Add atlas and 1-relation examples

.github/workflows/docs.yml

@@ -20,7 +20,9 @@ jobs:
       - uses: actions/setup-python@v6
         with:
           python-version: 3.x
-      - run: pipx run --with mkdocs-material mkdocs build --clean
+      - run:
+          pipx run --with mkdocs-material --with mkdocs-awesome-nav mkdocs build
+          --clean
       - uses: actions/upload-pages-artifact@v4
         with:
           path: site

.github/workflows/tests.yml

@@ -13,6 +13,8 @@ jobs:
       - uses: actions/checkout@v6
       - name: Build in strict mode
         # The strict flag treats warnings as errors
-        run: pipx run --with mkdocs-material mkdocs build --clean --strict
+        run:
+          pipx run --with mkdocs-material --with mkdocs-awesome-nav mkdocs build
+          --clean --strict
 
 # TODO: test the code snippets

.gitignore

@@ -317,4 +317,4 @@ TSWLatexianTemp*
 .cache/
 .DS_Store
 __pycache__/*
-
+site/*

docs/.nav.yml

@@ -0,0 +1,55 @@
+nav:
+  - Home: index.md
+  - Semigroups in GAP:
+      - gap/index.md
+      - "GAP: Installation": gap/install.md
+      - "GAP: First steps": gap/first-steps.md
+      - "GAP: Semigroups defined by generators": gap/generated.md
+      - "GAP: Finitely presented semigroups": gap/fp.md
+      - "GAP: Worksheet": gap/worksheet.md
+  - Semigroups in Python:
+      - py/index.md
+      - "Python: Installation": py/install.md
+      - "Python: First steps": py/first-steps.md
+      - "Python: Semigroups defined by generators": py/generated.md
+      - "Python: Finitely presented semigroups": py/fp.md
+      - "Python: Worksheet": py/worksheet.md
+  - Examples:
+      - examples/index.md
+      - examples/short.md
+      - "Verifying presentations for sporadic simple groups":
+          - examples/atlas/index.md
+          - "Mathieu groups":
+              - "Mathieu group M11": examples/atlas/mathieu/m11.md
+              - "Mathieu group M12": examples/atlas/mathieu/m12.md
+              - "Mathieu group M22": examples/atlas/mathieu/m22.md
+              - "Mathieu group M23":
+                  - examples/atlas/mathieu/m23/index.md
+                  - "M11, P1": examples/atlas/mathieu/m23/p1_m11.md
+                  - "M22, P1": examples/atlas/mathieu/m23/p1_m22.md
+                  - "M11, P2": examples/atlas/mathieu/m23/p2_m11.md
+                  - "M22, P2": examples/atlas/mathieu/m23/p2_m22.md
+              - "Mathieu group M24":
+                  - examples/atlas/mathieu/m24/index.md
+          - "Leech lattice groups":
+              - examples/atlas/leech-lattice/hs.md
+              - "Janko group J2, Hall-Janko group HJ":
+                  - examples/atlas/leech-lattice/j2/index.md
+                  - "P1": examples/atlas/leech-lattice/j2/j2-p1.md
+                  - "P2": examples/atlas/leech-lattice/j2/j2-p2.md
+              - "Conway group Co2":
+                  - examples/atlas/leech-lattice/co2/index.md
+              - "McLaughlin group McL":
+                  - examples/atlas/leech-lattice/mcl/index.md
+          - "Monster sections":
+              - "Held group He":
+                  - examples/atlas/monster-sections/he/index.md
+              - "Fischer group Fi22":
+                  - examples/atlas/monster-sections/fi22/index.md
+          - "Pariahs":
+              - examples/atlas/pariahs/*
+              - "Janko group J4":
+                  - examples/atlas/pariahs/j4/index.md
+          - "Miscellaneous":
+              - examples/atlas/misc/t.md
+      - "Finding complete rewriting systems for 1-relation monoids": examples/1-relation

docs/examples/1-relation/000.md

@@ -0,0 +1,44 @@
+#\#000 ababbaaaaa=baaaaaba
+
+## Original presentation
+
+\(
+\left\langle
+  a, b \;\middle|\; a b a b^{2} a^{5} = b a^{5} b a
+\right\rangle
+\)
+
+## Modified presentation
+
+\(
+\left\langle
+  a, b, c, d \;\middle|\; a d = c b a,\; c = b a^{5},\; d = b a b c
+\right\rangle
+\)
+
+## Complete rewriting system
+
+Using recursive path order (`RPOCmp`) with \(c < a < d < b\):
+
+\(
+\begin{aligned}
+  b a b c &\rightarrow d \\
+  b a^{5} &\rightarrow c \\
+  c b a &\rightarrow a d \\
+  b a b a d &\rightarrow d b a \\
+  a d b c &\rightarrow c d \\
+  a d a^{4} &\rightarrow c^{2} \\
+  b a^{4} c d &\rightarrow c d b c \\
+  b a^{4} c^{2} &\rightarrow c d a^{4} \\
+  a d b a d &\rightarrow c d b a \\
+  c b c d &\rightarrow a d^{2} b c \\
+  c b c^{2} &\rightarrow a d^{2} a^{4} \\
+  c^{2} d b c &\rightarrow a d a^{3} c d \\
+  c^{2} d a^{4} &\rightarrow a d a^{3} c^{2} \\
+  b a^{4} c a d &\rightarrow c d a^{4} b a \\
+  c b c a d &\rightarrow a d^{2} a^{4} b a \\
+  c^{2} d b a d &\rightarrow a d a^{3} c d b a
+\end{aligned}
+\)
+
+<!-- Generated from examples-1-relation-000-049.cpp, test case 000. -->

