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| | NNC_Polyhedron (dimension_type num_dimensions=0, Degenerate_Element kind=UNIVERSE) |
| | Builds either the universe or the empty NNC polyhedron. More...
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| | NNC_Polyhedron (const Constraint_System &cs) |
| | Builds an NNC polyhedron from a system of constraints. More...
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| | NNC_Polyhedron (Constraint_System &cs, Recycle_Input dummy) |
| | Builds an NNC polyhedron recycling a system of constraints. More...
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| | NNC_Polyhedron (const Generator_System &gs) |
| | Builds an NNC polyhedron from a system of generators. More...
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| | NNC_Polyhedron (Generator_System &gs, Recycle_Input dummy) |
| | Builds an NNC polyhedron recycling a system of generators. More...
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| | NNC_Polyhedron (const Congruence_System &cgs) |
| | Builds an NNC polyhedron from a system of congruences. More...
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| | NNC_Polyhedron (Congruence_System &cgs, Recycle_Input dummy) |
| | Builds an NNC polyhedron recycling a system of congruences. More...
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| | NNC_Polyhedron (const C_Polyhedron &y, Complexity_Class complexity=ANY_COMPLEXITY) |
| | Builds an NNC polyhedron from the C polyhedron y. More...
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| template<typename Interval > |
| | NNC_Polyhedron (const Box< Interval > &box, Complexity_Class complexity=ANY_COMPLEXITY) |
| | Builds an NNC polyhedron out of a box. More...
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| | NNC_Polyhedron (const Grid &grid, Complexity_Class complexity=ANY_COMPLEXITY) |
| | Builds an NNC polyhedron out of a grid. More...
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| template<typename U > |
| | NNC_Polyhedron (const BD_Shape< U > &bd, Complexity_Class complexity=ANY_COMPLEXITY) |
| | Builds a NNC polyhedron out of a BD shape. More...
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| template<typename U > |
| | NNC_Polyhedron (const Octagonal_Shape< U > &os, Complexity_Class complexity=ANY_COMPLEXITY) |
| | Builds a NNC polyhedron out of an octagonal shape. More...
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| NNC_Polyhedron (const NNC_Polyhedron &y, Complexity_Class complexity=ANY_COMPLEXITY) |
| | Ordinary copy constructor.
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NNC_Polyhedron & | operator= (const NNC_Polyhedron &y) |
| | The assignment operator. (*this and y can be dimension-incompatible.)
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NNC_Polyhedron & | operator= (const C_Polyhedron &y) |
| | Assigns to *this the C polyhedron y.
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| ~NNC_Polyhedron () |
| | Destructor.
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| bool | poly_hull_assign_if_exact (const NNC_Polyhedron &y) |
| | If the poly-hull of *this and y is exact it is assigned to *this and true is returned, otherwise false is returned. More...
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bool | upper_bound_assign_if_exact (const NNC_Polyhedron &y) |
| | Same as poly_hull_assign_if_exact(y).
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| void | positive_time_elapse_assign (const Polyhedron &y) |
| | Assigns to *this (the best approximation of) the result of computing the positive time-elapse between *this and y. More...
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| template<typename Source_Linear_System , typename Dest_Linear_System > |
| dimension_type | conversion (Source_Linear_System &source, const dimension_type start, Dest_Linear_System &dest, Bit_Matrix &sat, dimension_type num_lines_or_equalities) |
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| template<typename Source_Linear_System , typename Dest_Linear_System > |
| bool | minimize (const bool con_to_gen, Source_Linear_System &source, Dest_Linear_System &dest, Bit_Matrix &sat) |
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| template<typename Source_Linear_System1 , typename Source_Linear_System2 , typename Dest_Linear_System > |
| bool | add_and_minimize (const bool con_to_gen, Source_Linear_System1 &source1, Dest_Linear_System &dest, Bit_Matrix &sat, const Source_Linear_System2 &source2) |
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| template<typename Source_Linear_System , typename Dest_Linear_System > |
| bool | add_and_minimize (const bool con_to_gen, Source_Linear_System &source, Dest_Linear_System &dest, Bit_Matrix &sat) |
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| template<typename Linear_System1 > |
| dimension_type | simplify (Linear_System1 &sys, Bit_Matrix &sat) |
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dimension_type | space_dimension () const |
| | Returns the dimension of the vector space enclosing *this.
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dimension_type | affine_dimension () const |
| | Returns , if *this is empty; otherwise, returns the affine dimension of *this.
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const Constraint_System & | constraints () const |
| | Returns the system of constraints.
