libsemigroups  v3.1.3
C++ library for semigroups and monoids
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presentation.hpp
1//
2// libsemigroups - C++ library for semigroups and monoids
3// Copyright (C) 2022-2025 James D. Mitchell
4//
5// This program is free software: you can redistribute it and/or modify
6// it under the terms of the GNU General Public License as published by
7// the Free Software Foundation, either version 3 of the License, or
8// (at your option) any later version.
9//
10// This program is distributed in the hope that it will be useful,
11// but WITHOUT ANY WARRANTY; without even the implied warranty of
12// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13// GNU General Public License for more details.
14//
15// You should have received a copy of the GNU General Public License
16// along with this program. If not, see <http://www.gnu.org/licenses/>.
17//
18
19// This file contains the declaration of a class template for semigroup or
20// monoid presentations. The idea is to provide a shallow wrapper around a
21// vector of words, with some checks that the vector really defines a
22// presentation, (i.e. it's consistent with its alphabet etc), and some related
23// functionality.
24
25#ifndef LIBSEMIGROUPS_PRESENTATION_HPP_
26#define LIBSEMIGROUPS_PRESENTATION_HPP_
27
28#include <algorithm> // for reverse, sort
29#include <cmath> // for pow
30#include <cstring> // for size_t, strlen
31#include <initializer_list> // for initializer_list
32#include <iterator> // for distance
33#include <limits> // for numeric_limits
34#include <map> // for map
35#include <numeric> // for accumulate
36#include <string> // for basic_string, operator==
37#include <tuple> // for tie, tuple
38#include <type_traits> // for enable_if_t
39#include <unordered_map> // for operator==, operator!=
40#include <unordered_set> // for unordered_set
41#include <utility> // for move, pair
42#include <vector> // for vector, operator!=
43
44#include "adapters.hpp" // for Hash, EqualTo
45#include "constants.hpp" // for Max, UNDEFINED, operator==
46#include "debug.hpp" // for LIBSEMIGROUPS_ASSERT
47#include "is_specialization_of.hpp"
48#include "order.hpp" // for ShortLexCompare
49#include "ranges.hpp" // for seq, operator|, rx, take, chain, is_sorted
50#include "types.hpp" // for word_type
51#include "ukkonen.hpp" // for GreedyReduceHelper, Ukkonen
52#include "word-range.hpp" // for operator+
53
54#include "detail/fmt.hpp" // for format
55#include "detail/print.hpp" // for isprint etc
56#include "detail/string.hpp" // for maximum_common_prefix
57#include "detail/uf.hpp" // for Duf
58
59namespace libsemigroups {
60
76
79
102 template <typename Word>
104 public:
106 using word_type = Word;
107
110 using letter_type = typename word_type::value_type;
111
114
117
120
121 private:
122 word_type _alphabet;
124 bool _contains_empty_word;
125
126 public:
133
138
150
155
160
165
170
172
184 [[nodiscard]] word_type const& alphabet() const noexcept {
185 return _alphabet;
186 }
187
188 // TODO(later) alphabet_no_checks
189
210 // TODO(1) Rename alphabet_size
212
232
252
270
284 [[nodiscard]] letter_type letter_no_checks(size_type i) const {
285 LIBSEMIGROUPS_ASSERT(i < _alphabet.size());
286 return _alphabet[i];
287 }
288
299 [[nodiscard]] letter_type letter(size_type i) const;
300
317 [[nodiscard]] size_type index_no_checks(letter_type val) const {
318 return _alphabet_map.find(val)->second;
319 }
320
331 [[nodiscard]] size_type index(letter_type val) const;
332
346 [[nodiscard]] bool in_alphabet(letter_type val) const {
347 return _alphabet_map.find(val) != _alphabet_map.cend();
348 }
349
385 template <typename Iterator1, typename Iterator2>
386 Presentation& add_rule_no_checks(Iterator1 lhs_begin,
387 Iterator1 lhs_end,
388 Iterator2 rhs_begin,
389 Iterator2 rhs_end) {
390 rules.emplace_back(lhs_begin, lhs_end);
391 rules.emplace_back(rhs_begin, rhs_end);
392 return *this;
393 }
394
409 template <typename Iterator1, typename Iterator2>