docs/examples/1-relation/001.md

@@ -0,0 +1,35 @@
+#\#001 aabaababba=baaba
+
+## Original presentation
+
+\(
+\left\langle
+  a, b \;\middle|\; a^{2} b a^{2} b a b^{2} a = b a^{2} b a
+\right\rangle
+\)
+
+## Modified presentation
+
+\(
+\left\langle
+  a, b, c, d \;\middle|\; a^{2} c d c = c a c,\; c = b a,\; d = a c b
+\right\rangle
+\)
+
+## Complete rewriting system
+
+Using recursive path order (`RPOCmp`) with \(a < d < c < b\):
+
+\(
+\begin{aligned}
+  b a &\rightarrow c \\
+  a c b &\rightarrow d \\
+  a^{2} c d c &\rightarrow c a c \\
+  b c a c &\rightarrow c a c d c \\
+  b d &\rightarrow c^{2} b \\
+  a c^{2} &\rightarrow d a \\
+  b c d &\rightarrow c a c d c b
+\end{aligned}
+\)
+
+<!-- Generated from examples-1-relation-000-049.cpp, test case 001. -->

docs/examples/1-relation/002.md

@@ -0,0 +1,44 @@
+#\#002 abbabbaaaa=babba
+
+## Original presentation
+
+\(
+\left\langle
+  a, b \;\middle|\; a b^{2} a b^{2} a^{4} = b a b^{2} a
+\right\rangle
+\)
+
+## Modified presentation
+
+\(
+\left\langle
+  a, b, c, d \;\middle|\; c^{2} d a = b c a,\; c = a b^{2},\; d = a^{3}
+\right\rangle
+\)
+
+## Complete rewriting system
+
+Using recursive path order (`RPOCmp`) with \(c < d < a < b\):
+
+\(
+\begin{aligned}
+  b c a &\rightarrow c^{2} d a \\
+  a b^{2} &\rightarrow c \\
+  a^{3} &\rightarrow d \\
+  b c d &\rightarrow c^{2} d^{2} \\
+  a d &\rightarrow d a \\
+  d b^{2} &\rightarrow a^{2} c \\
+  b c^{2} &\rightarrow c^{2} d c \\
+  a c^{2} a &\rightarrow d c^{2} d c d^{2} c d a \\
+  a c^{2} d &\rightarrow d c^{2} d c d^{2} c d^{2} \\
+  a c^{3} &\rightarrow d c^{2} d c d^{2} c d c \\
+  d c^{2} d c d^{2} c d^{2} c d c &\rightarrow c^{3} \\
+  d c^{2} d c d^{2} c d^{2} c d^{2} &\rightarrow c^{2} d \\
+  d c^{2} d c d^{2} c d^{2} c d a &\rightarrow c^{2} a \\
+  d c^{2} d c d^{2} c d^{2} c^{3} a &\rightarrow c^{4} d c d^{2} c d^{2} c d a \\
+  d c^{2} d c d^{2} c d^{2} c^{3} d &\rightarrow c^{4} d c d^{2} c d^{2} c d^{2} \\
+  d c^{2} d c d^{2} c d^{2} c^{4} &\rightarrow c^{4} d c d^{2} c d^{2} c d c
+\end{aligned}
+\)
+
+<!-- Generated from examples-1-relation-000-049.cpp, test case 002. -->

docs/examples/1-relation/003.md

@@ -0,0 +1,38 @@
+#\#003 babbabaaba=abba
+
+## Original presentation
+
+\(
+\left\langle
+  a, b \;\middle|\; b a b^{2} a b a^{2} b a = a b^{2} a
+\right\rangle
+\)
+
+## Modified presentation
+
+\(
+\left\langle
+  a, b, c, d, e \;\middle|\; c d c = e c,\; c = b a,\; d = b c^{2} a,\; e = a b
+\right\rangle
+\)
+
+## Complete rewriting system
+
+Using recursive path order (`RPOCmp`) with \(c < d < e < a < b\):
+
+\(
+\begin{aligned}
+  b a &\rightarrow c \\
+  b c^{2} a &\rightarrow d \\
+  a b &\rightarrow e \\
+  e c &\rightarrow c d c \\
+  b e &\rightarrow c b \\
+  b c^{2} e &\rightarrow d b \\
+  a d &\rightarrow c d c^{2} a \\
+  a c &\rightarrow e a \\
+  b c d c &\rightarrow c b c \\
+  b c^{3} d c &\rightarrow d b c
+\end{aligned}
+\)
+
+<!-- Generated from examples-1-relation-000-049.cpp, test case 003. -->

