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Tune Grobner equations

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\brief convert p == 0 into a solved form v == r, such that
   v has bounds [lo, oo) iff r has bounds [lo', oo)
   v has bounds (oo,hi]  iff r has bounds (oo,hi']

   The solved form allows the Grobner solver identify more bounds conflicts.
   A bad leading term can miss bounds conflicts.
   For example for x + y + z == 0 where x, y : [0, oo) and z : (oo,0]
   we prefer to solve z == -x - y instead of x == -z - y
   because the solution -z - y has neither an upper, nor a lower bound.

The Grobner solver is augmented with a notion of a substitution that is applied before the solver is run.
This commit is contained in:
Nikolaj Bjorner 2022-07-11 16:14:26 -07:00
parent f33c933241
commit 316ed778e0
5 changed files with 127 additions and 13 deletions
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4
src/math/grobner/pdd_solver.h
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@ -118,6 +118,7 @@ private:
equation_vector m_solved; // equations with solved variables, triangular
equation_vector m_processed;
equation_vector m_to_simplify;
vector<std::tuple<unsigned, pdd, u_dependency*>> m_subst;
mutable u_dependency_manager m_dep_manager;
equation_vector m_all_eqs;
equation* m_conflict;
@ -136,6 +137,9 @@ public:
void add(pdd const& p) { add(p, nullptr); }
void add(pdd const& p, u_dependency * dep);
void simplify(pdd& p, u_dependency*& dep);
void add_subst(unsigned v, pdd const& p, u_dependency* dep);
void simplify();
void saturate();