410 Presentation& add_rule(Iterator1 lhs_begin,
411 Iterator1 lhs_end,
412 Iterator2 rhs_begin,
413 Iterator2 rhs_end) {
414 throw_if_letter_not_in_alphabet(lhs_begin, lhs_end);
415 throw_if_letter_not_in_alphabet(rhs_begin, rhs_end);
416 return add_rule_no_checks(lhs_begin, lhs_end, rhs_begin, rhs_end);
417 }
418
429
441
452
472
487
504 [[nodiscard]] bool contains_empty_word() const noexcept {
505 return _contains_empty_word;
506 }
507
527 Presentation& contains_empty_word(bool val) noexcept {
528 _contains_empty_word = val;
529 return *this;
530 }
531
542 decltype(_alphabet_map) alphabet_map;
544 }
545
557
572 template <typename Iterator1, typename Iterator2>
573 void throw_if_letter_not_in_alphabet(Iterator1 first, Iterator2 last) const;
574
591 void throw_if_bad_rules() const;
592
608
609 private:
610 void try_set_alphabet(decltype(_alphabet_map)& alphabet_map,
611 word_type& old_alphabet);
613 decltype(_alphabet_map)& alphabet_map) const;
614 }; // class Presentation
615
624 template <typename Word>
626
635 template <typename Word>
637
648 namespace presentation {
649
662 template <typename Iterator>
663 void throw_if_odd_number_of_rules(Iterator first, Iterator last) {
664 if ((std::distance(first, last) % 2) == 1) {
666 "expected even number of words in \"rules\", found {}",
667 std::distance(first, last));
668 }
669 }
670
682 template <typename Word>
686
705 template <typename Word>
707 std::string_view arg = "1st");
708
722 template <typename Word>
724
743 template <typename Word, typename Iterator>
745 Iterator first,
746 Iterator last) {
747 // TODO(0) check if there are an odd number of rules
748 for (auto it = first; it != last; ++it) {
749 p.throw_if_letter_not_in_alphabet(it->cbegin(), it->cend());
750 }
751 }
752
775 template <typename Word>
776 void throw_if_bad_inverses(Presentation<Word> const& p, Word const& vals);
777
802 template <typename Word>
804
821 template <typename Word>
823 Word const& lhop,
824 Word const& rhop) {
825 p.add_rule_no_checks(lhop.begin(), lhop.end(), rhop.begin(), rhop.end());
826 }
827
841 template <typename Word>
842 void add_rule(Presentation<Word>& p, Word const& lhop, Word const& rhop) {
843 p.add_rule(lhop.begin(), lhop.end(), rhop.begin(), rhop.end());
844 }
845
862 char const* lhop,
863 char const* rhop);
864
877 char const* lhop,
878 char const* rhop);
879
893 std::string const& lhop,
894 char const* rhop);
895
909 char const* lhop,
910 std::string const& rhop);
911
929 std::string const& lhop,
930 char const* rhop);
931
949 char const* lhop,
950 std::string const& rhop);
951
969 template <typename Word, typename Letter>
975
989 template <typename Word, typename Letter>
993 p.add_rule(lhop.begin(), lhop.end(), rhop.begin(), rhop.end());
994 }
995
1014 template <typename Word, typename Iterator>
1015 void add_rules(Presentation<Word>& p, Iterator first, Iterator last) {
1016 for (auto it = first; it != last; it += 2) {
1017 add_rule(p, *it, *(it + 1));
1018 }
1019 }
1020
1038 template <typename Word, typename Iterator>
1040 Iterator first,
1041 Iterator last) {
1042 for (auto it = first; it != last; it += 2) {
1043 add_rule_no_checks(p, *it, *(it + 1));
1044 }
1045 }
1046
1062 template <typename Word>
1067
1084 template <typename Word>
1086 add_rules(p, q.rules.cbegin(), q.rules.cend());
1087 }
1088
1106 template <typename Word>
1107 [[nodiscard]] bool contains_rule(Presentation<Word>& p,
1108 Word const& lhs,
1109 Word const& rhs);
1110
1125 template <typename Word>
1128
1143 template <typename Word>
1146
1170 template <typename Word>
1172 Word const& vals,
1174 = UNDEFINED);
1175
1200 char const* vals,
1201 char e = UNDEFINED);
1202
1217 template <typename Word>
1219
1232 template <typename Word>
1234
1255 template <typename Word>
1257
1270 template <typename Word>
1272
1288 template <typename Word, typename Compare>
1289 bool sort_each_rule(Presentation<Word>& p, Compare cmp);
1290
1291 // TODO(later) is_each_rule_sorted?
