The Java base class for (C and NNC) convex polyhedra. More...

Inheritance diagram for parma_polyhedra_library.Polyhedron:

Collaboration diagram for parma_polyhedra_library.Polyhedron:

Public Member Functions
Member Functions that Do Not Modify the Polyhedron
native long	space_dimension ()
	Returns the dimension of the vector space enclosing `this`. More...

native long	affine_dimension ()
	Returns , if `this` is empty; otherwise, returns the affine dimension of `this`. More...

native Constraint_System	constraints ()
	Returns the system of constraints. More...

native Congruence_System	congruences ()
	Returns a system of (equality) congruences satisfied by `this`. More...

native Constraint_System	minimized_constraints ()
	Returns the system of constraints, with no redundant constraint. More...

native Congruence_System	minimized_congruences ()
	Returns a system of (equality) congruences satisfied by `this`, with no redundant congruences and having the same affine dimension as `this`. More...

native boolean	is_empty ()
	Returns `true` if and only if `this` is an empty polyhedron. More...

native boolean	is_universe ()
	Returns `true` if and only if `this` is a universe polyhedron. More...

native boolean	is_bounded ()
	Returns `true` if and only if `this` is a bounded polyhedron. More...

native boolean	is_discrete ()
	Returns `true` if and only if `this` is discrete. More...

native boolean	is_topologically_closed ()
	Returns `true` if and only if `this` is a topologically closed subset of the vector space. More...

native boolean	contains_integer_point ()
	Returns `true` if and only if `this` contains at least one integer point. More...

native boolean	constrains (Variable var)
	Returns `true` if and only if `var` is constrained in `this`. More...

native boolean	bounds_from_above (Linear_Expression expr)
	Returns `true` if and only if `expr` is bounded from above in `this`. More...

native boolean	bounds_from_below (Linear_Expression expr)
	Returns `true` if and only if `expr` is bounded from below in `this`. More...

native boolean	maximize (Linear_Expression expr, Coefficient sup_n, Coefficient sup_d, By_Reference< Boolean > maximum)
	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...

native boolean	minimize (Linear_Expression expr, Coefficient inf_n, Coefficient inf_d, By_Reference< Boolean > minimum)
	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...

native boolean	maximize (Linear_Expression expr, Coefficient sup_n, Coefficient sup_d, By_Reference< Boolean > maximum, Generator g)
	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...

native boolean	minimize (Linear_Expression expr, Coefficient inf_n, Coefficient inf_d, By_Reference< Boolean > minimum, Generator g)
	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...

native Poly_Con_Relation	relation_with (Constraint c)
	Returns the relations holding between the polyhedron `this` and the constraint `c`. More...

native Poly_Gen_Relation	relation_with (Generator c)
	Returns the relations holding between the polyhedron `this` and the generator `g`. More...

native Poly_Con_Relation	relation_with (Congruence c)
	Returns the relations holding between the polyhedron `this` and the congruence `c`. More...

native boolean	contains (Polyhedron y)
	Returns `true` if and only if `this` contains `y`. More...

native boolean	strictly_contains (Polyhedron y)
	Returns `true` if and only if `this` strictly contains `y`. More...

native boolean	is_disjoint_from (Polyhedron y)
	Returns `true` if and only if `this` and `y` are disjoint. More...

native boolean	equals (Polyhedron y)
	Returns `true` if and only if `this` and `y` are equal. More...

boolean	equals (Object y)
	Returns `true` if and only if `this` and `y` are equal. More...

native int	hashCode ()
	Returns a hash code for `this`. More...

native long	external_memory_in_bytes ()
	Returns the size in bytes of the memory managed by `this`. More...

native long	total_memory_in_bytes ()
	Returns the total size in bytes of the memory occupied by `this`. More...

native String	toString ()
	Returns a string representing `this`. More...

native String	ascii_dump ()
	Returns a string containing a low-level representation of `this`. More...

native boolean	OK ()
	Checks if all the invariants are satisfied. More...

Space Dimension Preserving Member Functions that May Modify the Polyhedron
native void	add_constraint (Constraint c)
	Adds a copy of constraint `c` to the system of constraints of `this` (without minimizing the result). More...

native void	add_congruence (Congruence cg)
	Adds a copy of congruence `cg` to `this`, if `cg` can be exactly represented by a polyhedron. More...

native void	add_constraints (Constraint_System cs)
	Adds a copy of the constraints in `cs` to the system of constraints of `this` (without minimizing the result). More...

native void	add_congruences (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...

native void	refine_with_constraint (Constraint c)
	Uses a copy of constraint `c` to refine `this`. More...

native void	refine_with_congruence (Congruence cg)
	Uses a copy of congruence `cg` to refine `this`. More...

native void	refine_with_constraints (Constraint_System cs)
	Uses a copy of the constraints in `cs` to refine `this`. More...

native void	refine_with_congruences (Congruence_System cgs)
	Uses a copy of the congruences in `cgs` to refine `this`. More...

native void	intersection_assign (Polyhedron y)
	Assigns to `this` the intersection of `this` and `y`. The result is not guaranteed to be minimized. More...