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const Constraint_System & | minimized_constraints () const |
| | Returns the system of constraints, with no redundant constraint.
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const Generator_System & | generators () const |
| | Returns the system of generators.
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const Generator_System & | minimized_generators () const |
| | Returns the system of generators, with no redundant generator.
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Congruence_System | congruences () const |
| | Returns a system of (equality) congruences satisfied by *this.
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Congruence_System | minimized_congruences () const |
| | Returns a system of (equality) congruences satisfied by *this, with no redundant congruences and having the same affine dimension as *this.
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| Poly_Con_Relation | relation_with (const Constraint &c) const |
| | Returns the relations holding between the polyhedron *this and the constraint c. More...
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| Poly_Gen_Relation | relation_with (const Generator &g) const |
| | Returns the relations holding between the polyhedron *this and the generator g. More...
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| Poly_Con_Relation | relation_with (const Congruence &cg) const |
| | Returns the relations holding between the polyhedron *this and the congruence c. More...
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bool | is_empty () const |
| | Returns true if and only if *this is an empty polyhedron.
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bool | is_universe () const |
| | Returns true if and only if *this is a universe polyhedron.
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bool | is_topologically_closed () const |
| | Returns true if and only if *this is a topologically closed subset of the vector space.
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| bool | is_disjoint_from (const Polyhedron &y) const |
| | Returns true if and only if *this and y are disjoint. More...
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bool | is_discrete () const |
| | Returns true if and only if *this is discrete.
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bool | is_bounded () const |
| | Returns true if and only if *this is a bounded polyhedron.
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bool | contains_integer_point () const |
| | Returns true if and only if *this contains at least one integer point.
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| bool | constrains (Variable var) const |
| | Returns true if and only if var is constrained in *this. More...
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| bool | bounds_from_above (const Linear_Expression &expr) const |
| | Returns true if and only if expr is bounded from above in *this. More...
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| bool | bounds_from_below (const Linear_Expression &expr) const |
| | Returns true if and only if expr is bounded from below in *this. More...
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| bool | maximize (const Linear_Expression &expr, Coefficient &sup_n, Coefficient &sup_d, bool &maximum) const |
| | Returns true if and only if *this is not empty and expr is bounded from above in *this, in which case the supremum value is computed. More...
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| bool | maximize (const Linear_Expression &expr, Coefficient &sup_n, Coefficient &sup_d, bool &maximum, Generator &g) const |
| | Returns true if and only if *this is not empty and expr is bounded from above in *this, in which case the supremum value and a point where expr reaches it are computed. More...
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| bool | minimize (const Linear_Expression &expr, Coefficient &inf_n, Coefficient &inf_d, bool &minimum) const |
| | Returns true if and only if *this is not empty and expr is bounded from below in *this, in which case the infimum value is computed. More...
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| bool | minimize (const Linear_Expression &expr, Coefficient &inf_n, Coefficient &inf_d, bool &minimum, Generator &g) const |
| | Returns true if and only if *this is not empty and expr is bounded from below in *this, in which case the infimum value and a point where expr reaches it are computed. More...
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| bool | frequency (const Linear_Expression &expr, Coefficient &freq_n, Coefficient &freq_d, Coefficient &val_n, Coefficient &val_d) const |
| | Returns true if and only if there exist a unique value val such that *this saturates the equality expr = val. More...
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| bool | contains (const Polyhedron &y) const |
| | Returns true if and only if *this contains y. More...
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| bool | strictly_contains (const Polyhedron &y) const |
| | Returns true if and only if *this strictly contains y. More...
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| bool | OK (bool check_not_empty=false) const |
| | Checks if all the invariants are satisfied. More...
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| void | add_constraint (const Constraint &c) |
| | Adds a copy of constraint c to the system of constraints of *this (without minimizing the result). More...
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| void | add_generator (const Generator &g) |
| | Adds a copy of generator g to the system of generators of *this (without minimizing the result). More...
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| void | add_congruence (const Congruence &cg) |
| | Adds a copy of congruence cg to *this, if cg can be exactly represented by a polyhedron. More...
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| void | add_constraints (const Constraint_System &cs) |
| | Adds a copy of the constraints in cs to the system of constraints of *this (without minimizing the result). More...
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| void | add_recycled_constraints (Constraint_System &cs) |
| | Adds the constraints in cs to the system of constraints of *this (without minimizing the result). More...
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| void | add_generators (const Generator_System &gs) |
| | Adds a copy of the generators in gs to the system of generators of *this (without minimizing the result). More...