1292
1305 template <typename Word, typename Compare>
1306 void sort_rules(Presentation<Word>& p, Compare cmp);
1307
1317 template <typename Word>
1321
1339 template <typename Word, typename Compare>
1340 bool are_rules_sorted(Presentation<Word> const& p, Compare cmp);
1341
1356 template <typename Word>
1358 return are_rules_sorted(p, ShortLexCompare());
1359 }
1360
1377 // TODO(later) complexity
1378 template <typename Word>
1380
1395 // TODO(later) complexity
1396 template <typename Word, typename Iterator>
1399 Iterator first,
1400 Iterator last);
1401
1418 // TODO(later) complexity
1419 template <typename Word>
1422 return replace_word_with_new_generator(p, w.cbegin(), w.cend());
1423 }
1424
1441 char const* w);
1442
1455 // TODO(later) complexity
1456 template <typename Word>
1458 Word const& existing,
1459 Word const& replacement);
1460
1484 template <typename Word, typename Iterator1, typename Iterator2>
1486 Iterator1 first_existing,
1487 Iterator1 last_existing,
1488 Iterator2 first_replacement,
1489 Iterator2 last_replacement);
1490
1504 char const* existing,
1505 char const* replacement) {
1507 existing,
1508 existing + std::strlen(existing),
1509 replacement,
1510 replacement + std::strlen(replacement));
1511 }
1512
1529 template <typename Word>
1531 Word const& existing,
1532 Word const& replacement);
1533
1550 template <typename Iterator>
1551 size_t length(Iterator first, Iterator last);
1552
1564 template <typename Word>
1565 size_t length(Presentation<Word> const& p) {
1566 return length(p.rules.cbegin(), p.rules.cend());
1567 }
1568
1578 template <typename Word>
1580 for (auto& rule : p.rules) {
1581 std::reverse(rule.begin(), rule.end());
1582 }
1583 }
1584
1596 // This is the only place that JDE can find where a helper that modifies its
1597 // first argument is not void. This is deliberate, since if we weren't to
1598 // return anything, the first parameter would go out of scope immediately
1599 // after this call and this function would be pointless .