native void	upper_bound_assign (Polyhedron y)
	Assigns to `this` the upper bound of `this` and `y`. More...

native void	difference_assign (Polyhedron y)
	Assigns to `this` the poly-difference of `this` and `y`. The result is not guaranteed to be minimized. More...

native void	time_elapse_assign (Polyhedron y)
	Assigns to `this` the result of computing the time-elapse between `this` and `y`. More...

native void	topological_closure_assign ()
	Assigns to `this` its topological closure. More...

native boolean	simplify_using_context_assign (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...

native void	affine_image (Variable var, Linear_Expression expr, Coefficient denominator)
	Assigns to `this` the affine image of `this` under the function mapping variable `var` to the affine expression specified by `expr` and `denominator`. More...

native void	affine_preimage (Variable var, Linear_Expression expr, Coefficient denominator)
	Assigns to `this` the affine preimage of `this` under the function mapping variable `var` to the affine expression specified by `expr` and `denominator`. More...

native void	bounded_affine_image (Variable var, Linear_Expression lb_expr, Linear_Expression ub_expr, Coefficient denominator)
	Assigns to `this` the image of `this` with respect to the bounded affine relation $\frac{\mathrm{lb\_expr}}{\mathrm{denominator}} \leq \mathrm{var}' \leq \frac{\mathrm{ub\_expr}}{\mathrm{denominator}}$ . More...

native void	bounded_affine_preimage (Variable var, Linear_Expression lb_expr, Linear_Expression ub_expr, Coefficient denominator)
	Assigns to `this` the preimage of `this` with respect to the bounded affine relation $\frac{\mathrm{lb\_expr}}{\mathrm{denominator}} \leq \mathrm{var}' \leq \frac{\mathrm{ub\_expr}}{\mathrm{denominator}}$ . More...

native void	generalized_affine_image (Variable var, Relation_Symbol relsym, Linear_Expression expr, Coefficient denominator)
	Assigns to `this` the image of `this` with respect to the generalized affine relation $\mathrm{var}' \relsym \frac{\mathrm{expr}}{\mathrm{denominator}}$ , where $\mathord{\relsym}$ is the relation symbol encoded by `relsym`. More...

native void	generalized_affine_preimage (Variable var, Relation_Symbol relsym, Linear_Expression expr, Coefficient denominator)
	Assigns to `this` the preimage of `this` with respect to the generalized affine relation $\mathrm{var}' \relsym \frac{\mathrm{expr}}{\mathrm{denominator}}$ , where $\mathord{\relsym}$ is the relation symbol encoded by `relsym`. More...

native void	generalized_affine_image (Linear_Expression lhs, Relation_Symbol relsym, Linear_Expression rhs)
	Assigns to `this` the image of `this` with respect to the generalized affine relation $\mathrm{lhs}' \relsym \mathrm{rhs}$ , where $\mathord{\relsym}$ is the relation symbol encoded by `relsym`. More...

native void	generalized_affine_preimage (Linear_Expression lhs, Relation_Symbol relsym, Linear_Expression rhs)
	Assigns to `this` the preimage of `this` with respect to the generalized affine relation $\mathrm{lhs}' \relsym \mathrm{rhs}$ , where $\mathord{\relsym}$ is the relation symbol encoded by `relsym`. More...

native void	unconstrain_space_dimension (Variable var)
	Computes the cylindrification of `this` with respect to space dimension `var`, assigning the result to `this`. More...

native void	unconstrain_space_dimensions (Variables_Set vars)
	Computes the cylindrification of `this` with respect to the set of space dimensions `vars`, assigning the result to `this`. More...

native void	widening_assign (Polyhedron y, By_Reference< Integer > tp)
	Assigns to `this` the result of computing the H79-widening between `this` and `y`. More...

Member Functions that May Modify the Dimension of the Vector Space
native void	swap (Polyhedron y)
	Swaps `this` with polyhedron `y`. (`this` and `y` can be dimension-incompatible.) More...

native void	add_space_dimensions_and_embed (long m)
	Adds `m` new space dimensions and embeds the old polyhedron in the new vector space. More...

native void	add_space_dimensions_and_project (long m)
	Adds `m` new space dimensions to the polyhedron and does not embed it in the new vector space. More...

native void	concatenate_assign (Polyhedron y)
	Assigns to `this` the concatenation of `this` and `y`, taken in this order. More...

native void	remove_space_dimensions (Variables_Set vars)
	Removes all the specified dimensions from the vector space. More...

native void	remove_higher_space_dimensions (long new_dimension)
	Removes the higher dimensions of the vector space so that the resulting space will have dimension `new_dimension`. More...

native void	expand_space_dimension (Variable var, long m)
	Creates `m` copies of the space dimension corresponding to `var`. More...

native void	fold_space_dimensions (Variables_Set vars, Variable dest)
	Folds the space dimensions in `vars` into `dest`. More...

native void	map_space_dimensions (Partial_Function pfunc)
	Remaps the dimensions of the vector space according to a partial function. More...

