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Representations for one-to-one mappings
[Components for Mappings]

Compounds
class	printer_of_bij_mapping
	helper class for custom output of a bijective map. More...
class	bijective_mapping
	Represents a one-to-one mapping T1 -> T2. More...
class	inverse_mapping
	Represents a mapping T2 --> T1 which is the inverse of some bijective_mapping<T1,T2>. More...
class	domain_of_bijective_mapping
	Represents the domain of definition of a mapping. More...
class	range_of_bijective_mapping
	Represents the range (image) of a bijective mapping . More...
Functions
template<class T1, class T2> void	write_bm (bijective_mapping< T1, T2 > const &m, ostream &out)
	write a bijective map to ostream. More...
template<class T1, class T2> void	read_bm (bijective_mapping< T1, T2 > &m, istream &in)
	read a bijective map from istream. More...
template<class T1, class T2> printer_of_bij_mapping< T1, T2 >	Printer (bijective_mapping< T1, T2 > const &m)
	helper function for custom output of a bijective map. More...

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Detailed Description

Contents

This module contains class templates for representing bijective mappings:

• class bijective_mapping<T1,T2> : A one-to-one mapping (short f)
• class inverse_mapping<T1,T2> : Inverse of a bijective_mapping (short inv)
• class domain_of_bijective_mapping<T1,T2>: domain of definition of a bijective mapping (short dom)
• class range_of_bijective_mapping<T1,T2>: range (image) of a bijective mapping. (short ran)
• some helper classes and functions for I/O: read_bm, write_bm, printer_of_bij_mapping, Printer

Template parameters

(same for bijective_mapping<T1,T2>, inverse_mapping<T1,T2>, domain_of_bijective_mapping<T1,T2>, range_of_bijective_mapping<T1,T2>)

• T1 is Hashable, that is, hash<T1> is defined.
• T1 is Equality Comparable, that is, equal_to<T1> is defined.
• T2 is Assignable and Default Constructible.

Description:

• class bijective_mapping<T1,T2>;
  • the master class with value semantics, giving an interface to a mapping T1 -> T2
  • Template parameters:
    • T1, T2: hash<T> must be defined. (default definitions in STL only for integral types)
  • class printer_of_bij_mapping<T1,T2> is used for output
  • functions read_bm, write_bm are used for I/O
• The other 3 classes have reference semantics with respect to bm:
  • class inverse_mapping<T1,T2>
    • gives a function interface to the inverse (which is really calculated and stored in bm<T1,T2>)
  • class domain_of_bijective_mapping<T1,T2> (dom)
    • gives a set interface to the domain (of definition) of bm;
  • class range_of_bijective_mapping<T1,T2> (ran)
    • gives a set interface to the range (or image) of bm;

Invariants:

• T1 x: inv(f(x)) == x
• T2 y: f(inv(y)) == y
• T1 x: f.defined(x) <=> dom(f).is_member(x)
• T2 y: inv.defined(y) <=> ran(f).is_member(y)
• dom(f).size() == ran(f).size()
• f(* (dom(f).begin() + n) == * (ran(f).begin() + n),

Example:

• see test-bijective.C

See also:

bijective-mapping.h

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Function Documentation

template<class T1, class T2> void write_bm (  bijective_mapping< T1, T2 > const &    m, ostream &    out )

write a bijective map to ostream. Definition at line 10 of file bijective-mapping.C. Referenced by main.

template<class T1, class T2> void read_bm (  bijective_mapping< T1, T2 > &    m, istream &    in )

read a bijective map from istream. Definition at line 19 of file bijective-mapping.C. Referenced by main.

template<class T1, class T2> printer_of_bij_mapping<T1,T2> Printer (  bijective_mapping< T1, T2 > const &    m )  [inline]

helper function for custom output of a bijective map. Usage: bijective_mapping<int,int> bm; ... cout << Printer(bm) << endl; Definition at line 137 of file bijective-mapping.h.

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Copyright (c) Guntram Berti 1997-2002. See the GrAL Homepage for up-to-date information.

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