1600 template <typename Word>
1602 for (auto& rule : p.rules) {
1603 std::reverse(rule.begin(), rule.end());
1604 }
1605 return std::move(p);
1606 }
1607
1622 template <typename Word>
1624
1638 template <typename Word>
1639 void change_alphabet(Presentation<Word>& p, Word const& new_alphabet);
1640
1653 char const* new_alphabet) {
1654 change_alphabet(p, std::string(new_alphabet));
1655 }
1656
1674 template <typename Iterator>
1675 Iterator longest_rule(Iterator first, Iterator last);
1676
1692 template <typename Word>
1695 return longest_rule(p.rules.cbegin(), p.rules.cend());
1696 }
1697
1715 template <typename Iterator>
1716 Iterator shortest_rule(Iterator first, Iterator last);
1717
1733 template <typename Word>
1736 return shortest_rule(p.rules.cbegin(), p.rules.cend());
1737 }
1738
1753 template <typename Iterator>
1754 typename Iterator::value_type::size_type longest_rule_length(Iterator first,
1755 Iterator last);
1756
1770 template <typename Word>
1771 typename Word::size_type longest_rule_length(Presentation<Word> const& p) {
1772 return longest_rule_length(p.rules.cbegin(), p.rules.cend());
1773 }
1774
1789 template <typename Iterator>
1790 typename Iterator::value_type::size_type
1791 shortest_rule_length(Iterator first, Iterator last);
1792
1806 template <typename Word>
1807 typename Word::size_type shortest_rule_length(Presentation<Word> const& p) {
1808 return shortest_rule_length(p.rules.cbegin(), p.rules.cend());
1809 }
1810
1825 template <typename Word>
1827
1843 template <typename Word>
1846
1863 template <typename Word>
1866
1883 template <typename Word>
1885
1908 template <typename Word>
1910
1933 // not noexcept because std::vector::operator[] isn't
1934 template <typename Word>
1936
1956 // not noexcept because is_strongly_compressible isn't
1957 template <typename Word>
1959
1988 template <typename Word>
1989 bool reduce_to_2_generators(Presentation<Word>& p, size_t index = 0);
1990
2006 template <typename Word>
2008 Word const& letters) {
2009 for (auto x : letters) {
2010 add_rule_no_checks(p, {x, x}, {x});
2011 }
2012 }
2013
2029 template <typename Word>
2031 word_type const& letters) {
2032 for (auto x : letters) {
2033 add_rule_no_checks(p, {x, x}, {});
2034 }
2035 }
2036
2053 template <typename Word>
2055 Word const& letters1,
2056 Word const& letters2);
2057
2073 template <typename Word>
2075 Word const& letters) {
2076 add_commutes_rules_no_checks(p, letters, letters);
2077 }
2078
2095 template <typename Word>
2097 Word const& letters,
2099
2127 template <typename Word1, typename Word2>
2129 Word2 const& letters,
2130 Word2 const& inverses);
2131
2138 template <typename Word>
2140 Word const& letters,
2141 Word const& inverses) {
2142 balance_no_checks<Word, Word>(p, letters, inverses);
2143 }
2144
2152 char const* letters,
2153 char const* inverses) {
2155 p, std::string_view(letters), std::string_view(inverses));
2156 }
2157
2165 std::string_view letters,
2166 std::string_view inverses) {
2168 }
2169
2170 // TODO(later) add balance that checks p contains empty word, no duplicate
2171 // letters in alphabet, and inverses are valid.
2172
2173 // TODO version of balance that only specified inverses, and uses the
2174 // alphabet as the letters
2175
2198 template <typename Word1, typename Word2>
2200 Word2 const& relator);
2201
2209 template <typename Word>
2211 Word const& relator) {
2213 }
2214
2222 char const* relator) {
2224 p, std::string_view(relator));
2225 }
2226
2247 template <typename Word1, typename Word2>
2248 void add_cyclic_conjugates(Presentation<Word1>& p, Word2 const& relator);
2249
2257 template <typename Word>
2258 void add_cyclic_conjugates(Presentation<Word>& p, Word const& relator) {
2260 }
2261
2269 char const* relator) {
2271 p, std::string_view(relator));
2272 }
2273
2286 std::string const& var_name);
2287
2300 std::string const& var_name);
2301
2302 } // namespace presentation
2303
2317 template <typename Word>
2318 class InversePresentation : public Presentation<Word> {