Ad Hoc Functions for (C or NNC) Polyhedra
The functions listed here below, being specific of the polyhedron domains, do not have a correspondence in other semantic geometric descriptions.
native Generator_System	generators ()
	Returns the system of generators. More...

native Generator_System	minimized_generators ()
	Returns the system of generators, with no redundant generator. More...

native void	add_generator (Generator g)
	Adds a copy of generator `g` to the system of generators of `this` (without minimizing the result). More...

native void	add_generators (Generator_System gs)
	Adds a copy of the generators in `gs` to the system of generators of `this` (without minimizing the result). More...

native void	poly_hull_assign (Polyhedron y)
	Same as upper_bound_assign. More...

native void	poly_difference_assign (Polyhedron y)
	Same as difference_assign. More...

native void	BHRZ03_widening_assign (Polyhedron y, By_Reference< Integer > tp)
	Assigns to `this` the result of computing the BHRZ03-widening between `this` and `y`. More...

native void	H79_widening_assign (Polyhedron y, By_Reference< Integer > tp)
	Assigns to `this` the result of computing the H79-widening between `this` and `y`. More...

native void	limited_BHRZ03_extrapolation_assign (Polyhedron y, Constraint_System cs, By_Reference< Integer > tp)
	Improves the result of the BHRZ03-widening computation by also enforcing those constraints in `cs` that are satisfied by all the points of `this`. More...

native void	limited_H79_extrapolation_assign (Polyhedron y, Constraint_System cs, By_Reference< Integer > tp)
	Improves the result of the H79-widening computation by also enforcing those constraints in `cs` that are satisfied by all the points of `this`. More...

native void	bounded_BHRZ03_extrapolation_assign (Polyhedron y, Constraint_System cs, By_Reference< Integer > tp)
	Improves the result of the BHRZ03-widening computation by also enforcing those constraints in `cs` that are satisfied by all the points of `this`, plus all the constraints of the form $\pm x \leq r$ and $\pm x < r$ , with $r \in \Qset$ , that are satisfied by all the points of `this`. More...

native void	bounded_H79_extrapolation_assign (Polyhedron y, Constraint_System cs, By_Reference< Integer > tp)
	Improves the result of the H79-widening computation by also enforcing those constraints in `cs` that are satisfied by all the points of `this`, plus all the constraints of the form $\pm x \leq r$ and $\pm x < r$ , with $r \in \Qset$ , that are satisfied by all the points of `this`. More...

Additional Inherited Members
Protected Member Functions inherited from parma_polyhedra_library.PPL_Object
	PPL_Object ()
	Builds an object that points to `null'. More...

Detailed Description

The Java base class for (C and NNC) convex polyhedra.

The base class Polyhedron provides declarations for most of the methods common to classes C_Polyhedron and NNC_Polyhedron. Note that the user should always use the derived classes. Moreover, C and NNC polyhedra can not be freely interchanged: as specified in the main manual, most library functions require their arguments to be topologically compatible.

Definition at line 38 of file Fake_Class_for_Doxygen.java.

Member Function Documentation

native void parma_polyhedra_library.Polyhedron.add_congruence ( Congruence cg )

Adds a copy of congruence cg to this, if cg can be exactly represented by a polyhedron.

Exceptions

Invalid_Argument_Exception Thrown if this and congruence cg are dimension-incompatible, of if cg is a proper congruence which is neither a tautology, nor a contradiction.

native void parma_polyhedra_library.Polyhedron.add_congruences ( Congruence_System cgs )

Adds a copy of the congruences in cgs to this, if all the congruences can be exactly represented by a polyhedron.

Parameters

cgs	The congruences to be added.

Exceptions

Invalid_Argument_Exception Thrown if this and cgs are dimension-incompatible, of if there exists in cgs a proper congruence which is neither a tautology, nor a contradiction.

native void parma_polyhedra_library.Polyhedron.add_constraint ( Constraint c )

Adds a copy of constraint c to the system of constraints of this (without minimizing the result).

Parameters

c	The constraint that will be added to the system of constraints of `this`.

Exceptions

Invalid_Argument_Exception Thrown if this and constraint c are topology-incompatible or dimension-incompatible.

native void parma_polyhedra_library.Polyhedron.add_constraints ( Constraint_System cs )

Adds a copy of the constraints in cs to the system of constraints of this (without minimizing the result).

Parameters

cs	Contains the constraints that will be added to the system of constraints of `this`.

Exceptions

Invalid_Argument_Exception Thrown if this and cs are topology-incompatible or dimension-incompatible.

native void parma_polyhedra_library.Polyhedron.add_generator ( Generator g )

Adds a copy of generator g to the system of generators of this (without minimizing the result).

Exceptions

Invalid_Argument_Exception Thrown if this and generator g are topology-incompatible or dimension-incompatible, or if this is an empty polyhedron and g is not a point.

native void parma_polyhedra_library.Polyhedron.add_generators ( Generator_System gs )

Adds a copy of the generators in gs to the system of generators of this (without minimizing the result).

Parameters

gs	Contains the generators that will be added to the system of generators of `this`.