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| void | add_recycled_generators (Generator_System &gs) |
| | Adds the generators in gs to the system of generators of *this (without minimizing the result). More...
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| void | add_congruences (const Congruence_System &cgs) |
| | Adds a copy of the congruences in cgs to *this, if all the congruences can be exactly represented by a polyhedron. More...
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| void | add_recycled_congruences (Congruence_System &cgs) |
| | Adds the congruences in cgs to *this, if all the congruences can be exactly represented by a polyhedron. More...
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| void | refine_with_constraint (const Constraint &c) |
| | Uses a copy of constraint c to refine *this. More...
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| void | refine_with_congruence (const Congruence &cg) |
| | Uses a copy of congruence cg to refine *this. More...
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| void | refine_with_constraints (const Constraint_System &cs) |
| | Uses a copy of the constraints in cs to refine *this. More...
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| void | refine_with_congruences (const Congruence_System &cgs) |
| | Uses a copy of the congruences in cgs to refine *this. More...
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| template<typename FP_Format , typename Interval_Info > |
| void | refine_with_linear_form_inequality (const Linear_Form< Interval< FP_Format, Interval_Info > > &left, const Linear_Form< Interval< FP_Format, Interval_Info > > &right, bool is_strict=false) |
| | Refines *this with the constraint expressed by left right if is_strict is set, with the constraint left right otherwise. More...
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| template<typename FP_Format , typename Interval_Info > |
| void | generalized_refine_with_linear_form_inequality (const Linear_Form< Interval< FP_Format, Interval_Info > > &left, const Linear_Form< Interval< FP_Format, Interval_Info > > &right, Relation_Symbol relsym) |
| | Refines *this with the constraint expressed by left right, where is the relation symbol specified by relsym.. More...
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| template<typename FP_Format , typename Interval_Info > |
| void | refine_fp_interval_abstract_store (Box< Interval< FP_Format, Interval_Info > > &store) const |
| | Refines store with the constraints defining *this. More...
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| void | unconstrain (Variable var) |
| | Computes the cylindrification of *this with respect to space dimension var, assigning the result to *this. More...
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| void | unconstrain (const Variables_Set &vars) |
| | Computes the cylindrification of *this with respect to the set of space dimensions vars, assigning the result to *this. More...
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| void | intersection_assign (const Polyhedron &y) |
| | Assigns to *this the intersection of *this and y. More...
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| void | poly_hull_assign (const Polyhedron &y) |
| | Assigns to *this the poly-hull of *this and y. More...
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void | upper_bound_assign (const Polyhedron &y) |
| | Same as poly_hull_assign(y).
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| void | poly_difference_assign (const Polyhedron &y) |
| | Assigns to *this the poly-difference of *this and y. More...
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void | difference_assign (const Polyhedron &y) |
| | Same as poly_difference_assign(y).
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| bool | simplify_using_context_assign (const Polyhedron &y) |
| | Assigns to *this a meet-preserving simplification of *this with respect to y. If false is returned, then the intersection is empty. More...
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| void | affine_image (Variable var, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one()) |
| | Assigns to *this the affine image of *this under the function mapping variable var to the affine expression specified by expr and denominator. More...
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| template<typename FP_Format , typename Interval_Info > |
| void | affine_form_image (Variable var, const Linear_Form< Interval< FP_Format, Interval_Info > > &lf) |
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| void | affine_preimage (Variable var, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one()) |
| | Assigns to *this the affine preimage of *this under the function mapping variable var to the affine expression specified by expr and denominator. More...
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| void | generalized_affine_image (Variable var, Relation_Symbol relsym, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one()) |
| | Assigns to *this the image of *this with respect to the generalized affine relation , where is the relation symbol encoded by relsym. More...
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| void | generalized_affine_preimage (Variable var, Relation_Symbol relsym, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one()) |
| | Assigns to *this the preimage of *this with respect to the generalized affine relation , where is the relation symbol encoded by relsym. More...
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| void | generalized_affine_image (const Linear_Expression &lhs, Relation_Symbol relsym, const Linear_Expression &rhs) |
| | Assigns to *this the image of *this with respect to the generalized affine relation , where is the relation symbol encoded by relsym. More...
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| void | generalized_affine_preimage (const Linear_Expression &lhs, Relation_Symbol relsym, const Linear_Expression &rhs) |
| | Assigns to *this the preimage of *this with respect to the generalized affine relation , where is the relation symbol encoded by relsym. More...
