Break a rational expression into a polynomial. More...

#include <split.hh>

Inheritance diagram for vcsn::rat::split_visitor< RatExpSet >:

Collaboration diagram for vcsn::rat::split_visitor< RatExpSet >:

Public Types
using	ratexpset_t = RatExpSet

using	context_t = context_t_of< ratexpset_t >

using	labelset_t = labelset_t_of< context_t >

using	label_t = label_t_of< context_t >

using	ratexp_t = typename ratexpset_t::value_t

using	weightset_t = weightset_t_of< ratexpset_t >

using	weight_t = typename weightset_t::value_t

using	polynomialset_t = ratexp_polynomialset_t< ratexpset_t >

using	polynomial_t = typename polynomialset_t::value_t

using	super_t = typename ratexpset_t::const_visitor

Public Member Functions
	split_visitor (const ratexpset_t &rs)

polynomial_t	operator() (const ratexp_t &v)
	Break a ratexp into a polynomial. More...

polynomial_t	split (const ratexp_t &v)
	Easy recursion. More...

	VCSN_RAT_VISIT (zero,)

	VCSN_RAT_VISIT (one,)

	VCSN_RAT_VISIT (atom, e)

	VCSN_RAT_VISIT (sum, e)

polynomial_t	product (const ratexp_t &l, const ratexp_t &r)
	The split-product of l with r. More...

polynomial_t	product (const polynomial_t &l, const ratexp_t &r)
	The split-product of l with r. More...

	VCSN_RAT_VISIT (prod, e)
	Handle an n-ary product. More...

polynomial_t	conjunction (const ratexp_t &l, const ratexp_t &r)
	The split-product of l with r. More...

polynomial_t	conjunction (const polynomial_t &l, const ratexp_t &r)
	The split-product of l with r. More...

	VCSN_RAT_VISIT (conjunction, e)
	Handle an n-ary conjunction. More...

	VCSN_RAT_VISIT (star, e)

	VCSN_RAT_VISIT (lweight, e)

	VCSN_RAT_VISIT (rweight, e)

Static Public Member Functions
static constexpr const char *	me ()

Private Attributes
ratexpset_t	rs_

weightset_t	ws_ = *rs_.weightset()
	Shorthand to the weightset. More...

polynomialset_t	ps_ = make_ratexp_polynomialset(rs_)

polynomial_t	res_
	The result. More...

Detailed Description

template<typename RatExpSet>
class vcsn::rat::split_visitor< RatExpSet >

Break a rational expression into a polynomial.

This is based on the following paper:

/// @article{angrand.2010.jalc,
///   author =       {Pierre-Yves Angrand and Sylvain Lombardy and Jacques
///                   Sakarovitch},
///   journal =      {Journal of Automata, Languages and Combinatorics},
///   number =       {1/2},
///   pages =        {27--51},
///   title =        {On the Number of Broken Derived Terms of a Rational
///                   Expression},
///   volume =       15,
///   year =         2010,
///   abstract =     {Bounds are given on the number of broken derived
///                   terms (a variant of Antimirov's ``partial
///                   derivatives'') of a rational expression $E$. It is
///                   shown that this number is less than or equal to
///                   $2l(E) + 1$ in the general case, where $l(E)$ is the
///                   literal length of the expression $E$, and that the
///                   classical bound $l(E) + 1$ which holds for partial
///                   derivatives also holds for broken derived terms if E
///                   is in star normal form.\\In a second part of the
///                   paper, the influence of the bracketing of an
///                   expression on the number of its derived terms is
///                   also discussed.}
/// }
///

Definition at line 78 of file split.hh.

Member Typedef Documentation

template<typename RatExpSet >

using vcsn::rat::split_visitor< RatExpSet >::context_t = context_t_of<ratexpset_t>

Definition at line 83 of file split.hh.

template<typename RatExpSet >

using vcsn::rat::split_visitor< RatExpSet >::label_t = label_t_of<context_t>

Definition at line 85 of file split.hh.

template<typename RatExpSet >

using vcsn::rat::split_visitor< RatExpSet >::labelset_t = labelset_t_of<context_t>

Definition at line 84 of file split.hh.

template<typename RatExpSet >

using vcsn::rat::split_visitor< RatExpSet >::polynomial_t = typename polynomialset_t::value_t

Definition at line 91 of file split.hh.

template<typename RatExpSet >

using vcsn::rat::split_visitor< RatExpSet >::polynomialset_t = ratexp_polynomialset_t<ratexpset_t>

Definition at line 90 of file split.hh.

template<typename RatExpSet >

using vcsn::rat::split_visitor< RatExpSet >::ratexp_t = typename ratexpset_t::value_t

Definition at line 86 of file split.hh.

template<typename RatExpSet >

using vcsn::rat::split_visitor< RatExpSet >::ratexpset_t = RatExpSet

Definition at line 82 of file split.hh.

template<typename RatExpSet >

using vcsn::rat::split_visitor< RatExpSet >::super_t = typename ratexpset_t::const_visitor

Definition at line 93 of file split.hh.

template<typename RatExpSet >

using vcsn::rat::split_visitor< RatExpSet >::weight_t = typename weightset_t::value_t

Definition at line 88 of file split.hh.

template<typename RatExpSet >

using vcsn::rat::split_visitor< RatExpSet >::weightset_t = weightset_t_of<ratexpset_t>

Definition at line 87 of file split.hh.