Exceptions

Invalid_Argument_Exception Thrown if this and gs are topology-incompatible or dimension-incompatible, or if this is empty and the system of generators gs is not empty, but has no points.

native void parma_polyhedra_library.Polyhedron.add_space_dimensions_and_embed ( long m )

Adds m new space dimensions and embeds the old polyhedron in the new vector space.

Parameters

m	The number of dimensions to add.

Exceptions

Length_Error_Exception Thrown if adding m new space dimensions would cause the vector space to exceed dimension max_space_dimension().

native void parma_polyhedra_library.Polyhedron.add_space_dimensions_and_project ( long m )

Adds m new space dimensions to the polyhedron and does not embed it in the new vector space.

Parameters

m	The number of space dimensions to add.

Exceptions

Length_Error_Exception Thrown if adding m new space dimensions would cause the vector space to exceed dimension max_space_dimension().

native long parma_polyhedra_library.Polyhedron.affine_dimension ( )

Returns $0$ , if this is empty; otherwise, returns the affine dimension of this.

native void parma_polyhedra_library.Polyhedron.affine_image	(	Variable	var,
		Linear_Expression	expr,
		Coefficient	denominator
	)

Assigns to this the affine image of this under the function mapping variable var to the affine expression specified by expr and denominator.

Parameters

var	The variable to which the affine expression is assigned;
expr	The numerator of the affine expression;
denominator	The denominator of the affine expression (optional argument with default value 1).

Exceptions

Invalid_Argument_Exception Thrown if denominator is zero or if expr and this are dimension-incompatible or if var is not a space dimension of this.

native void parma_polyhedra_library.Polyhedron.affine_preimage	(	Variable	var,
		Linear_Expression	expr,
		Coefficient	denominator
	)

Assigns to this the affine preimage of this under the function mapping variable var to the affine expression specified by expr and denominator.

Parameters

var	The variable to which the affine expression is substituted;
expr	The numerator of the affine expression;
denominator	The denominator of the affine expression (optional argument with default value 1).

Exceptions

Invalid_Argument_Exception Thrown if denominator is zero or if expr and this are dimension-incompatible or if var is not a space dimension of this.

native String parma_polyhedra_library.Polyhedron.ascii_dump ( )

Returns a string containing a low-level representation of this.

Useful for debugging purposes.

native void parma_polyhedra_library.Polyhedron.BHRZ03_widening_assign	(	Polyhedron	y,
		By_Reference< Integer >	tp
	)

Assigns to this the result of computing the BHRZ03-widening between this and y.

Parameters

y	A polyhedron that must be contained in `this`;
tp	A reference to an unsigned variable storing the number of available tokens (to be used when applying the widening with tokens delay technique).

Exceptions

Invalid_Argument_Exception Thrown if this and y are topology-incompatible or dimension-incompatible.

native void parma_polyhedra_library.Polyhedron.bounded_affine_image	(	Variable	var,
		Linear_Expression	lb_expr,
		Linear_Expression	ub_expr,
		Coefficient	denominator
	)

Assigns to this the image of this with respect to the bounded affine relation $\frac{\mathrm{lb\_expr}}{\mathrm{denominator}} \leq \mathrm{var}' \leq \frac{\mathrm{ub\_expr}}{\mathrm{denominator}}$ .

Parameters

var	The variable updated by the affine relation;
lb_expr	The numerator of the lower bounding affine expression;
ub_expr	The numerator of the upper bounding affine expression;
denominator	The (common) denominator for the lower and upper bounding affine expressions (optional argument with default value 1).

Exceptions

Invalid_Argument_Exception Thrown if denominator is zero or if lb_expr (resp., ub_expr) and this are dimension-incompatible or if var is not a space dimension of this.

native void parma_polyhedra_library.Polyhedron.bounded_affine_preimage	(	Variable	var,
		Linear_Expression	lb_expr,
		Linear_Expression	ub_expr,
		Coefficient	denominator
	)

Assigns to this the preimage of this with respect to the bounded affine relation $\frac{\mathrm{lb\_expr}}{\mathrm{denominator}} \leq \mathrm{var}' \leq \frac{\mathrm{ub\_expr}}{\mathrm{denominator}}$ .

Parameters

var	The variable updated by the affine relation;
lb_expr	The numerator of the lower bounding affine expression;
ub_expr	The numerator of the upper bounding affine expression;
denominator	The (common) denominator for the lower and upper bounding affine expressions (optional argument with default value 1).

Exceptions

Invalid_Argument_Exception Thrown if denominator is zero or if lb_expr (resp., ub_expr) and this are dimension-incompatible or if var is not a space dimension of this.

native void parma_polyhedra_library.Polyhedron.bounded_BHRZ03_extrapolation_assign	(	Polyhedron	y,
		Constraint_System	cs,
		By_Reference< Integer >	tp
	)

Improves the result of the BHRZ03-widening computation by also enforcing those constraints in cs that are satisfied by all the points of this, plus all the constraints of the form $\pm x \leq r$ and $\pm x < r$ , with $r \in \Qset$ , that are satisfied by all the points of this.

