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 a rule to the presentation. |
|
Add a rule to the presentation and check. |
|
Add rules for an identity element. |
|
Add rules for inverses. |
|
Add rules for a zero element. |
|
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 or re-order the alphabet. |
|
Return a |
|
Returns the first letter not in the alphabet of a presentation. |
|
Greedily reduce the length of the presentation using
|
|
Returns |
|
Return the sum of the lengths of the rules. |
|
Return a possible letter by index. |
|
Returns the longest common subword of the rules. |
|
Returns an iterator pointing at the left hand side of the first rule of maximal length. |
|
Returns the maximum length of a rule. |
|
Convert a monoid presentation to a semigroup presentation. |
|
Modify the presentation so that the alphabet is \(\{0, \ldots, n - 1\}\) (or equivalent) and rewrites the rules. |
|
If there are rules \(u = v\) and \(v = w\) where \(|w| < |v| `, then replace :math:`u = v\) by \(u = w\). |
|
Reduce the number of generators in a f$1f$-relation presentation to 2. |
|
Return an iterator pointing at the left hand side of a redundant rule. |
|
Remove duplicate rules. |
|
Remove any trivially redundant generators. |
|
Remove rules consisting of identical words. |
|
Replace non-overlapping instances of a subword. |
|
Replace instances of a word occupying either side of a rule. |
|
Reverse every word in every rule. |
|
Returns an iterator pointing at the left hand side of the first rule of minimal length. |
|
Returns the minimum length of a rule. |
|
Sort each rule \(u = v\) so that the left hand side is shortlex greater than the right hand side. |
|
Sort the rules \(u_1 = v_1, \ldots, u_n = v_n\) so that \(u_1v_1 < \cdots < u_nv_n\). |
|
Strongly compress a 1-relation presentation. |
Full API¶
Warning
doxygennamespace: Cannot find namespace “libsemigroups::presentation” in doxygen xml output for project “libsemigroups” from directory: ../build/xml