AbstractHomomorphism< K > Class Template Reference

#include <abshom.H>

Inheritance diagram for AbstractHomomorphism< K >:

List of all members.

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Detailed Description

template<class K>
class AbstractHomomorphism< K >

AbstractHomomorphism class: maps between polynomial algebras.

This models a ring homomorphism between a polynomial ring on a countable set of variables, to another such ring (or itself, if you want). So quite simply, it remembers a bunch of polynomials, corresponding to some integers. Objects of this class know how to compose themselves using the * operator (f * g is really f AFTER g). In particular, these objects can be used in order to evaluate polynomials

See also:

of.

Definition at line 22 of file abshom.H.

Public Member Functions
void	clear ()
	undefine everything (ie set to zero)
Polynomial< K >	of_generator (long var) const
void	set_image (long var, const Polynomial< K > &P)
	set f(var)= P
bool	has_image_set (long var) const
	returns true iff var has already an image defined
void	make_identity (long n)
	turns this into the identity on the first n variables
void	swap (long i, long j)
	self-obvious...
Polynomial< K >	of (const Polynomial< K > &P) const
	evaluate
AbstractHomomorphism< K > &	operator *= (const AbstractHomomorphism< K > &f)
	* = composition
AbstractHomomorphism< K >	operator * (const AbstractHomomorphism< K > &f) const
	* = composition
Protected Attributes
map< long, Polynomial< K > >	images
	the images of the generators -- nondefined means 0
long	highest_var
	the highest index of a variable showing up in 'images'
Friends
ostream &	operator<< (ostream &os, const AbstractHomomorphism< K > &f)
	print
ofstream &	operator<< (ofstream &file, AbstractHomomorphism< K > &f)
	write to file
void	operator>> (ifstream &file, AbstractHomomorphism< K > &f)
	read from file

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Member Function Documentation

template<class K> void AbstractHomomorphism< K >::clear (   )  [inline]

undefine everything (ie set to zero) Definition at line 45 of file abshom.H. Referenced by GradedAlgebra< F_2 >::even_subalgebra(), AffineAlgebra< F_2 >::find_redundancies(), AffineAlgebra< F_2 >::find_unitary_redundancies(), HomFinder::populate_GL(), MilnorAnalyzer::re_setup(), AffineHomomorphism< F_2 >::read_from_GAP_file(), UnstableAlgebra::saturate_and_reduce(), MilnorAnalyzer::setup_for_Sq1(), and DerivationAnalyzer::write_gens().

template<class K> bool AbstractHomomorphism< K >::has_image_set (  long  var  )  const [inline]

returns true iff var has already an image defined Definition at line 67 of file abshom.H. Referenced by HomFinder::branch(), AffineHomomorphism< F_2 >::fill_zeroes(), and HomFinder::weight().

template<class K> void AbstractHomomorphism< K >::make_identity (  long  n  )  [inline]

turns this into the identity on the first n variables Definition at line 72 of file abshom.H. Referenced by AffineAlgebra< F_2 >::find_redundancies(), AffineAlgebra< F_2 >::find_unitary_redundancies(), AffineHomomorphism< F_2 >::make_identity(), and UnstableAlgebra::saturate_and_reduce().

template<class K> Polynomial<K> AbstractHomomorphism< K >::of (  const Polynomial< K > &  P  )  const [inline]

evaluate The funny name allows one to write f.of(P). highest_var must be set properly for this to work (which is none of the user's concern!) Definition at line 96 of file abshom.H. Referenced by SW_Maker::add_complex_relations(), HomFinder::branch(), DerivationAnalyzer::constant_subalgebra(), MilnorAnalyzer::re_setup(), and MilnorAnalyzer::setup_for_Sq1().

template<class K> AbstractHomomorphism<K> AbstractHomomorphism< K >::operator * (  const AbstractHomomorphism< K > &  f  )  const [inline]

* = composition Definition at line 135 of file abshom.H.

template<class K> AbstractHomomorphism<K>& AbstractHomomorphism< K >::operator *= (  const AbstractHomomorphism< K > &  f  )  [inline]

* = composition Definition at line 123 of file abshom.H.

template<class K> void AbstractHomomorphism< K >::set_image (  long  var, const Polynomial< K > &  P )  [inline]

set f(var)= P Definition at line 58 of file abshom.H. Referenced by SW_Maker::add_complex_relations(), HomFinder::branch(), DerivationAnalyzer::constant_subalgebra(), GradedAlgebra< F_2 >::even_subalgebra(), HomFinder::extend(), AffineHomomorphism< F_2 >::fill_zeroes(), AffineAlgebra< F_2 >::find_redundancies(), AffineAlgebra< F_2 >::find_unitary_redundancies(), AbstractHomomorphism< F_2 >::operator *(), AbstractHomomorphism< F_2 >::operator *=(), MilnorAnalyzer::re_setup(), AffineHomomorphism< F_2 >::read_from_GAP_file(), UnstableAlgebra::saturate_and_reduce(), HomFinder::set_hom_from_matrix(), DerivationAnalyzer::setup(), MilnorAnalyzer::setup_for_Sq1(), AffineHomomorphism< F_2 >::simple_section(), and HomFinder::sort().

template<class K> void AbstractHomomorphism< K >::swap (  long  i, long  j )  [inline]

self-obvious... Definition at line 82 of file abshom.H. Referenced by MilnorAnalyzer::re_setup(), and MilnorAnalyzer::setup_for_Sq1().

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Friends And Related Function Documentation

template<class K> ofstream& operator<< (  ofstream &  file, AbstractHomomorphism< K > &  f )  [friend]

write to file Definition at line 156 of file abshom.H.

template<class K> ostream& operator<< (  ostream &  os, const AbstractHomomorphism< K > &  f )  [friend]

print Definition at line 145 of file abshom.H.

template<class K> void operator>> (  ifstream &  file, AbstractHomomorphism< K > &  f )  [friend]

read from file Definition at line 170 of file abshom.H.

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Member Data Documentation

template<class K> long AbstractHomomorphism< K >::highest_var [protected]

the highest index of a variable showing up in 'images' This is useful to know when evaluating a polynomial, so the substitutions can go smoothly. The value is protected, so we can be sure that it is kept in a correct state. Note : In fact, we only make sure that highest_var contains an index that is >= to the highest index of a variable actually showing up. This is all we need. In some unlucky cases, there will be a tiny waste of memory when evaluating, if highest_var is too high. It does not seem worth fixing this (and speed would suffer). Definition at line 38 of file abshom.H.

template<class K> map<long, Polynomial<K> > AbstractHomomorphism< K >::images [protected]

the images of the generators -- nondefined means 0 Definition at line 25 of file abshom.H. Referenced by AbstractHomomorphism< F_2 >::operator *(), and AbstractHomomorphism< F_2 >::operator *=().

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

• include/abshom.H

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