... library

For the list of these libraries, readers are referred to the author's thesis.

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... operator

This technique is described in the presentation of François IRIGOIN, September 2005 the 20th , which can be found at APRON's site [APRb].

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... sc_feasibility_ofl_ctrl()

The tests of satisfiability for a constraint system with overflow control.

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... sc_projection_ofl_ctrl()

It projects the constraint system along a dimension, with overflow control.

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... sc_convex_hull()

It computes the convex hull of two constraint systems.

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... chernikova()

POLYLIB's implementation of Chernikova's algorithm that computes the polyhedral dual conversion.

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... analyses

However, we did not study the output of PIPS in these two cases.

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...throw_exception

A C implementation whose concept is similar to Java's throw/catch mechanism.

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... general

We posted this solution on the POLYLIB's mailing list, and the response was negative.

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... sc_convex_hull

It computes the convex hull of two constraint systems.

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... considered

We do not consider the Ehrhart polynomials here [Cla96].

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... polyhedron

In 2-D, it is a polyhedron of at most eight edges.

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... available

$C^3$, New POLKA and PPL have dimension permutation operators but not POLYLIB. Thus, POLYLIB has this problem, too.

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... no

We can indeed return a polyhedron of dependences.

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... semantic

It simply verifies whether the given constraint system is the constant SC_EMPTY or not.

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... polyhedra

Which can be found in the package union of the $C^3$ library.

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...fragma

Fragmented issues which are not structured, concerning concrete implementations.

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...

For Presburger formulae, we also have the existential $\exists$ and universal $\forall$ quantifiers.

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... add_dimension

This operator adds a new dimension to the constraint system.

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... remove_dimension

This operator removes a dimension from the constraint system.

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... sc_weak_consistent_p(Psysteme)

These two operators verify whether the constraint system in question is valid or not, due to possible programming errors.

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... representations

The Chernikova algorithm performing the dual conversion is rational, not integer

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... system

The empty constraint has a semantic meaning, whereas the undefined constraint system is simply used as a programming trick. For example, the undefined constraint system can be used to indicate the case where an exception occurred.

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... ph)

These three functions verify whether the polyhedron is bounded or not.

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... sc\_universe

In $C^3$, the term $R^n$, the whole space, is used instead of the constant universe.

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...dontknow

The NOT_EMPTY term is chosen for unknown answer, so the approximation step is hidden inside the operator.

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... library

For example, we can print out the constraint system if an exception is raised.

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... useful

However, we do not have any result concerning this issue.

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... is_disjoint_from

Test whether the polyhedron is disjoint from another.

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... operators

Grouping and separating similar dimensions of the polyhedron.

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... itself

This occasionally happens in $C^3$ when out-of-memory space or overflow exceptions are raised.

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... surjective

For example, if we have five polyhedral algorithms and only two octagonal algorithms for the projection operator, then the enumeration is surjective (five to two) in the octagonal case.

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... defined

In fact, these functions can be considered as some generic operators like the minimization, normalization or canonization operators.

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... release

At the time of this writing, we have the $0.7$ release.

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... show

At the VMCAI 2005 and NSAD 2005 workshops.

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... documented

APRON's prototype does not supply this kind of documentation.

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