Parameters

y	A polyhedron that must be contained in `this`;
cs	The system of constraints used to improve the widened polyhedron;
tp	A reference to an unsigned variable storing the number of available tokens (to be used when applying the widening with tokens delay technique).

Exceptions

Invalid_Argument_Exception Thrown if this, y and cs are topology-incompatible or dimension-incompatible.

native void parma_polyhedra_library.Polyhedron.bounded_H79_extrapolation_assign	(	Polyhedron	y,
		Constraint_System	cs,
		By_Reference< Integer >	tp
	)

Improves the result of the H79-widening computation by also enforcing those constraints in cs that are satisfied by all the points of this, plus all the constraints of the form $\pm x \leq r$ and $\pm x < r$ , with $r \in \Qset$ , that are satisfied by all the points of this.

Parameters

y	A polyhedron that must be contained in `this`;
cs	The system of constraints used to improve the widened polyhedron;
tp	A reference to an unsigned variable storing the number of available tokens (to be used when applying the widening with tokens delay technique).

Exceptions

Invalid_Argument_Exception Thrown if this, y and cs are topology-incompatible or dimension-incompatible.

native boolean parma_polyhedra_library.Polyhedron.bounds_from_above ( Linear_Expression expr )

Returns true if and only if expr is bounded from above in this.

Exceptions

Invalid_Argument_Exception Thrown if expr and this are dimension-incompatible.

native boolean parma_polyhedra_library.Polyhedron.bounds_from_below ( Linear_Expression expr )

Returns true if and only if expr is bounded from below in this.

Exceptions

Invalid_Argument_Exception Thrown if expr and this are dimension-incompatible.

native void parma_polyhedra_library.Polyhedron.concatenate_assign ( Polyhedron y )

Assigns to this the concatenation of this and y, taken in this order.

Exceptions

Invalid_Argument_Exception	Thrown if `this` and `y` are topology-incompatible.
Length_Error_Exception	Thrown if the concatenation would cause the vector space to exceed dimension `max_space_dimension()`.

native Congruence_System parma_polyhedra_library.Polyhedron.congruences ( )

Returns a system of (equality) congruences satisfied by this.

native boolean parma_polyhedra_library.Polyhedron.constrains ( Variable var )

Returns true if and only if var is constrained in this.

Exceptions

Invalid_Argument_Exception Thrown if var is not a space dimension of this.

native Constraint_System parma_polyhedra_library.Polyhedron.constraints ( )

Returns the system of constraints.

native boolean parma_polyhedra_library.Polyhedron.contains ( Polyhedron y )

Returns true if and only if this contains y.

Exceptions

Invalid_Argument_Exception Thrown if this and y are topology-incompatible or dimension-incompatible.

native boolean parma_polyhedra_library.Polyhedron.contains_integer_point ( )

Returns true if and only if this contains at least one integer point.

native void parma_polyhedra_library.Polyhedron.difference_assign ( Polyhedron y )

Assigns to this the poly-difference of this and y. The result is not guaranteed to be minimized.

Exceptions

Invalid_Argument_Exception Thrown if this and y are topology-incompatible or dimension-incompatible.

native boolean parma_polyhedra_library.Polyhedron.equals ( Polyhedron y )

Returns true if and only if this and y are equal.

boolean parma_polyhedra_library.Polyhedron.equals ( Object y )

Returns true if and only if this and y are equal.

native void parma_polyhedra_library.Polyhedron.expand_space_dimension	(	Variable	var,
		long	m
	)

Creates m copies of the space dimension corresponding to var.

Parameters

var	The variable corresponding to the space dimension to be replicated;
m	The number of replicas to be created.

Exceptions

Invalid_Argument_Exception	Thrown if `var` does not correspond to a dimension of the vector space.
Length_Error_Exception	Thrown if adding `m` new space dimensions would cause the vector space to exceed dimension `max_space_dimension()`.

native long parma_polyhedra_library.Polyhedron.external_memory_in_bytes ( )

Returns the size in bytes of the memory managed by this.

native void parma_polyhedra_library.Polyhedron.fold_space_dimensions	(	Variables_Set	vars,
		Variable	dest
	)

Folds the space dimensions in vars into dest.

Parameters

vars	The set of Variable objects corresponding to the space dimensions to be folded;
dest	The variable corresponding to the space dimension that is the destination of the folding operation.

Exceptions

Invalid_Argument_Exception Thrown if this is dimension-incompatible with dest or with one of the Variable objects contained in vars. Also thrown if dest is contained in vars.

native void parma_polyhedra_library.Polyhedron.generalized_affine_image	(	Variable	var,
		Relation_Symbol	relsym,
		Linear_Expression	expr,
		Coefficient	denominator
	)

Assigns to this the image of this with respect to the generalized affine relation $\mathrm{var}' \relsym \frac{\mathrm{expr}}{\mathrm{denominator}}$ , where $\mathord{\relsym}$ is the relation symbol encoded by relsym.

Parameters

var	The left hand side variable of the generalized affine relation;
relsym	The relation symbol;
expr	The numerator of the right hand side affine expression;
denominator	The denominator of the right hand side affine expression (optional argument with default value 1).