2319 public:
2323
2327
2330
2333
2336
2337 private:
2338 word_type _inverses;
2339
2340 public:
2341 using Presentation<Word>::Presentation;
2342
2343 // TODO(later) init functions
2344
2353 : Presentation<Word>(p), _inverses() {}
2354
2364 : Presentation<Word>(p), _inverses() {}
2365
2382
2409
2418 word_type const& inverses() const noexcept {
2419 return _inverses;
2420 }
2421
2433
2450 // TODO(0) check if this is used appropriately after rename
2453 }
2454 };
2455
2474 // TODO(later) also we could do a more sophisticated version of this
2475 template <typename Word>
2477 Presentation<Word> const& rhop) {
2478 return lhop.alphabet() == rhop.alphabet() && lhop.rules == rhop.rules;
2479 }
2480
2499 // TODO(later) also we could do a more sophisticated version of this
2500 template <typename Word>
2502 InversePresentation<Word> const& rhop) {
2503 return lhop.alphabet() == rhop.alphabet() && lhop.rules == rhop.rules
2504 && lhop.inverses() == rhop.inverses();
2505 }
2506
2525 template <typename Word>
2527 Presentation<Word> const& rhop) {
2528 return !(lhop == rhop);
2529 }
2530
2549 template <typename Word>
2551 InversePresentation<Word> const& rhop) {
2552 return !(lhop == rhop);
2553 }
2554
2566 template <typename Word>
2568
2580 template <typename Word>
2582
2583 namespace detail {
2584
2585 class GreedyReduceHelper {
2586 private:
2587 size_t _best;
2588 int _best_goodness;
2589 std::vector<size_t> _distance_from_root;
2590 std::vector<size_t> _num_leafs;
2591 std::vector<size_t> _scratch;
2592 std::vector<size_t> _suffix_index;
2593
2594 public:
2595 using const_iterator = typename Ukkonen::const_iterator;
2596
2597 explicit GreedyReduceHelper(Ukkonen const& u);
2598
2599 GreedyReduceHelper() = delete;
2600 GreedyReduceHelper(GreedyReduceHelper const&) = delete;
2601 GreedyReduceHelper(GreedyReduceHelper&&) = delete;
2602 GreedyReduceHelper& operator=(GreedyReduceHelper const&) = delete;
2603 GreedyReduceHelper& operator=(GreedyReduceHelper&&) = delete;
2604 ~GreedyReduceHelper();
2605
2606 void pre_order(Ukkonen const& u, size_t v);
2607 void post_order(Ukkonen const& u, size_t v);
2609 };
2610 } // namespace detail
2611
2622 // clang-format off
2623 // NOLINTNEXTLINE(whitespace/line_length)
2625 // clang-format on
2626 template <typename Thing>
2627 static constexpr bool IsInversePresentation [[deprecated]]
2629
2642 template <typename Thing>
2643 static constexpr bool IsPresentation [[deprecated]]
2645
2646} // namespace libsemigroups
2647
2648#include "presentation.tpp"
2649
2650#endif // LIBSEMIGROUPS_PRESENTATION_HPP_
T cbegin(T... args)
For an implementation of inverse presentations for semigroups or monoids.
Definition presentation.hpp:2318
typename Presentation< Word >::size_type size_type
Size type for rules.
Definition presentation.hpp:2335
typename Presentation< Word >::letter_type letter_type
Type of the letters in the words that constitute the rules of an InversePresentation object.
Definition presentation.hpp:2326
void throw_if_bad_alphabet_rules_or_inverses() const
Check if the InversePresentation is valid.
Definition presentation.hpp:2449
typename Presentation< Word >::iterator iterator
Type of an iterator to either side of a rule.
Definition presentation.hpp:2332
InversePresentation(Presentation< Word > const &p)
Construct an InversePresentation from a Presentation reference.
Definition presentation.hpp:2352
typename Presentation< Word >::word_type word_type
Type of the words in the rules of an InversePresentation object.
Definition presentation.hpp:2322
letter_type inverse(letter_type x) const
Return the inverse of a letter in the alphabet.
InversePresentation & inverses(word_type const &w)
Set the inverse of each letter in the alphabet.
Definition presentation.hpp:2404
InversePresentation(Presentation< Word > &&p)
Construct an InversePresentation from a Presentation rvalue reference.
Definition presentation.hpp:2363
word_type const & inverses() const noexcept
Return the inverse of each letter in the alphabet.
