|  | 
|  | 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. ( *thisandycan be dimension-incompatible.)
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| NNC_Polyhedron & | operator= (const C_Polyhedron &y) | 
|  | Assigns to *thisthe C polyhedrony.
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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 *thisandyis exact it is assigned to*thisandtrueis returned, otherwisefalseis 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*thisandy.  More...
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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 *thisis 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 *thisand the constraintc.  More...
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| Poly_Gen_Relation | relation_with (const Generator &g) const | 
|  | Returns the relations holding between the polyhedron *thisand the generatorg.  More...
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| Poly_Con_Relation | relation_with (const Congruence &cg) const | 
|  | Returns the relations holding between the polyhedron *thisand the congruencec.  More...
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| bool | is_empty () const | 
|  | Returns trueif and only if*thisis an empty polyhedron.
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| bool | is_universe () const | 
|  | Returns trueif and only if*thisis a universe polyhedron.
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| bool | is_topologically_closed () const | 
|  | Returns trueif and only if*thisis a topologically closed subset of the vector space.
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| bool | is_disjoint_from (const Polyhedron &y) const | 
|  | Returns trueif and only if*thisandyare disjoint.  More...
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| bool | is_discrete () const | 
|  | Returns trueif and only if*thisis discrete.
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| bool | is_bounded () const | 
|  | Returns trueif and only if*thisis a bounded polyhedron.
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| bool | contains_integer_point () const | 
|  | Returns trueif and only if*thiscontains at least one integer point.
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| bool | constrains (Variable var) const | 
|  | Returns trueif and only ifvaris constrained in*this.  More...
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| bool | bounds_from_above (const Linear_Expression &expr) const | 
|  | Returns trueif and only ifexpris bounded from above in*this.  More...
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| bool | bounds_from_below (const Linear_Expression &expr) const | 
|  | Returns trueif and only ifexpris 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 trueif and only if*thisis not empty andexpris 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 trueif and only if*thisis not empty andexpris bounded from above in*this, in which case the supremum value and a point whereexprreaches it are computed.  More...
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| bool | minimize (const Linear_Expression &expr, Coefficient &inf_n, Coefficient &inf_d, bool &minimum) const | 
|  | Returns trueif and only if*thisis not empty andexpris 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 trueif and only if*thisis not empty andexpris bounded from below in*this, in which case the infimum value and a point whereexprreaches 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 trueif and only if there exist a unique valuevalsuch that*thissaturates the equalityexpr = val.  More...
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| bool | contains (const Polyhedron &y) const | 
|  | Returns trueif and only if*thiscontainsy.  More...
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| bool | strictly_contains (const Polyhedron &y) const | 
|  | Returns trueif and only if*thisstrictly containsy.  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 cto 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 gto 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 cgto*this, ifcgcan 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 csto 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 csto 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 gsto 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 gsto 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 cgsto*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 cgsto*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 cto refine*this.  More...
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| void | refine_with_congruence (const Congruence &cg) | 
|  | Uses a copy of congruence cgto refine*this.  More...
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| void | refine_with_constraints (const Constraint_System &cs) | 
|  | Uses a copy of the constraints in csto refine*this.  More...
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|  | 
| void | refine_with_congruences (const Congruence_System &cgs) | 
|  | Uses a copy of the congruences in cgsto 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 *thiswith the constraint expressed byleft  rightifis_strictis set, with the constraintleft  rightotherwise.  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 *thiswith the constraint expressed byleft  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 storewith the constraints defining*this.  More...
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| void | unconstrain (Variable var) | 
|  | Computes the cylindrification of *thiswith respect to space dimensionvar, assigning the result to*this.  More...
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| void | unconstrain (const Variables_Set &vars) | 
|  | Computes the cylindrification of *thiswith respect to the set of space dimensionsvars, assigning the result to*this.  More...
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| void | intersection_assign (const Polyhedron &y) | 
|  | Assigns to *thisthe intersection of*thisandy.  More...