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| void | bounded_affine_image (Variable var, const Linear_Expression &lb_expr, const Linear_Expression &ub_expr, Coefficient_traits::const_reference denominator=Coefficient_one()) |
| | Assigns to *this the image of *this with respect to the bounded affine relation . More...
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| void | bounded_affine_preimage (Variable var, const Linear_Expression &lb_expr, const Linear_Expression &ub_expr, Coefficient_traits::const_reference denominator=Coefficient_one()) |
| | Assigns to *this the preimage of *this with respect to the bounded affine relation . More...
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| void | time_elapse_assign (const Polyhedron &y) |
| | Assigns to *this the result of computing the time-elapse between *this and y. More...
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| void | positive_time_elapse_assign (const Polyhedron &y) |
| | Assigns to *this (the best approximation of) the result of computing the positive time-elapse between *this and y. More...
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| void | wrap_assign (const Variables_Set &vars, Bounded_Integer_Type_Width w, Bounded_Integer_Type_Representation r, Bounded_Integer_Type_Overflow o, const Constraint_System *cs_p=0, unsigned complexity_threshold=16, bool wrap_individually=true) |
| | Wraps the specified dimensions of the vector space. More...
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| void | drop_some_non_integer_points (Complexity_Class complexity=ANY_COMPLEXITY) |
| | Possibly tightens *this by dropping some points with non-integer coordinates. More...
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| void | drop_some_non_integer_points (const Variables_Set &vars, Complexity_Class complexity=ANY_COMPLEXITY) |
| | Possibly tightens *this by dropping some points with non-integer coordinates for the space dimensions corresponding to vars. More...
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void | topological_closure_assign () |
| | Assigns to *this its topological closure.
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| void | BHRZ03_widening_assign (const Polyhedron &y, unsigned *tp=0) |
| | Assigns to *this the result of computing the BHRZ03-widening between *this and y. More...
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| void | limited_BHRZ03_extrapolation_assign (const Polyhedron &y, const Constraint_System &cs, unsigned *tp=0) |
| | Assigns to *this the result of computing the limited extrapolation between *this and y using the BHRZ03-widening operator. More...
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| void | bounded_BHRZ03_extrapolation_assign (const Polyhedron &y, const Constraint_System &cs, unsigned *tp=0) |
| | Assigns to *this the result of computing the bounded extrapolation between *this and y using the BHRZ03-widening operator. More...
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| void | H79_widening_assign (const Polyhedron &y, unsigned *tp=0) |
| | Assigns to *this the result of computing the H79_widening between *this and y. More...
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void | widening_assign (const Polyhedron &y, unsigned *tp=0) |
| | Same as H79_widening_assign(y, tp).
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| void | limited_H79_extrapolation_assign (const Polyhedron &y, const Constraint_System &cs, unsigned *tp=0) |
| | Assigns to *this the result of computing the limited extrapolation between *this and y using the H79-widening operator. More...
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| void | bounded_H79_extrapolation_assign (const Polyhedron &y, const Constraint_System &cs, unsigned *tp=0) |
| | Assigns to *this the result of computing the bounded extrapolation between *this and y using the H79-widening operator. More...
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| void | add_space_dimensions_and_embed (dimension_type m) |
| | Adds m new space dimensions and embeds the old polyhedron in the new vector space. More...
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| void | add_space_dimensions_and_project (dimension_type m) |
| | Adds m new space dimensions to the polyhedron and does not embed it in the new vector space. More...
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| void | concatenate_assign (const Polyhedron &y) |
| | Assigns to *this the concatenation of *this and y, taken in this order. More...
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| void | remove_space_dimensions (const Variables_Set &vars) |
| | Removes all the specified dimensions from the vector space. More...
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| void | remove_higher_space_dimensions (dimension_type new_dimension) |
| | Removes the higher dimensions of the vector space so that the resulting space will have dimension new_dimension. More...
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| template<typename Partial_Function > |
| void | map_space_dimensions (const Partial_Function &pfunc) |
| | Remaps the dimensions of the vector space according to a partial function. More...
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| void | expand_space_dimension (Variable var, dimension_type m) |
| | Creates m copies of the space dimension corresponding to var. More...
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| void | fold_space_dimensions (const Variables_Set &vars, Variable dest) |
| | Folds the space dimensions in vars into dest. More...
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| ~Polyhedron () |
| | Destructor.
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| void | m_swap (Polyhedron &y) |
| | Swaps *this with polyhedron y. (*this and y can be dimension-incompatible.) More...
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void | ascii_dump () const |
| | Writes to std::cerr an ASCII representation of *this.
