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Parma_Polyhedra_Library::Congruence_System Class Reference
C++ Language Interface

A system of congruences. More...

`#include <ppl.hh>`

## Classes
class | const_iterator
| An iterator over a system of congruences. More...

## Public Member Functions
| Congruence_System (Representation r=default_representation)
| Default constructor: builds an empty system of congruences.
| Congruence_System (dimension_type d, Representation r=default_representation)
| Builds an empty (i.e. zero rows) system of dimension `d`.
| Congruence_System (const Congruence &cg, Representation r=default_representation)
| Builds the singleton system containing only congruence `cg`.
| Congruence_System (const Constraint &c, Representation r=default_representation)
| If `c` represents the constraint , builds the singleton system containing only constraint . More...
| Congruence_System (const Constraint_System &cs, Representation r=default_representation)
| Builds a system containing copies of any equalities in `cs`.
| Congruence_System (const Congruence_System &cgs)
| Ordinary copy constructor. More...
| Congruence_System (const Congruence_System &cgs, Representation r)
| Copy constructor with specified representation.
| ~Congruence_System ()
| Destructor.
Congruence_System & | operator= (const Congruence_System &y)
| Assignment operator.
Representation | representation () const
| Returns the current representation of *this.
void | set_representation (Representation r)
| Converts *this to the specified representation.
dimension_type | space_dimension () const
| Returns the dimension of the vector space enclosing `*this`.
bool | is_equal_to (const Congruence_System &y) const
| Returns `true` if and only if `*this` is exactly equal to `y`.
bool | has_linear_equalities () const
| Returns `true` if and only if `*this` contains one or more linear equalities.
void | clear ()
| Removes all the congruences and sets the space dimension to 0.
void | insert (const Congruence &cg)
| Inserts in `*this` a copy of the congruence `cg`, increasing the number of space dimensions if needed. More...
void | insert (Congruence &cg, Recycle_Input)
| Inserts in `*this` the congruence `cg`, stealing its contents and increasing the number of space dimensions if needed. More...
void | insert (const Constraint &c)
| Inserts in `*this` a copy of the equality constraint `c`, seen as a modulo 0 congruence, increasing the number of space dimensions if needed. More...
void | insert (const Congruence_System &y)
| Inserts in `*this` a copy of the congruences in `y`, increasing the number of space dimensions if needed. More...
void | insert (Congruence_System &cgs, Recycle_Input)
| Inserts into `*this` the congruences in `cgs`, increasing the number of space dimensions if needed.
bool | empty () const
| Returns `true` if and only if `*this` has no congruences.
const_iterator | begin () const
| Returns the const_iterator pointing to the first congruence, if `this` is not empty; otherwise, returns the past-the-end const_iterator.
const_iterator | end () const
| Returns the past-the-end const_iterator.
bool | OK () const
| Checks if all the invariants are satisfied.
void | ascii_dump () const
| Writes to `std::cerr` an ASCII representation of `*this`.
void | ascii_dump (std::ostream &s) const
| Writes to `s` an ASCII representation of `*this`.
void | print () const
| Prints `*this` to `std::cerr` using `operator<<`.
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.
memory_size_type | total_memory_in_bytes () const
| Returns the total size in bytes of the memory occupied by `*this`.
memory_size_type | external_memory_in_bytes () const
| Returns the size in bytes of the memory managed by `*this`.
dimension_type | num_equalities () const
| Returns the number of equalities.
dimension_type | num_proper_congruences () const
| Returns the number of proper congruences.
void | m_swap (Congruence_System &y)
| Swaps `*this` with `y`.
void | add_unit_rows_and_space_dimensions (dimension_type dims)
| Adds `dims` rows and `dims` space dimensions to the matrix, initializing the added rows as in the unit congruence system. More...
void | permute_space_dimensions (const std::vector< Variable > &cycle)
| Permutes the space dimensions of the system. More...
void | swap_space_dimensions (Variable v1, Variable v2)
| Swaps the columns having indexes `i` and `j`.
bool | set_space_dimension (dimension_type new_space_dim)
| Sets the number of space dimensions to `new_space_dim`. More...

## Static Public Member Functions
static dimension_type | max_space_dimension ()
| Returns the maximum space dimension a Congruence_System can handle.
static void | initialize ()
| Initializes the class.
static void | finalize ()
| Finalizes the class.
static const Congruence_System & | zero_dim_empty ()
| Returns the system containing only Congruence::zero_dim_false().

## Protected Member Functions
bool | satisfies_all_congruences (const Grid_Generator &g) const
| Returns `true` if `g` satisfies all the congruences.

## Related Functions
(Note that these are not member functions.)
bool | operator== (const Congruence_System &x, const Congruence_System &y)
std::ostream & | operator<< (std::ostream &s, const Congruence_System &cgs)
| Output operator. More...
void | swap (Congruence_System &x, Congruence_System &y)
void | swap (Congruence_System &x, Congruence_System &y)

## Detailed Description

A system of congruences.