Constructor & Destructor Documentation

template<typename RatExpSet >

vcsn::rat::split_visitor< RatExpSet >::split_visitor ( const ratexpset_t & rs )

inline

Definition at line 97 of file split.hh.

Member Function Documentation

template<typename RatExpSet >

polynomial_t vcsn::rat::split_visitor< RatExpSet >::conjunction	(	const ratexp_t &	l,
		const ratexp_t &	r
	)

inline

The split-product of l with r.

Returns split(l) x split(r). FIXME: This is inefficient, we split the lhs way too often.

Definition at line 182 of file split.hh.

References vcsn::polynomialset< Context >::add_here(), vcsn::polynomialset< Context >::del_weight(), vcsn::polynomialset< Context >::get_weight(), vcsn::polynomialset< Context >::lmul(), vcsn::rat::split_visitor< RatExpSet >::ps_, vcsn::rat::split_visitor< RatExpSet >::rs_, and vcsn::rat::split_visitor< RatExpSet >::split().

Referenced by vcsn::rat::split_visitor< RatExpSet >::VCSN_RAT_VISIT().

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template<typename RatExpSet >

polynomial_t vcsn::rat::split_visitor< RatExpSet >::conjunction	(	const polynomial_t &	l,
		const ratexp_t &	r
	)

inline

The split-product of l with r.

Returns l x split(r).

Definition at line 204 of file split.hh.

References vcsn::polynomialset< Context >::add_here(), vcsn::polynomialset< Context >::lmul(), and vcsn::rat::split_visitor< RatExpSet >::ps_.

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template<typename RatExpSet >

static constexpr const char* vcsn::rat::split_visitor< RatExpSet >::me ( )

inlinestatic

Definition at line 95 of file split.hh.

template<typename RatExpSet >

polynomial_t vcsn::rat::split_visitor< RatExpSet >::operator() ( const ratexp_t & v )

inline

Break a ratexp into a polynomial.

Definition at line 102 of file split.hh.

References vcsn::rat::split_visitor< RatExpSet >::split().

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template<typename RatExpSet >

polynomial_t vcsn::rat::split_visitor< RatExpSet >::product	(	const ratexp_t &	l,
		const ratexp_t &	r
	)

inline

The split-product of l with r.

Returns split(l) x split(r). FIXME: This is inefficient, we split the lhs way too often.

Definition at line 144 of file split.hh.

References vcsn::polynomialset< Context >::add(), vcsn::polynomialset< Context >::del_weight(), vcsn::polynomialset< Context >::get_weight(), vcsn::polynomialset< Context >::lmul(), vcsn::rat::split_visitor< RatExpSet >::ps_, vcsn::polynomialset< Context >::rmul(), vcsn::rat::split_visitor< RatExpSet >::rs_, and vcsn::rat::split_visitor< RatExpSet >::split().

Referenced by vcsn::rat::split_visitor< RatExpSet >::product(), and vcsn::rat::split_visitor< RatExpSet >::VCSN_RAT_VISIT().

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template<typename RatExpSet >

polynomial_t vcsn::rat::split_visitor< RatExpSet >::product	(	const polynomial_t &	l,
		const ratexp_t &	r
	)

inline

The split-product of l with r.

Returns l x split(r).

Definition at line 161 of file split.hh.

References vcsn::polynomialset< Context >::add_here(), vcsn::polynomialset< Context >::lmul(), vcsn::rat::split_visitor< RatExpSet >::product(), and vcsn::rat::split_visitor< RatExpSet >::ps_.

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template<typename RatExpSet >

polynomial_t vcsn::rat::split_visitor< RatExpSet >::split ( const ratexp_t & v )

inline

Easy recursion.

Definition at line 108 of file split.hh.

References vcsn::rat::split_visitor< RatExpSet >::res_.

Referenced by vcsn::rat::split_visitor< RatExpSet >::conjunction(), vcsn::rat::split_visitor< RatExpSet >::operator()(), and vcsn::rat::split_visitor< RatExpSet >::product().

template<typename RatExpSet >

vcsn::rat::split_visitor< RatExpSet >::VCSN_RAT_VISIT ( zero )

inline

Definition at line 114 of file split.hh.

References vcsn::rat::split_visitor< RatExpSet >::ps_, vcsn::rat::split_visitor< RatExpSet >::res_, and vcsn::polynomialset< Context >::zero().

