Presentation helpers

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

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

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

Contents

add_rule	Add a rule to the presentation.
add_rule_and_check	Add a rule to the presentation and check.
add_identity_rules	Add rules for an identity element.
add_inverse_rules	Add rules for inverses.
add_zero_rules	Add rules for a zero element.
are_rules_sorted	Check if the rules \(u_1 = v_1, \ldots, u_n = v_n\) satisfy \(u_1v_1 < \cdots < u_nv_n\) where \(<\) is the shortlex order.
change_alphabet	Change or re-order the alphabet.
character	Return a char by index (ordered for readability).
first_unused_letter	Returns the first letter not in the alphabet of a presentation.
greedy_reduce_length	Greedily reduce the length of the presentation using longest_common_subword.
is_strongly_compressible	Returns true if the 1-relation presentation can be strongly compressed.
length	Return the sum of the lengths of the rules.
letter	Return a possible letter by index.
longest_common_subword	Returns the longest common subword of the rules.
longest_rule	Returns an iterator pointing at the left hand side of the first rule of maximal length.
longest_rule_length	Returns the maximum length of a rule.
make_semigroup	Convert a monoid presentation to a semigroup presentation.
normalize_alphabet	Modify the presentation so that the alphabet is \(\{0, \ldots, n - 1\}\) (or equivalent) and rewrites the rules.
reduce_complements	If there are rules \(u = v\) and \(v = w\) where \(|w| < |v| `, then replace :math:`u = v\) by \(u = w\).
reduce_to_2_generators	Reduce the number of generators in a f$1f$-relation presentation to 2.
redundant_rule	Return an iterator pointing at the left hand side of a redundant rule.
remove_duplicate_rules	Remove duplicate rules.
remove_redundant_generators	Remove any trivially redundant generators.
remove_trivial_rules	Remove rules consisting of identical words.
replace_subword	Replace non-overlapping instances of a subword.
replace_word	Replace instances of a word occupying either side of a rule.
reverse	Reverse every word in every rule.
shortest_rule	Returns an iterator pointing at the left hand side of the first rule of minimal length.
shortest_rule_length	Returns the minimum length of a rule.
sort_each_rule	Sort each rule \(u = v\) so that the left hand side is shortlex greater than the right hand side.
sort_rules	Sort the rules \(u_1 = v_1, \ldots, u_n = v_n\) so that \(u_1v_1 < \cdots < u_nv_n\).
strongly_compress	Strongly compress a 1-relation presentation.

Full API

Warning

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