An object of the class Congruence_System is a system of congruences, i.e., a multiset of objects of the class Congruence. When inserting congruences in a system, space dimensions are automatically adjusted so that all the congruences in the system are defined on the same vector space.

  In all the examples it is assumed that variables `x` and `y` are defined as follows:
  Variable x(0);
  Variable y(1);

Example 1
  The following code builds a system of congruences corresponding to an integer grid in :
  Congruence_System cgs;
  cgs.insert(x %= 0);
  cgs.insert(y %= 0);
  Note that: the congruence system is created with space dimension zero; the first and second congruence insertions increase the space dimension to and , respectively.

Example 2
  By adding to the congruence system of the previous example, the congruence :
  cgs.insert((x + y %= 1) / 2);
  we obtain the grid containing just those integral points where the sum of the `x` and `y` values is odd.

Example 3
  The following code builds a system of congruences corresponding to the grid in containing just the integral points on the `x` axis:
  Congruence_System cgs;
  cgs.insert(x %= 0);
  cgs.insert((y %= 0) / 0);

Note
  After inserting a multiset of congruences in a congruence system, there are no guarantees that an exact copy of them can be retrieved: in general, only an equivalent congruence system will be available, where original congruences may have been reordered, removed (if they are trivial, duplicate or implied by other congruences), linearly combined, etc.

## Constructor & Destructor Documentation

Parma_Polyhedra_Library::Congruence_System::Congruence_System | ( | const Constraint & | c,
|  | Representation | r = `default_representation`
| ) |  |
| inline explicit

If `c` represents the constraint , builds the singleton system containing only constraint .

Exceptions

  std::invalid_argument | Thrown if `c` is not an equality constraint.

Parma_Polyhedra_Library::Congruence_System::Congruence_System | ( | const Congruence_System & | cgs | ) |
| inline

Ordinary copy constructor.

Note
  The new Congruence_System will have the same Representation as `cgs' so that it's indistinguishable from `cgs'.

## Member Function Documentation

void Parma_Polyhedra_Library::Congruence_System::insert | ( | const Congruence & | cg | ) |
| inline

Inserts in `*this` a copy of the congruence `cg`, increasing the number of space dimensions if needed.

The copy of `cg` will be strongly normalized after being inserted.

void Parma_Polyhedra_Library::Congruence_System::insert | ( | Congruence & | cg,
|  | Recycle_Input |
| ) |  |
| inline

Inserts in `*this` the congruence `cg`, stealing its contents and increasing the number of space dimensions if needed.

`cg` will be strongly normalized.

void Parma_Polyhedra_Library::Congruence_System::insert | ( | const Constraint & | c | ) |

Inserts in `*this` a copy of the equality constraint `c`, seen as a modulo 0 congruence, increasing the number of space dimensions if needed.

The modulo 0 congruence will be strongly normalized after being inserted.

Exceptions

  std::invalid_argument | Thrown if `c` is a relational constraint.

void Parma_Polyhedra_Library::Congruence_System::insert | ( | const Congruence_System & | y | ) |

Inserts in `*this` a copy of the congruences in `y`, increasing the number of space dimensions if needed.

The inserted copies will be strongly normalized.

void Parma_Polyhedra_Library::Congruence_System::add_unit_rows_and_space_dimensions | ( | dimension_type | dims | ) |

Adds `dims` rows and `dims` space dimensions to the matrix, initializing the added rows as in the unit congruence system.

Parameters

  dims | The number of rows and space dimensions to be added: must be strictly positive.

Turns the matrix into the matrix where is the unit matrix of the form . The matrix is expanded avoiding reallocation whenever possible.

void Parma_Polyhedra_Library::Congruence_System::permute_space_dimensions | ( | const std::vector< Variable > & | cycle | ) |

Permutes the space dimensions of the system.

Parameters

  cycle | A vector representing a cycle of the permutation according to which the columns must be rearranged.

The `cycle` vector represents a cycle of a permutation of space dimensions. For example, the permutation can be represented by the vector containing .

bool Parma_Polyhedra_Library::Congruence_System::set_space_dimension | ( | dimension_type | new_space_dim | ) |

Sets the number of space dimensions to `new_space_dim`.

If `new_space_dim` is lower than the current space dimension, the coefficients referring to the removed space dimensions are lost.

## Friends And Related Function Documentation

bool operator== | ( | const Congruence_System & | x,
|  | const Congruence_System & | y
| ) |  |
| related

std::ostream & operator<< | ( | std::ostream & | s,
|  | const Congruence_System & | cgs
| ) |  |
| related

Output operator.

Writes `true` if `cgs` is empty. Otherwise, writes on `s` the congruences of `cgs`, all in one row and separated by ", ".

void swap | ( | Congruence_System & | x,
|  | Congruence_System & | y
| ) |  |
| related

void swap | ( | Congruence_System & | x,
|  | Congruence_System & | y
| ) |  |
| related

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

- ppl.hh