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void | ascii_dump (std::ostream &s) const |
| | Writes to s an ASCII representation of *this.
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void | print () const |
| | Prints *this to std::cerr using operator<<.
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bool | ascii_load (std::istream &s) |
| | Loads from s an ASCII representation (as produced by ascii_dump(std::ostream&) const) and sets *this accordingly. Returns true if successful, false otherwise.
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memory_size_type | total_memory_in_bytes () const |
| | Returns the total size in bytes of the memory occupied by *this.
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memory_size_type | external_memory_in_bytes () const |
| | Returns the size in bytes of the memory managed by *this.
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| int32_t | hash_code () const |
| | Returns a 32-bit hash code for *this. More...
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typedef Coefficient | coefficient_type |
| | The numeric type of coefficients.
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static dimension_type | max_space_dimension () |
| | Returns the maximum space dimension all kinds of Polyhedron can handle.
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static bool | can_recycle_constraint_systems () |
| | Returns true indicating that this domain has methods that can recycle constraints.
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static void | initialize () |
| | Initializes the class.
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static void | finalize () |
| | Finalizes the class.
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static bool | can_recycle_congruence_systems () |
| | Returns false indicating that this domain cannot recycle congruences.
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| | Polyhedron (Topology topol, dimension_type num_dimensions, Degenerate_Element kind) |
| | Builds a polyhedron having the specified properties. More...
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| | Polyhedron (const Polyhedron &y, Complexity_Class complexity=ANY_COMPLEXITY) |
| | Ordinary copy constructor. More...
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| | Polyhedron (Topology topol, const Constraint_System &cs) |
| | Builds a polyhedron from a system of constraints. More...
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| | Polyhedron (Topology topol, Constraint_System &cs, Recycle_Input dummy) |
| | Builds a polyhedron recycling a system of constraints. More...
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| | Polyhedron (Topology topol, const Generator_System &gs) |
| | Builds a polyhedron from a system of generators. More...
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| | Polyhedron (Topology topol, Generator_System &gs, Recycle_Input dummy) |
| | Builds a polyhedron recycling a system of generators. More...
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| template<typename Interval > |
| | Polyhedron (Topology topol, const Box< Interval > &box, Complexity_Class complexity=ANY_COMPLEXITY) |
| | Builds a polyhedron from a box. More...
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Polyhedron & | operator= (const Polyhedron &y) |
| | The assignment operator. (*this and y can be dimension-incompatible.)
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| void | drop_some_non_integer_points (const Variables_Set *vars_p, Complexity_Class complexity) |
| | Possibly tightens *this by dropping some points with non-integer coordinates for the space dimensions corresponding to *vars_p. More...
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| template<typename FP_Format , typename Interval_Info > |
| void | overapproximate_linear_form (const Linear_Form< Interval< FP_Format, Interval_Info > > &lf, const dimension_type lf_dimension, Linear_Form< Interval< FP_Format, Interval_Info > > &result) |
| | Helper function that overapproximates an interval linear form. More...
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| void | positive_time_elapse_assign_impl (const Polyhedron &y) |
| | Assuming *this is NNC, assigns to *this the result of the "positive time-elapse" between *this and y. More...
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| template<typename FP_Format , typename Interval_Info > |
| static void | convert_to_integer_expression (const Linear_Form< Interval< FP_Format, Interval_Info > > &lf, const dimension_type lf_dimension, Linear_Expression &result) |
| | Helper function that makes result become a Linear_Expression obtained by normalizing the denominators in lf. More...
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| template<typename FP_Format , typename Interval_Info > |
| static void | convert_to_integer_expressions (const Linear_Form< Interval< FP_Format, Interval_Info > > &lf, const dimension_type lf_dimension, Linear_Expression &res, Coefficient &res_low_coeff, Coefficient &res_hi_coeff, Coefficient &denominator) |
| | Normalization helper function. More...
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| std::ostream & | operator<< (std::ostream &s, const Polyhedron &ph) |
| | Output operator. More...
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| void | swap (Polyhedron &x, Polyhedron &y) |
| | Swaps x with y. More...
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| bool | operator== (const Polyhedron &x, const Polyhedron &y) |
| | Returns true if and only if x and y are the same polyhedron. More...
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| bool | operator!= (const Polyhedron &x, const Polyhedron &y) |
| | Returns true if and only if x and y are different polyhedra. More...
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| void | swap (Polyhedron &x, Polyhedron &y) |
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| bool | operator!= (const Polyhedron &x, const Polyhedron &y) |
| |