Exceptions

Invalid_Argument_Exception Thrown if denominator is zero or if expr and this are dimension-incompatible or if var is not a space dimension of this or if this is a C_Polyhedron and relsym is a strict relation symbol.

native void parma_polyhedra_library.Polyhedron.generalized_affine_image	(	Linear_Expression	lhs,
		Relation_Symbol	relsym,
		Linear_Expression	rhs
	)

Assigns to this the image of this with respect to the generalized affine relation $\mathrm{lhs}' \relsym \mathrm{rhs}$ , where $\mathord{\relsym}$ is the relation symbol encoded by relsym.

Parameters

lhs	The left hand side affine expression;
relsym	The relation symbol;
rhs	The right hand side affine expression.

Exceptions

Invalid_Argument_Exception Thrown if this is dimension-incompatible with lhs or rhs or if this is a C_Polyhedron and relsym is a strict relation symbol.

native void parma_polyhedra_library.Polyhedron.generalized_affine_preimage	(	Variable	var,
		Relation_Symbol	relsym,
		Linear_Expression	expr,
		Coefficient	denominator
	)

Assigns to this the preimage of this with respect to the generalized affine relation $\mathrm{var}' \relsym \frac{\mathrm{expr}}{\mathrm{denominator}}$ , where $\mathord{\relsym}$ is the relation symbol encoded by relsym.

Parameters

var	The left hand side variable of the generalized affine relation;
relsym	The relation symbol;
expr	The numerator of the right hand side affine expression;
denominator	The denominator of the right hand side affine expression (optional argument with default value 1).

Exceptions

Invalid_Argument_Exception Thrown if denominator is zero or if expr and this are dimension-incompatible or if var is not a space dimension of this or if this is a C_Polyhedron and relsym is a strict relation symbol.

native void parma_polyhedra_library.Polyhedron.generalized_affine_preimage	(	Linear_Expression	lhs,
		Relation_Symbol	relsym,
		Linear_Expression	rhs
	)

Assigns to this the preimage of this with respect to the generalized affine relation $\mathrm{lhs}' \relsym \mathrm{rhs}$ , where $\mathord{\relsym}$ is the relation symbol encoded by relsym.

Parameters

lhs	The left hand side affine expression;
relsym	The relation symbol;
rhs	The right hand side affine expression.

Exceptions

Invalid_Argument_Exception Thrown if this is dimension-incompatible with lhs or rhs or if this is a C_Polyhedron and relsym is a strict relation symbol.

native Generator_System parma_polyhedra_library.Polyhedron.generators ( )

Returns the system of generators.

native void parma_polyhedra_library.Polyhedron.H79_widening_assign	(	Polyhedron	y,
		By_Reference< Integer >	tp
	)

Assigns to this the result of computing the H79-widening between this and y.

Parameters

y	A polyhedron that must be contained in `this`;
tp	A reference to an unsigned variable storing the number of available tokens (to be used when applying the widening with tokens delay technique).

Exceptions

Invalid_Argument_Exception Thrown if this and y are topology-incompatible or dimension-incompatible.

native int parma_polyhedra_library.Polyhedron.hashCode ( )

Returns a hash code for this.

If x and y are such that x == y, then x.hash_code() == y.hash_code().

native void parma_polyhedra_library.Polyhedron.intersection_assign ( Polyhedron y )

Assigns to this the intersection of this and y. The result is not guaranteed to be minimized.

Exceptions

Invalid_Argument_Exception Thrown if this and y are topology-incompatible or dimension-incompatible.

native boolean parma_polyhedra_library.Polyhedron.is_bounded ( )

Returns true if and only if this is a bounded polyhedron.

native boolean parma_polyhedra_library.Polyhedron.is_discrete ( )

Returns true if and only if this is discrete.

native boolean parma_polyhedra_library.Polyhedron.is_disjoint_from ( Polyhedron y )

Returns true if and only if this and y are disjoint.

Exceptions

Invalid_Argument_Exception Thrown if x and y are topology-incompatible or dimension-incompatible.

native boolean parma_polyhedra_library.Polyhedron.is_empty ( )

Returns true if and only if this is an empty polyhedron.

native boolean parma_polyhedra_library.Polyhedron.is_topologically_closed ( )

Returns true if and only if this is a topologically closed subset of the vector space.

native boolean parma_polyhedra_library.Polyhedron.is_universe ( )

Returns true if and only if this is a universe polyhedron.

native void parma_polyhedra_library.Polyhedron.limited_BHRZ03_extrapolation_assign	(	Polyhedron	y,
		Constraint_System	cs,
		By_Reference< Integer >	tp
	)

Improves the result of the BHRZ03-widening computation by also enforcing those constraints in cs that are satisfied by all the points of this.

Parameters

y	A polyhedron that must be contained in `this`;
cs	The system of constraints used to improve the widened polyhedron;
tp	A reference to an unsigned variable storing the number of available tokens (to be used when applying the widening with tokens delay technique).