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| void | poly_hull_assign (const Polyhedron &y) | 
|  | Assigns to *thisthe poly-hull of*thisandy.  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 *thisthe poly-difference of*thisandy.  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 *thisa meet-preserving simplification of*thiswith respect toy. Iffalseis 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 *thisthe affine image of*thisunder the function mapping variablevarto the affine expression specified byexpranddenominator.  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) | 
|  | 
| void | affine_preimage (Variable var, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one()) | 
|  | Assigns to *thisthe affine preimage of*thisunder the function mapping variablevarto the affine expression specified byexpranddenominator.  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 *thisthe image of*thiswith 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 *thisthe preimage of*thiswith 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 *thisthe image of*thiswith 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 *thisthe preimage of*thiswith 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 *thisthe image of*thiswith 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 *thisthe preimage of*thiswith respect to the bounded affine relation .  More... 
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|  | 
| void | time_elapse_assign (const Polyhedron &y) | 
|  | Assigns to *thisthe result of computing the time-elapse between*thisandy.  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*thisandy.  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 *thisby 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 *thisby dropping some points with non-integer coordinates for the space dimensions corresponding tovars.  More...
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|  | 
| void | topological_closure_assign () | 
|  | Assigns to *thisits topological closure.
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| void | BHRZ03_widening_assign (const Polyhedron &y, unsigned *tp=0) | 
|  | Assigns to *thisthe result of computing the BHRZ03-widening between*thisandy.  More...
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| void | limited_BHRZ03_extrapolation_assign (const Polyhedron &y, const Constraint_System &cs, unsigned *tp=0) | 
|  | Assigns to *thisthe result of computing the limited extrapolation between*thisandyusing 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 *thisthe result of computing the bounded extrapolation between*thisandyusing the BHRZ03-widening operator.  More...
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| void | H79_widening_assign (const Polyhedron &y, unsigned *tp=0) | 
|  | Assigns to *thisthe result of computing the H79_widening between*thisandy.  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 *thisthe result of computing the limited extrapolation between*thisandyusing 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 *thisthe result of computing the bounded extrapolation between*thisandyusing the H79-widening operator.  More...
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|  | 
| void | add_space_dimensions_and_embed (dimension_type m) | 
|  | Adds mnew 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 mnew 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 *thisthe concatenation of*thisandy, 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 mcopies of the space dimension corresponding tovar.  More...
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| void | fold_space_dimensions (const Variables_Set &vars, Variable dest) | 
|  | Folds the space dimensions in varsintodest.  More...
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|  | 
|  | ~Polyhedron () | 
|  | Destructor. 
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|  | 
| void | m_swap (Polyhedron &y) | 
|  | Swaps *thiswith polyhedrony. (*thisandycan be dimension-incompatible.)  More...
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| void | ascii_dump () const | 
|  | Writes to std::cerran ASCII representation of*this.
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|  | 
| void | ascii_dump (std::ostream &s) const | 
|  | Writes to san ASCII representation of*this.
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| void | print () const | 
|  | Prints *thistostd::cerrusingoperator<<.
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| bool | ascii_load (std::istream &s) | 
|  | Loads from san ASCII representation (as produced by ascii_dump(std::ostream&) const) and sets*thisaccordingly. Returnstrueif successful,falseotherwise.
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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 trueindicating 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 falseindicating 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. ( *thisandycan be dimension-incompatible.)
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|  | 
| void | drop_some_non_integer_points (const Variables_Set *vars_p, Complexity_Class complexity) | 
|  | Possibly tightens *thisby 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 *thisis NNC, assigns to*thisthe result of the "positive time-elapse" between*thisandy.  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 resultbecome a Linear_Expression obtained by normalizing the denominators inlf.  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 xwithy.  More...
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|  | 
| bool | operator== (const Polyhedron &x, const Polyhedron &y) | 
|  | Returns trueif and only ifxandyare the same polyhedron.  More...
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|  | 
| bool | operator!= (const Polyhedron &x, const Polyhedron &y) | 
|  | Returns trueif and only ifxandyare different polyhedra.  More...
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|  | 
| void | swap (Polyhedron &x, Polyhedron &y) | 
|  | 
| bool | operator!= (const Polyhedron &x, const Polyhedron &y) | 
|  |