Inherits Parma_Polyhedra_Library::Dense_Row.
Public Member Functions |
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| Congruence (const Congruence &cg) |
| | Ordinary copy constructor.
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| | Congruence (const Constraint &c) |
| | Copy-constructs (modulo 0) from equality constraint c.
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| ~Congruence () |
| | Destructor.
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Congruence & | operator= (const Congruence &y) |
| | Assignment operator.
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dimension_type | space_dimension () const |
| | Returns the dimension of the vector space enclosing *this.
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| Coefficient_traits::const_reference | coefficient (Variable v) const |
| | Returns the coefficient of v in *this.
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Coefficient_traits::const_reference | inhomogeneous_term () const |
| | Returns the inhomogeneous term of *this.
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Coefficient_traits::const_reference | modulus () const |
| | Returns a const reference to the modulus of *this.
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| Congruence & | operator/= (Coefficient_traits::const_reference k) |
| | Multiplies k into the modulus of *this.
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| bool | is_tautological () const |
| | Returns true if and only if *this is a tautology (i.e., an always true congruence).
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| bool | is_inconsistent () const |
| | Returns true if and only if *this is inconsistent (i.e., an always false congruence).
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| bool | is_proper_congruence () const |
| | Returns true if the modulus is greater than zero.
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| bool | is_equality () const |
| | Returns true if *this is an equality.
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bool | is_equal_at_dimension (dimension_type dim, const Congruence &cg) const |
| | Returns true if *this is equal to cg in dimension dim.
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memory_size_type | total_memory_in_bytes () const |
| | Returns a lower bound to 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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void | ascii_dump () const |
| | Writes to std::cerr an ASCII representation of *this.
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void | ascii_dump (std::ostream &s) const |
| | Writes to s an ASCII representation of *this.
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void | print () const |
| | Prints *this to std::cerr using operator<<.
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bool | ascii_load (std::istream &s) |
| | Loads from s an ASCII representation of the internal representation of *this.
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void | m_swap (Congruence &y) |
| | Swaps *this with y.
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bool | OK () const |
| | Checks if all the invariants are satisfied.
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Static Public Member Functions |
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static dimension_type | max_space_dimension () |
| | Returns the maximum space dimension a Congruence can handle.
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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 const Congruence & | zero_dim_integrality () |
| | Returns a reference to the true (zero-dimension space) congruence , also known as the integrality congruence.
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static const Congruence & | zero_dim_false () |
| | Returns a reference to the false (zero-dimension space) congruence .
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static Congruence | create (const Linear_Expression &e1, const Linear_Expression &e2) |
| | Returns the congruence .
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static Congruence | create (const Linear_Expression &e, Coefficient_traits::const_reference n) |
| | Returns the congruence .
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static Congruence | create (Coefficient_traits::const_reference n, const Linear_Expression &e) |
| | Returns the congruence .
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Protected Member Functions |
| void | sign_normalize () |
| | Normalizes the signs.
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| void | normalize () |
| | Normalizes signs and the inhomogeneous term.
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| void | strong_normalize () |
| | Calls normalize, then divides out common factors.
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Related Functions |
(Note that these are not member functions.)
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| std::ostream & | operator<< (std::ostream &s, const Congruence &c) |
| | Output operators.
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| void | swap (Congruence &x, Congruence &y) |
| | Swaps x with y.
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| bool | operator== (const Congruence &x, const Congruence &y) |
| | Returns true if and only if x and y are equivalent.
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| bool | operator!= (const Congruence &x, const Congruence &y) |
| | Returns false if and only if x and y are equivalent.
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| Congruence | operator%= (const Linear_Expression &e1, const Linear_Expression &e2) |
| | Returns the congruence .
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| Congruence | operator%= (const Linear_Expression &e, Coefficient_traits::const_reference n) |
| | Returns the congruence .
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| Congruence | operator/ (const Congruence &cg, Coefficient_traits::const_reference k) |
| | Returns a copy of cg, multiplying k into the copy's modulus.
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| Congruence | operator/ (const Constraint &c, Coefficient_traits::const_reference m) |
| | Creates a congruence from c, with m as the modulus.
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| Congruence | operator%= (const Linear_Expression &e1, const Linear_Expression &e2) |
| Congruence | operator%= (const Linear_Expression &e, Coefficient_traits::const_reference n) |
| Congruence | operator/ (const Congruence &cg, Coefficient_traits::const_reference k) |
| Congruence | operator/ (const Constraint &c, Coefficient_traits::const_reference m) |
| bool | operator== (const Congruence &x, const Congruence &y) |
| bool | operator!= (const Congruence &x, const Congruence &y) |
| void | swap (Congruence &x, Congruence &y) |
A linear congruence.
An object of the class Congruence is a congruence:
where
is the dimension of the space,
is the integer coefficient of variable
,
is the integer inhomogeneous term and
is the integer modulus; if
, then
represents the equality congruence
and, if
, then the congruence
is said to be a proper congruence.
- How to build a congruence
- Congruences
are typically built by applying the congruence symbol `%=' to a pair of linear expressions. Congruences with modulus m are typically constructed by building a congruence
using the given pair of linear expressions and then adding the modulus m using the modulus symbol is `/'.
The space dimension of a congruence is defined as the maximum space dimension of the arguments of its constructor.
- In the following examples it is assumed that variables
x, y and z are defined as follows: Variable x(0);
Variable y(1);
Variable z(2);
- Example 1
- The following code builds the equality congruence
, having space dimension
: The following code builds the congruence
, having space dimension
: The following code builds the congruence
, having space dimension
: An unsatisfiable congruence on the zero-dimension space
can be specified as follows: Equivalent, but more involved ways are the following: In contrast, the following code defines an unsatisfiable congruence having space dimension
:
- How to inspect a congruence
- Several methods are provided to examine a congruence and extract all the encoded information: its space dimension, its modulus and the value of its integer coefficients.
- Example 2
- The following code shows how it is possible to access the modulus as well as each of the coefficients. Given a congruence with linear expression
e and modulus m (in this case
), we construct a new congruence with the same modulus m but where the linear expression is
(
). Congruence cg1((x - 5*y + 3*z %= 4) / 5);
cout << "Congruence cg1: " << cg1 << endl;
const Coefficient& m = cg1.modulus();
if (m == 0)
cout << "Congruence cg1 is an equality." << endl;
else {
Linear_Expression e;
for (dimension_type i = cg1.space_dimension(); i-- > 0; )
e += 2 * cg1.coefficient(Variable(i)) * Variable(i);
e += 2 * cg1.inhomogeneous_term();
Congruence cg2((e %= 0) / m);
cout << "Congruence cg2: " << cg2 << endl;
}
The actual output could be the following: Note that, in general, the particular output obtained can be syntactically different from the (semantically equivalent) congruence considered.