Definition presentation.hpp:2418
InversePresentation & inverses_no_checks(word_type const &w)
Set the inverse of each letter in the alphabet.
typename Presentation< Word >::const_iterator const_iterator
Type of a const iterator to either side of a rule.
Definition presentation.hpp:2329
For an implementation of presentations for semigroups or monoids.
Definition presentation.hpp:103
letter_type add_generator()
Add a generator.
Presentation & remove_generator(letter_type x)
Remove x as a generator.
Presentation & alphabet(word_type &&lphbt)
Set the alphabet from rvalue reference.
void throw_if_bad_alphabet_or_rules() const
Check if the alphabet and rules are valid.
Definition presentation.hpp:604
void throw_if_bad_rules() const
Check if every word in every rule consists only of letters belonging to the alphabet.
Presentation & add_generator_no_checks(letter_type x)
Add x as a generator.
Presentation & add_generator(letter_type x)
Add x as a generator.
Presentation & contains_empty_word(bool val) noexcept
Set whether whether the empty word is a valid relation word.
Definition presentation.hpp:527
typename std::vector< word_type >::size_type size_type
Size type for rules.
Definition presentation.hpp:119
void throw_if_letter_not_in_alphabet(letter_type c) const
Check if a letter belongs to the alphabet or not.
size_type index_no_checks(letter_type val) const
Return the index of a letter in the alphabet.
Definition presentation.hpp:317
Presentation & alphabet(size_type n)
Set the alphabet by size.
Presentation & alphabet_from_rules()
Set the alphabet to be the letters in the rules.
Presentation & operator=(Presentation &&)
Default move assignment operator.
Presentation & add_rule_no_checks(Iterator1 lhs_begin, Iterator1 lhs_end, Iterator2 rhs_begin, Iterator2 rhs_end)
Add a rule to the presentation.
Definition presentation.hpp:386
typename std::vector< word_type >::iterator iterator
Type of an iterator to either side of a rule.
Definition presentation.hpp:116
Presentation(Presentation const &)
Default copy constructor.
void throw_if_alphabet_has_duplicates() const
Check if the alphabet is valid.
Definition presentation.hpp:541
letter_type letter_no_checks(size_type i) const
Return a letter in the alphabet by index.
Definition presentation.hpp:284
void throw_if_letter_not_in_alphabet(Iterator1 first, Iterator2 last) const
Check if every letter in a range belongs to the alphabet.
Presentation(Presentation &&)
Default move constructor.
letter_type letter(size_type i) const
Return a letter in the alphabet by index.
std::vector< word_type > rules
Data member holding the rules of the presentation.
Definition presentation.hpp:132
Presentation & operator=(Presentation const &)
Default copy assignment operator.
bool contains_empty_word() const noexcept
Return whether the empty word is a valid relation word.
Definition presentation.hpp:504
Presentation & alphabet(word_type const &lphbt)
Set the alphabet const reference.
size_type index(letter_type val) const
Return the index of a letter in the alphabet.
Presentation & init()
Remove the alphabet and all rules.
word_type const & alphabet() const noexcept
Return the alphabet of the presentation.
Definition presentation.hpp:184
Word word_type
Type of the words in the rules of a Presentation object.
Definition presentation.hpp:106
typename word_type::value_type letter_type
Type of the letters in the words that constitute the rules of a Presentation object.
Definition presentation.hpp:110
Presentation & remove_generator_no_checks(letter_type x)
Remove x as a generator.
Presentation()
Default constructor.
typename std::vector< word_type >::const_iterator const_iterator
Type of a const iterator to either side of a rule.
Definition presentation.hpp:113
Presentation & add_rule(Iterator1 lhs_begin, Iterator1 lhs_end, Iterator2 rhs_begin, Iterator2 rhs_end)
Add a rule to the presentation and check it is valid.
Definition presentation.hpp:410
bool in_alphabet(letter_type val) const
Check if a letter belongs to the alphabet or not.
