solve such a situation:
1. We prevent the creation of 0-dim constraints, throwing an exception when executing Constraint c0(e0 == e1);
2. we force the creation of a dimension when building constraints (e.g., we force c0 to be the 1-dim constraint ``0*Variable(0) == 1''). This is not a very clean solution, since in the code above the user thinks ph to be a 0-dim polyhedron. By silently converting it to a 1-dim polyhedron, we probably trigger some dimension-incompatibility problems later in the code.
3. we remove all assertions of this kind. Non-empty 0-dim constraint systems will be legal and will contain constraints that are either always false (like the one above) or always true (like the positivity constraint 1 >= 0). Note that the representation of the empty polyhedron needs not to be changed, i.e., we just look at the status flag and do not need to explicitly insert have a matrix for the always false constraint.
The easiest-to-implement solution is 1. The cleanest one, in my opinion, is solution 3. Here are some other reasons:
a) consider an 0-dim empty polyhedron ph; if a user invokes the method ph.constraints(), the user will obtain an exception. If a 0-dim constraint can be built, the implementation can return a constraint system including it.
b) the same considerations can be extended to systems of generators. The following code build the 0-dim vertex (the only point of the 0-dim universe polyhedron):
LinExpression e0 = LinExpression(0); Generator g0(vertex(e0)); // Built the 0-dim vertex. GenSys gs; gs.insert(g0); Polyhedron ph(gs);
error6: ../../ppl/src/Polyhedron.cc:183: Parma_Polyhedra_Library::Polyhedron::Polyhedron (Parma_Polyhedra_Library::GenSys &): Assertion `gs.num_columns() != 1' failed.
Also, we now throw an exception when we inkoke ph.generators() for a 0-dim universe polyhedron. In constrast, we could just return the system of generators containing the 0-dim vertex. It seems to me that, when inserting an n-dimension (n > 0) generator in a 0-dim system of generators, the 0-dim vertex (if present in the system) would be correctly dimension-expanded to the origin of the space \Rset^n.
Is anyone foreseeing other problems for such a change ?
-- Enea Zaffanella Dipartimento di Matematica - Universita' di Parma Via M. D'Azeglio, 85/A I 43100 - PARMA (Italy) Tel: +39 0521 032317 Fax: +39 0521 032350