present-helper.rst

Presentation helpers

Defined in present.hpp and knuth-bendix.hpp.

This page contains the documentation for various helper functions for manipulating :cppPresentation objects. All such functions are contained in the namespace presentation.

These functions are available in the present.hpp file except :cppredundant_rule which is in knuth-bendix.hpp.

Contents

:cppadd_rule	Add a rule to the presentation.
:cppadd_rule_and_check	Add a rule to the presentation and check.
:cppadd_identity_rules	Add rules for an identity element.
:cppadd_inverse_rules	Add rules for inverses.
:cppadd_zero_rules	Add rules for a zero element.
:cppare_rules_sorted	Check if the rules u1 = v1, …, un = vn satisfy u1v1 < ⋯ < unvn where < is the shortlex order.
:cppchange_alphabet	Change or re-order the alphabet.
:cppcharacter	Return a char by index (ordered for readability).
:cppfirst_unused_letter	Returns the first letter not in the alphabet of a presentation.
:cppgreedy_reduce_length	Greedily reduce the length of the presentation using :cpplongest_common_subword.
:cppis_strongly_compressible	Returns true if the 1-relation presentation can be strongly compressed.
:cpplength	Return the sum of the lengths of the rules.
:cppletter	Return a possible letter by index.
:cpplongest_common_subword	Returns the longest common subword of the rules.
:cpplongest_rule	Returns an iterator pointing at the left hand side of the first rule of maximal length.
:cpplongest_rule_length	Returns the maximum length of a rule.
:cppmake_semigroup	Convert a monoid presentation to a semigroup presentation.
:cppnormalize_alphabet	Modify the presentation so that the alphabet is {0, …, n − 1} (or equivalent) and rewrites the rules.
:cppreduce_complements	If there are rules u = v and v = w where |w| < |v|, then replace u = v by u = w.
:cppreduce_to_2_generators	Reduce the number of generators in a f$1f$-relation presentation to 2.
:cppredundant_rule	Return an iterator pointing at the left hand side of a redundant rule.
:cppremove_duplicate_rules	Remove duplicate rules.
:cppremove_redundant_generators	Remove any trivially redundant generators.
:cppremove_trivial_rules	Remove rules consisting of identical words.
:cppreplace_subword	Replace non-overlapping instances of a subword.
:cppreplace_word	Replace instances of a word occupying either side of a rule.
:cppreverse	Reverse every word in every rule.
:cppshortest_rule	Returns an iterator pointing at the left hand side of the first rule of minimal length.
:cppshortest_rule_length	Returns the minimum length of a rule.
:cppsort_each_rule	Sort each rule u = v so that the left hand side is shortlex greater than the right hand side.
:cppsort_rules	Sort the rules u1 = v1, …, un = vn so that u1v1 < ⋯ < unvn.
:cppstrongly_compress	Strongly compress a 1-relation presentation.

Full API

libsemigroups::presentation