Definition presentation.hpp:346
For an implementation of Ukkonen's algorithm.
Definition ukkonen.hpp:90
typename word_type::const_iterator const_iterator
Alias for word_type iterators.
Definition ukkonen.hpp:106
T distance(T... args)
T cend(T... args)
std::string to_human_readable_repr(Action< Element, Point, Func, Traits, LeftOrRight > const &action)
Return a human readable representation of an Action object.
bool operator!=(Bipartition const &x, Bipartition const &y)
Check bipartitions for inequality.
Definition bipart.hpp:1629
Undefined const UNDEFINED
Value for something undefined.
#define LIBSEMIGROUPS_EXCEPTION(...)
Throw a LibsemigroupsException.
Definition exception.hpp:99
Presentation(Presentation< Word > const &) -> Presentation< Word >
Deduction guide.
bool operator==(Presentation< Word > const &lhop, Presentation< Word > const &rhop)
Compare for equality.
Definition presentation.hpp:2476
static constexpr bool IsPresentation
Helper variable template.
Definition presentation.hpp:2644
static constexpr bool IsInversePresentation
Helper variable template.
Definition presentation.hpp:2628
constexpr bool is_specialization_of_v
Helper variable template for is_specialization_of.
Definition is_specialization_of.hpp:83
std::vector< letter_type > word_type
Type for a word over the generators of a semigroup.
Definition types.hpp:99
T move(T... args)
Namespace for Presentation helper functions.
Definition obvinf.hpp:60
Iterator::value_type::size_type longest_rule_length(Iterator first, Iterator last)
Return the maximum length of a rule in the given range.
void add_commutes_rules_no_checks(Presentation< Word > &p, Word const &letters1, Word const &letters2)
Add rules so specific letters commute.
Presentation< Word >::letter_type replace_word_with_new_generator(Presentation< Word > &p, Iterator first, Iterator last)
Replace non-overlapping instances of a subword via iterators.
bool reduce_to_2_generators(Presentation< Word > &p, size_t index=0)
Reduce the number of generators in a -relation presentation to 2.
void add_idempotent_rules_no_checks(Presentation< Word > &p, Word const &letters)
Add rules that define each letter as an idempotent.
Definition presentation.hpp:2007
void throw_if_bad_inverses(Presentation< Word > const &p, Word const &vals)
throw_if_bad_alphabet_or_rules if vals act as semigroup inverses in p.
Iterator longest_rule(Iterator first, Iterator last)
Return an iterator pointing at the left-hand side of the first rule of maximal length in the given ra...
void add_involution_rules_no_checks(Presentation< Word > &p, word_type const &letters)
Add rules that define involution.
Definition presentation.hpp:2030
void throw_if_odd_number_of_rules(Iterator first, Iterator last)
Throw if the distance between iterators is not even.
Definition presentation.hpp:663
void reverse(Presentation< Word > &p)
Reverse every rule.
Definition presentation.hpp:1579
bool contains_rule(Presentation< Word > &p, Word const &lhs, Word const &rhs)
Check if a presentation contains a rule.
void greedy_reduce_length_and_number_of_gens(Presentation< Word > &p)
Greedily reduce the length and number of generators of the presentation.
Word longest_subword_reducing_length(Presentation< Word > &p)
Return the longest common subword of the rules.
bool sort_each_rule(Presentation< Word > &p)
Sort the left-hand and right-hand side of each rule by shortlex.
bool are_rules_sorted(Presentation< Word > const &p, Compare cmp)
Check the rules are sorted relative to cmp .
void add_rules(Presentation< Word > &p, Iterator first, Iterator last)
Add the rules stored in the range [first, last).
Definition presentation.hpp:1015
Iterator shortest_rule(Iterator first, Iterator last)
Return an iterator pointing at the left-hand side of the first rule of minimal length in the given ra...
void balance_no_checks(Presentation< Word1 > &p, Word2 const &letters, Word2 const &inverses)
Balance the length of the left-hand and right-hand sides.
