# Parma_Polyhedra_Library::Congruence_System Class Reference
[C++ Language Interface]

A system of congruences. More...

`#include <ppl.hh>`

Inherits Parma_Polyhedra_Library::Matrix.

List of all members.

## Classes
class | const_iterator
| An iterator over a system of congruences. More...
## Public Member Functions
| Congruence_System ()
| Default constructor: builds an empty system of congruences.
| Congruence_System (const Congruence &cg)
| Builds the singleton system containing only congruence `cg`.
| Congruence_System (const Constraint &c)
| If `c` represents the constraint , builds the singleton system containing only constraint .
| Congruence_System (const Constraint_System &cs)
| Builds a system containing copies of any equalities in `cs`.
| Congruence_System (const Congruence_System &cgs)
| Ordinary copy constructor.
| ~Congruence_System ()
| Destructor.
Congruence_System & | operator= (const Congruence_System &cgs)
| Assignment operator.
dimension_type | space_dimension () const
| Returns the dimension of the vector space enclosing `*this`.
bool | is_equal_to (const Congruence_System &cgs) const
| Returns `true` if and only if `*this` is exactly equal to `cgs`.
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.
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.
void | insert (const Congruence_System &cgs)
| Inserts in `*this` a copy of the congruences in `cgs`, increasing the number of space dimensions if needed.
void | recycling_insert (Congruence_System &cgs)
| 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 | swap (Congruence_System &cgs)
| Swaps `*this` with `y`.
void | add_unit_rows_and_columns (dimension_type dims)
| Adds `dims` rows and `dims` columns of zeroes to the matrix, initializing the added rows as in the unit congruence system.
## 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.)
std::ostream & | operator<< (std::ostream &s, const Congruence_System &cgs)
| Output operator.
void | swap (Parma_Polyhedra_Library::Congruence_System &x, Parma_Polyhedra_Library::Congruence_System &y)
| Specializes `std::swap`.

## 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 | ) | `[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.

## 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 | ( | 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 & | cgs | ) |

Inserts in `*this` a copy of the congruences in `cgs`, 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_columns | ( | dimension_type | dims | ) |

Adds `dims` rows and `dims` columns of zeroes to the matrix, initializing the added rows as in the unit congruence system.

Parameters:

  | dims | The number of rows and columns 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.

## Friends And Related Function Documentation

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 | ( | Parma_Polyhedra_Library::Congruence_System & | x,
|  | Parma_Polyhedra_Library::Congruence_System & | y |
| ) |  |  | `[related]`

Specializes `std::swap`.

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

- ppl.hh