Exceptions

Invalid_Argument_Exception Thrown if this, y and cs are topology-incompatible or dimension-incompatible.

native void parma_polyhedra_library.Polyhedron.limited_H79_extrapolation_assign	(	Polyhedron	y,
		Constraint_System	cs,
		By_Reference< Integer >	tp
	)

Improves the result of the H79-widening computation by also enforcing those constraints in cs that are satisfied by all the points of this.

Parameters

y	A polyhedron that must be contained in `this`;
cs	The system of constraints used to improve the widened polyhedron;
tp	A reference to an unsigned variable storing the number of available tokens (to be used when applying the widening with tokens delay technique).

Exceptions

Invalid_Argument_Exception Thrown if this, y and cs are topology-incompatible or dimension-incompatible.

native void parma_polyhedra_library.Polyhedron.map_space_dimensions ( Partial_Function pfunc )

Remaps the dimensions of the vector space according to a partial function.

Parameters

pfunc The partial function specifying the destiny of each space dimension.

native boolean parma_polyhedra_library.Polyhedron.maximize	(	Linear_Expression	expr,
		Coefficient	sup_n,
		Coefficient	sup_d,
		By_Reference< Boolean >	maximum
	)

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.

Parameters

expr	The linear expression to be maximized subject to `this`;
sup_n	The numerator of the supremum value;
sup_d	The denominator of the supremum value;
maximum	`true` if and only if the supremum is also the maximum value.

Exceptions

Invalid_Argument_Exception Thrown if expr and this are dimension-incompatible.

If this is empty or expr is not bounded from above, false is returned and sup_n, sup_d and maximum are left untouched.

native boolean parma_polyhedra_library.Polyhedron.maximize	(	Linear_Expression	expr,
		Coefficient	sup_n,
		Coefficient	sup_d,
		By_Reference< Boolean >	maximum,
		Generator	g
	)

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.

Parameters

expr	The linear expression to be maximized subject to `this`;
sup_n	The numerator of the supremum value;
sup_d	The denominator of the supremum value;
maximum	`true` if and only if the supremum is also the maximum value;
g	When maximization succeeds, will be assigned the point or closure point where `expr` reaches its supremum value.

Exceptions

Invalid_Argument_Exception Thrown if expr and this are dimension-incompatible.

If this is empty or expr is not bounded from above, false is returned and sup_n, sup_d, maximum and g are left untouched.

native boolean parma_polyhedra_library.Polyhedron.minimize	(	Linear_Expression	expr,
		Coefficient	inf_n,
		Coefficient	inf_d,
		By_Reference< Boolean >	minimum
	)

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.

Parameters

expr	The linear expression to be minimized subject to `this`;
inf_n	The numerator of the infimum value;
inf_d	The denominator of the infimum value;
minimum	`true` if and only if the infimum is also the minimum value.

Exceptions

Invalid_Argument_Exception Thrown if expr and this are dimension-incompatible.

If this is empty or expr is not bounded from below, false is returned and inf_n, inf_d and minimum are left untouched.

native boolean parma_polyhedra_library.Polyhedron.minimize	(	Linear_Expression	expr,
		Coefficient	inf_n,
		Coefficient	inf_d,
		By_Reference< Boolean >	minimum,
		Generator	g
	)

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.

Parameters

expr	The linear expression to be minimized subject to `this`;
inf_n	The numerator of the infimum value;
inf_d	The denominator of the infimum value;
minimum	`true` if and only if the infimum is also the minimum value;
g	When minimization succeeds, will be assigned a point or closure point where `expr` reaches its infimum value.

Exceptions

Invalid_Argument_Exception Thrown if expr and this are dimension-incompatible.

If this is empty or expr is not bounded from below, false is returned and inf_n, inf_d, minimum and g are left untouched.

native Congruence_System parma_polyhedra_library.Polyhedron.minimized_congruences ( )

Returns a system of (equality) congruences satisfied by this, with no redundant congruences and having the same affine dimension as this.

native Constraint_System parma_polyhedra_library.Polyhedron.minimized_constraints ( )

Returns the system of constraints, with no redundant constraint.

native Generator_System parma_polyhedra_library.Polyhedron.minimized_generators ( )

Returns the system of generators, with no redundant generator.

native boolean parma_polyhedra_library.Polyhedron.OK ( )

Checks if all the invariants are satisfied.

native void parma_polyhedra_library.Polyhedron.poly_difference_assign ( Polyhedron y )

Same as difference_assign.

native void parma_polyhedra_library.Polyhedron.poly_hull_assign ( Polyhedron y )

Same as upper_bound_assign.

native void parma_polyhedra_library.Polyhedron.refine_with_congruence ( Congruence cg )

Uses a copy of congruence cg to refine this.

Exceptions

Invalid_Argument_Exception Thrown if this and congruence cg are dimension-incompatible.

native void parma_polyhedra_library.Polyhedron.refine_with_congruences ( Congruence_System cgs )

Uses a copy of the congruences in cgs to refine this.

Parameters

cgs	Contains the congruences used to refine the system of constraints of `this`.