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template<typename RatExpSet >

vcsn::rat::split_visitor< RatExpSet >::VCSN_RAT_VISIT ( one )

inline

Definition at line 119 of file split.hh.

References vcsn::rat::split_visitor< RatExpSet >::res_, vcsn::rat::split_visitor< RatExpSet >::rs_, and vcsn::rat::split_visitor< RatExpSet >::ws_.

template<typename RatExpSet >

vcsn::rat::split_visitor< RatExpSet >::VCSN_RAT_VISIT	(	atom	,
		e
	)

inline

Definition at line 124 of file split.hh.

References vcsn::rat::split_visitor< RatExpSet >::res_, vcsn::rat::split_visitor< RatExpSet >::rs_, and vcsn::rat::split_visitor< RatExpSet >::ws_.

template<typename RatExpSet >

vcsn::rat::split_visitor< RatExpSet >::VCSN_RAT_VISIT	(	sum	,
		e
	)

inline

Definition at line 129 of file split.hh.

References vcsn::polynomialset< Context >::add_here(), vcsn::rat::split_visitor< RatExpSet >::ps_, vcsn::rat::split_visitor< RatExpSet >::res_, and vcsn::polynomialset< Context >::zero().

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template<typename RatExpSet >

vcsn::rat::split_visitor< RatExpSet >::VCSN_RAT_VISIT	(	prod	,
		e
	)

inline

Handle an n-ary product.

Definition at line 170 of file split.hh.

References vcsn::rat::split_visitor< RatExpSet >::product(), and vcsn::rat::split_visitor< RatExpSet >::res_.

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template<typename RatExpSet >

vcsn::rat::split_visitor< RatExpSet >::VCSN_RAT_VISIT	(	conjunction	,
		e
	)

inline

Handle an n-ary conjunction.

Definition at line 213 of file split.hh.

References vcsn::rat::split_visitor< RatExpSet >::conjunction(), and vcsn::rat::split_visitor< RatExpSet >::res_.

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template<typename RatExpSet >

vcsn::rat::split_visitor< RatExpSet >::VCSN_RAT_VISIT	(	star	,
		e
	)

inline

Definition at line 226 of file split.hh.

References vcsn::rat::split_visitor< RatExpSet >::res_, and vcsn::rat::split_visitor< RatExpSet >::ws_.

template<typename RatExpSet >

vcsn::rat::split_visitor< RatExpSet >::VCSN_RAT_VISIT	(	lweight	,
		e
	)

inline

Definition at line 231 of file split.hh.

References vcsn::polynomialset< Context >::lmul(), vcsn::rat::split_visitor< RatExpSet >::ps_, and vcsn::rat::split_visitor< RatExpSet >::res_.

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template<typename RatExpSet >

vcsn::rat::split_visitor< RatExpSet >::VCSN_RAT_VISIT	(	rweight	,
		e
	)

inline

Definition at line 237 of file split.hh.

References vcsn::rat::split_visitor< RatExpSet >::ps_, vcsn::rat::split_visitor< RatExpSet >::res_, and vcsn::polynomialset< Context >::rmul().

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Member Data Documentation

template<typename RatExpSet >

polynomialset_t vcsn::rat::split_visitor< RatExpSet >::ps_ = make_ratexp_polynomialset(rs_)

private

Definition at line 247 of file split.hh.

Referenced by vcsn::rat::split_visitor< RatExpSet >::conjunction(), vcsn::rat::split_visitor< RatExpSet >::product(), and vcsn::rat::split_visitor< RatExpSet >::VCSN_RAT_VISIT().

template<typename RatExpSet >

polynomial_t vcsn::rat::split_visitor< RatExpSet >::res_

private

The result.

Definition at line 249 of file split.hh.

Referenced by vcsn::rat::split_visitor< RatExpSet >::split(), and vcsn::rat::split_visitor< RatExpSet >::VCSN_RAT_VISIT().

template<typename RatExpSet >

ratexpset_t vcsn::rat::split_visitor< RatExpSet >::rs_

private

Definition at line 244 of file split.hh.

Referenced by vcsn::rat::split_visitor< RatExpSet >::conjunction(), vcsn::rat::split_visitor< RatExpSet >::product(), and vcsn::rat::split_visitor< RatExpSet >::VCSN_RAT_VISIT().

template<typename RatExpSet >

weightset_t vcsn::rat::split_visitor< RatExpSet >::ws_ = *rs_.weightset()

private

Shorthand to the weightset.

Definition at line 246 of file split.hh.

Referenced by vcsn::rat::split_visitor< RatExpSet >::VCSN_RAT_VISIT().

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

vcsn/algos/split.hh

Public Types

Public Member Functions

Static Public Member Functions

Private Attributes

Detailed Description

template<typename RatExpSet> class vcsn::rat::split_visitor< RatExpSet >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename RatExpSet>
class vcsn::rat::split_visitor< RatExpSet >