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Vcsn
2.8
Be Rational
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Vcsn
2.8
Be Rational
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Break a rational expression into a polynomial. More...
#include <split.hh>
Public Types | |
| using | expressionset_t = ExpSet |
| using | context_t = context_t_of< expressionset_t > |
| using | labelset_t = labelset_t_of< context_t > |
| using | label_t = label_t_of< context_t > |
| using | expression_t = typename expressionset_t::value_t |
| using | weightset_t = weightset_t_of< expressionset_t > |
| using | weight_t = typename weightset_t::value_t |
| using | polynomialset_t = expression_polynomialset_t< expressionset_t > |
| using | polynomial_t = typename polynomialset_t::value_t |
| using | super_t = typename expressionset_t::const_visitor |
| template<type_t Type> | |
| using | variadic_t = typename super_t::template variadic_t< Type > |
| using | tuple_t = typename super_t::tuple_t |
Public Member Functions | |
| split_visitor (const expressionset_t &rs) | |
| polynomial_t | operator() (const expression_t &v) |
| Break an expression into a polynomial. More... | |
| polynomial_t | split (const expression_t &v) |
| Easy recursion. More... | |
| VCSN_RAT_VISIT (zero,) | |
| VCSN_RAT_VISIT (add, e) | |
| polynomial_t | multiply (const expression_t &l, const expression_t &r) |
| The split-multiplation of l with r. More... | |
| polynomial_t | multiply (const polynomial_t &l, const expression_t &r) |
| The split-multiplation of l with r. More... | |
| VCSN_RAT_VISIT (mul, e) | |
| Handle an n-ary multiplication. More... | |
| VCSN_RAT_VISIT (atom, e) | |
| VCSN_RAT_VISIT (complement, e) | |
| VCSN_RAT_VISIT (compose, e) | |
| VCSN_RAT_VISIT (conjunction, e) | |
| VCSN_RAT_VISIT (infiltrate, e) | |
| VCSN_RAT_VISIT (ldivide, e) | |
| VCSN_RAT_VISIT (name, e) | |
| VCSN_RAT_VISIT (one, e) | |
| VCSN_RAT_VISIT (shuffle, e) | |
| VCSN_RAT_VISIT (star, e) | |
| VCSN_RAT_VISIT (transposition, e) | |
| void | visit (const tuple_t &, std::true_type) override |
| VCSN_RAT_VISIT (lweight, e) | |
| VCSN_RAT_VISIT (rweight, e) | |
Static Public Member Functions | |
| static constexpr const char * | me () |
| Name of this algorithm, for error messages. More... | |
Private Attributes | |
| expressionset_t | rs_ |
| weightset_t | ws_ = *rs_.weightset() |
| Shorthand to the weightset. More... | |
| polynomialset_t | ps_ = make_expression_polynomialset(rs_) |
| polynomial_t | res_ |
| The result. More... | |
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.}
/// }
///
| using vcsn::rat::split_visitor< ExpSet >::context_t = context_t_of<expressionset_t> |
| using vcsn::rat::split_visitor< ExpSet >::expression_t = typename expressionset_t::value_t |
| using vcsn::rat::split_visitor< ExpSet >::expressionset_t = ExpSet |
| using vcsn::rat::split_visitor< ExpSet >::label_t = label_t_of<context_t> |
| using vcsn::rat::split_visitor< ExpSet >::labelset_t = labelset_t_of<context_t> |
| using vcsn::rat::split_visitor< ExpSet >::polynomial_t = typename polynomialset_t::value_t |
| using vcsn::rat::split_visitor< ExpSet >::polynomialset_t = expression_polynomialset_t<expressionset_t> |
| using vcsn::rat::split_visitor< ExpSet >::super_t = typename expressionset_t::const_visitor |
| using vcsn::rat::split_visitor< ExpSet >::tuple_t = typename super_t::tuple_t |
| using vcsn::rat::split_visitor< ExpSet >::variadic_t = typename super_t::template variadic_t<Type> |
| using vcsn::rat::split_visitor< ExpSet >::weight_t = typename weightset_t::value_t |
| using vcsn::rat::split_visitor< ExpSet >::weightset_t = weightset_t_of<expressionset_t> |
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The split-multiplation of l with r.
Returns split(l) x split(r).
Definition at line 134 of file split.hh.
References vcsn::label_of(), vcsn::res, vcsn::split(), and vcsn::weight_of().
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The split-multiplation of l with r.
Returns l x split(r).
FIXME: This is inefficient, we split the lhs way too often.
Definition at line 156 of file split.hh.
References vcsn::label_of(), vcsn::multiply(), vcsn::res, and vcsn::weight_of().
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Break an expression into a polynomial.
Definition at line 103 of file split.hh.
References vcsn::split().
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Handle an n-ary multiplication.
Definition at line 168 of file split.hh.
References vcsn::multiply(), and vcsn::res.
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1.8.13