Exceptions

Invalid_Argument_Exception Thrown if this and cgs are dimension-incompatible.

native void parma_polyhedra_library.Polyhedron.refine_with_constraint ( Constraint c )

Uses a copy of constraint c to refine this.

Exceptions

Invalid_Argument_Exception Thrown if this and constraint c are dimension-incompatible.

native void parma_polyhedra_library.Polyhedron.refine_with_constraints ( Constraint_System cs )

Uses a copy of the constraints in cs to refine this.

Parameters

cs	Contains the constraints used to refine the system of constraints of `this`.

Exceptions

Invalid_Argument_Exception Thrown if this and cs are dimension-incompatible.

native Poly_Con_Relation parma_polyhedra_library.Polyhedron.relation_with ( Constraint c )

Returns the relations holding between the polyhedron this and the constraint c.

Exceptions

Invalid_Argument_Exception Thrown if this and constraint c are dimension-incompatible.

native Poly_Gen_Relation parma_polyhedra_library.Polyhedron.relation_with ( Generator c )

Returns the relations holding between the polyhedron this and the generator g.

Exceptions

Invalid_Argument_Exception Thrown if this and generator g are dimension-incompatible.

native Poly_Con_Relation parma_polyhedra_library.Polyhedron.relation_with ( Congruence c )

Returns the relations holding between the polyhedron this and the congruence c.

Exceptions

Invalid_Argument_Exception Thrown if this and congruence c are dimension-incompatible.

native void parma_polyhedra_library.Polyhedron.remove_higher_space_dimensions ( long new_dimension )

Removes the higher dimensions of the vector space so that the resulting space will have dimension new_dimension.

Exceptions

Invalid_Argument_Exception Thrown if new_dimensions is greater than the space dimension of this.

native void parma_polyhedra_library.Polyhedron.remove_space_dimensions ( Variables_Set vars )

Removes all the specified dimensions from the vector space.

Parameters

vars	The set of Variable objects corresponding to the space dimensions to be removed.

Exceptions

Invalid_Argument_Exception Thrown if this is dimension-incompatible with one of the Variable objects contained in vars.

native boolean parma_polyhedra_library.Polyhedron.simplify_using_context_assign ( Polyhedron y )

Assigns to this a meet-preserving simplification of this with respect to y. If false is returned, then the intersection is empty.

Exceptions

Invalid_Argument_Exception Thrown if this and y are topology-incompatible or dimension-incompatible.

native long parma_polyhedra_library.Polyhedron.space_dimension ( )

Returns the dimension of the vector space enclosing this.

native boolean parma_polyhedra_library.Polyhedron.strictly_contains ( Polyhedron y )

Returns true if and only if this strictly contains y.

Exceptions

Invalid_Argument_Exception Thrown if this and y are topology-incompatible or dimension-incompatible.

native void parma_polyhedra_library.Polyhedron.swap ( Polyhedron y )

Swaps this with polyhedron y. (this and y can be dimension-incompatible.)

Exceptions

Invalid_Argument_Exception Thrown if x and y are topology-incompatible.

native void parma_polyhedra_library.Polyhedron.time_elapse_assign ( Polyhedron y )

Assigns to this the result of computing the time-elapse between this and y.

Exceptions

Invalid_Argument_Exception Thrown if this and y are topology-incompatible or dimension-incompatible.

native void parma_polyhedra_library.Polyhedron.topological_closure_assign ( )

Assigns to this its topological closure.

native String parma_polyhedra_library.Polyhedron.toString ( )

Returns a string representing this.

native long parma_polyhedra_library.Polyhedron.total_memory_in_bytes ( )

Returns the total size in bytes of the memory occupied by this.

native void parma_polyhedra_library.Polyhedron.unconstrain_space_dimension ( Variable var )

Computes the cylindrification of this with respect to space dimension var, assigning the result to this.

Parameters

var	The space dimension that will be unconstrained.

Exceptions

Invalid_Argument_Exception Thrown if var is not a space dimension of this.

native void parma_polyhedra_library.Polyhedron.unconstrain_space_dimensions ( Variables_Set vars )

Computes the cylindrification of this with respect to the set of space dimensions vars, assigning the result to this.

Parameters

vars	The set of space dimension that will be unconstrained.

Exceptions

Invalid_Argument_Exception Thrown if this is dimension-incompatible with one of the Variable objects contained in vars.

native void parma_polyhedra_library.Polyhedron.upper_bound_assign ( Polyhedron y )

Assigns to this the upper bound of this and y.

Exceptions

Invalid_Argument_Exception Thrown if this and y are topology-incompatible or dimension-incompatible.

native void parma_polyhedra_library.Polyhedron.widening_assign	(	Polyhedron	y,
		By_Reference< Integer >	tp
	)

Assigns to this the result of computing the H79-widening between this and y.

Parameters

y	A polyhedron that must be contained in `this`;
tp	A reference to an unsigned variable storing the number of available tokens (to be used when applying the widening with tokens delay technique).

Exceptions

Invalid_Argument_Exception Thrown if this and y are topology-incompatible or dimension-incompatible.

The documentation for this class was generated from the following file:

Fake_Class_for_Doxygen.java

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