Iterator::value_type::size_type shortest_rule_length(Iterator first, Iterator last)
Return the minimum length of a rule in the given range.
void remove_trivial_rules(Presentation< Word > &p)
Remove rules consisting of identical words.
void add_rules_no_checks(Presentation< Word > &p, Iterator first, Iterator last)
Add the rules stored in the range [first, last).
Definition presentation.hpp:1039
void replace_word(Presentation< Word > &p, Word const &existing, Word const &replacement)
Replace instances of a word on either side of a rule by another word.
void add_rule_no_checks(Presentation< Word > &p, Word const &lhop, Word const &rhop)
Add a rule to the presentation by reference.
Definition presentation.hpp:822
void throw_if_bad_rules(Presentation< Word > const &p, Iterator first, Iterator last)
Check rules against the alphabet of p.
Definition presentation.hpp:744
void sort_rules(Presentation< Word > &p, Compare cmp)
Sort all of the rules by cmp.
void replace_subword(Presentation< Word > &p, Word const &existing, Word const &replacement)
Replace non-overlapping instances of a subword by another word.
void add_identity_rules(Presentation< Word > &p, typename Presentation< Word >::letter_type e)
Add rules for an identity element.
Presentation< Word >::letter_type make_semigroup(Presentation< Word > &p)
Convert a monoid presentation to a semigroup presentation.
void reduce_complements(Presentation< Word > &p)
If there are rules and where , then replace by .
void normalize_alphabet(Presentation< Word > &p)
Normalize the alphabet to .
bool strongly_compress(Presentation< Word > &p)
Strongly compress a -relation presentation.
void add_cyclic_conjugates(Presentation< Word1 > &p, Word2 const &relator)
Add all cyclic permutations of a word as relators in a presentation.
void remove_redundant_generators(Presentation< Word > &p)
Remove any trivially redundant generators.
void greedy_reduce_length(Presentation< Word > &p)
Greedily reduce the length of the presentation using longest_subword_reducing_length.
void change_alphabet(Presentation< Word > &, Word const &)
Change or re-order the alphabet.
void add_inverse_rules(Presentation< Word > &p, Word const &vals, typename Presentation< Word >::letter_type e=UNDEFINED)
Add rules for inverses.
bool is_strongly_compressible(Presentation< Word > const &p)
Return true if the -relation presentation can be strongly compressed.
void remove_duplicate_rules(Presentation< Word > &p)
Remove duplicate rules.
size_t length(Iterator first, Iterator last)
Return the sum of the lengths of all values in the range [first, last).
std::string to_report_string(Presentation< Word > const &p)
Return a representation of a presentation to appear in the reporting output.
Presentation< Word >::letter_type first_unused_letter(Presentation< Word > const &p)
Return the first letter not in the alphabet of a presentation.
void add_cyclic_conjugates_no_checks(Presentation< Word1 > &p, Word2 const &relator)
Add all cyclic permutations of a word as relators in a presentation.
bool is_normalized(Presentation< Word > const &p)
Check if the presentation is normalized.
void add_rule(Presentation< Word > &p, Word const &lhop, Word const &rhop)
Add a rule to the presentation by reference and check.
Definition presentation.hpp:842
void throw_if_not_normalized(Presentation< Word > const &p, std::string_view arg="1st")
Throws if the presentation isn't normalized.
void add_zero_rules(Presentation< Word > &p, typename Presentation< Word >::letter_type z)
Add rules for a zero element.
std::string to_gap_string(Presentation< word_type > const &p, std::string const &var_name)
Return the code that would create p in GAP.
Namespace containing some operators for creating words.
Definition word-range.hpp:2095
Namespace for everything in the libsemigroups library.
Definition action.hpp:44
T reverse(T... args)
T strlen(T... args)
Empty base for presentation-like classes.
Definition presentation.hpp:78
A stateless struct with binary call operator using shortlex_compare.
Definition order.hpp:362