First commit

Author: james-d-mitchell

.gitignore

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+public/

.hugo_build.lock

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+---
+# Striking header background image, Ideal images are homogenous around the centre and contrasting to the text. Non-ideal images can use `title_guard`
+header_image: "images/smalloverlap_510x510.png"
+#
+# When set true, uses video from custom_header_video.html partial, instead of header_image
+header_use_video: false
+#
+# Optional header logo. CSS: `#blog-logo`, with max-height defined, optimize to prevent scaling
+header_logo: "images/text_symbolpng"
+#
+# Headers are safeHTML, you can use HTML tags such as b,i,u,br
+header_headline: "libsemigroups"
+header_subheadline: "library for semigroups & monoids"
+
+# Add a 'Go back to top' item to the navigation menu
+# Title: name of navigation menu entry
+# Weight (i. e. position in menu): none = no menu entry, first = add as first entry, last = ad as last entry
+nav_to_top_title: "Return To Top"
+nav_to_top_weight: last
+---

assets/favicon.ico

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+---
+title: "What is libsemigroups?"
+header_menu_title: "About"
+navigation_menu_title: "About"
+weight: 1
+header_menu: true
+---
+
+[libsemigroups][] is a C++17 library containing implementations of several
+algorithms for computing finite, and finitely presented, semigroups and
+monoids. The main algorithms implemented in [libsemigroups][] are:
+
+- the **Froidure-Pin** algorithm for computing semigroups and monoids defined
+  by a generating set consisting of elements whose multiplication and equality is
+  decidable;
+- **Kambites'** algorithm for solving the word problem in small overlap monoids,
+  and the algorithm for computing normal forms for small overlap monoids by the
+  authors of [libsemigroups][];
+- the **Knuth-Bendix** algorithm for finitely presented semigroups and monoids;
+- a version of **Sims'** low index subgroup algorithm for computing congruences of a
+  semigroup or monoid;
+- a generalized version of **Konieczny's** and **Lallement and Mcfadden's** algorithms;
+- **Radoszewski and Rytter's** algorithm from testing equality of words in free
+  bands;
+- a non-random version of the **Schreier-Sims** algorithm;
+- a version of **Stephen's** procedure from
+  for finitely presented inverse semigroups and monoids;
+- the **Todd-Coxeter** algorithm for finitely presented semigroups and monoids.
+
+[libsemigroups]: https://libsemigroups.github.io/libsemigroups/

assets/images/favicon.png

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+---
+title: "C/C++"
+header_menu_title: "C/C++"
+navigation_menu_title: "C/C++"
+weight: 2
+header_menu: true
+---
+
+[libsemigroups][] is a modern open source C++17 library designed to be:
+
+- **state of the art**: the mathematical underpinnings of the algorithms
+  in [libsemigroups][] use the current state of the art;
+- **extensible**: several of the implementations in [libsemigroups][] are generic
+  and easily adaptable to user-defined types;
+- **adaptable**: the behaviour the algorithms implemented in [libsemigroups][]
+  can be fine-tuned via many settings, and used interactively via the
+  functions;
+- **easy to use**: converting between different types of [libsemigroups][]
+  objects is easy; there are many helper functions to streamline common tasks;
+  high quality exception messages are implemented throughout the code base
+  (although you don't have to use these if you don't want to); long running
+  algorithms can provide detailed feedback on their progress; many data
+  structures can be visualised; and there are hundreds of examples.
+- **fast**: [libsemigroups][] is designed with performance in mind; several
+  classes implement parallel algorithms; we provide some "winner takes all"
+  mechanisms for running algorithms concurrently; and there are `_no_checks`
+  versions of most functions if performance is critical.
+
+[libsemigroups]: https://libsemigroups.github.io/libsemigroups/

assets/images/smalloverlap_510x510.png

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+---
+title: "GAP"
+header_menu_title: "GAP"
+navigation_menu_title: "GAP"
+weight: 3
+header_menu: true
+---
+
+[libsemigroups][] is the workhorse of the [GAP][] package [Semigroups][]
+performing fundamental computations for finite and fintely presented semigroups
+and monoids. Many of these beat the corresponding methods in the [GAP][]
+library, despite [libsemigroups][] not having any optimisations specific to
+groups.
+
+```julia
+F := FreeGroup(11);;
+R := [];;
+for i in [1 .. 11] do
+  Add(R, [F.(i) ^ 2, One(F)]);
+od;
+for i in [1 .. 10] do
+  Add(R, [F.(i) * F.(i + 1) * F.(i), F.(i + 1) * F.(i) * F.(i + 1)]);
+od;
+for i in [1 .. 9] do
+  for j in [i + 2 .. 11] do
+    Add(R, [F.(i) * F.(j), F.(j) * F.(i)]);
+  od;
+od;
+G := F / R;
+Size(G); # runs forever
+```
+
+But with the [Semigroups][] package loaded:
+
+```julia
+F := FreeMonoid(11);;
+R := [];;
+for i in [1 .. 11] do
+  Add(R, [F.(i) ^ 2, One(F)]);
+od;
+for i in [1 .. 10] do
+  Add(R, [F.(i) * F.(i + 1) * F.(i), F.(i + 1) * F.(i) * F.(i + 1)]);
+od;
+for i in [1 .. 9] do
+  for j in [i + 2 .. 11] do
+    Add(R, [F.(i) * F.(j), F.(j) * F.(i)]);
+  od;
+od;
+G := F / R;
+Size(G);  # 479001600
+time; # 60
+```
+
+[libsemigroups]: https://libsemigroups.github.io/libsemigroups/
+[GAP]: https://www.gap-system.org
+[Semigroups]: https://semigroups.github.io