docs/examples/1-relation/004.md

@@ -0,0 +1,50 @@
+#\#004 baabbaaaba=aabba
+
+## Original presentation
+
+\(
+\left\langle
+  a, b \;\middle|\; b a^{2} b^{2} a^{3} b a = a^{2} b^{2} a
+\right\rangle
+\)
+
+## Modified presentation
+
+\(
+\left\langle
+  a, b, c, d \;\middle|\; c d b a = a^{2} b^{2} a,\; c = b a^{2} b,\; d = b a^{3}
+\right\rangle
+\)
+
+## Complete rewriting system
+
+Using recursive path order (`RPOCmp`) with \(c < d < a < b\):
+
+\(
+\begin{aligned}
+  b a^{2} b &\rightarrow c \\
+  b a^{3} &\rightarrow d \\
+  a^{2} b^{2} a &\rightarrow c d b a \\
+  b a^{2} d &\rightarrow c a^{3} \\
+  b a^{2} c &\rightarrow c a^{2} b \\
+  b a c d b a &\rightarrow d b^{2} a \\
+  b c d b a &\rightarrow c b a \\
+  a^{2} b c &\rightarrow c d c \\
+  a^{2} b d &\rightarrow c d^{2} \\
+  d a b^{2} a &\rightarrow c^{2} d^{2} b a \\
+  d a b d &\rightarrow c^{2} d^{3} \\
+  d a b c &\rightarrow c^{2} d^{2} c \\
+  b a c d^{2} &\rightarrow d b d \\
+  b a c d c &\rightarrow d b c \\
+  b c d^{2} &\rightarrow c d \\
+  b c d c &\rightarrow c^{2} \\
+  a^{2} c b a &\rightarrow c d c d b a \\
+  d a c b a &\rightarrow c^{2} d^{2} c d b a \\
+  a^{2} c d &\rightarrow c d c d^{2} \\
+  a^{2} c^{2} &\rightarrow c d c d c \\
+  d a c d &\rightarrow c^{2} d^{2} c d^{2} \\
+  d a c^{2} &\rightarrow c^{2} d^{2} c d c
+\end{aligned}
+\)
+
+<!-- Generated from examples-1-relation-000-049.cpp, test case 004. -->

docs/examples/1-relation/005.md

@@ -0,0 +1,42 @@
+#\#005 baaaaabbba=aaaaa
+
+## Original presentation
+
+\(
+\left\langle
+  a, b \;\middle|\; b a^{5} b^{3} a = a^{5}
+\right\rangle
+\)
+
+## Modified presentation
+
+\(
+\left\langle
+  a, b, c, d \;\middle|\; b c^{2} d a = c^{2} a,\; c = a^{2},\; d = a b^{3}
+\right\rangle
+\)
+
+## Complete rewriting system
+
+Using recursive path order (`RPOCmp`) with \(a < d < b < c\):
+
+\(
+\begin{aligned}
+  c &\rightarrow a^{2} \\
+  b a^{4} d a &\rightarrow a^{5} \\
+  a b^{3} &\rightarrow d \\
+  a b^{2} a^{5} &\rightarrow d a^{4} d a \\
+  b a^{4} d^{2} &\rightarrow a^{4} d \\
+  a b^{2} a^{4} d &\rightarrow d a^{4} d^{2} \\
+  a b a^{4} d &\rightarrow d a^{4} d^{3} \\
+  a b a^{5} &\rightarrow d a^{4} d^{2} a \\
+  d a^{4} d^{4} &\rightarrow a^{5} d \\
+  d a^{4} d^{3} a &\rightarrow a^{6} \\
+  b a^{9} d &\rightarrow a^{8} d^{4} \\
+  b a^{10} &\rightarrow a^{8} d^{3} a \\
+  d a^{4} d^{2} a^{5} d &\rightarrow a^{9} d^{4} \\
+  d a^{4} d^{2} a^{6} &\rightarrow a^{9} d^{3} a
+\end{aligned}
+\)
+
+<!-- Generated from examples-1-relation-000-049.cpp, test case 005. -->

docs/examples/1-relation/007.md

@@ -0,0 +1,35 @@
+#\#007 abaaabaaba=babaaa
+
+## Original presentation
+
+\(
+\left\langle
+  a, b \;\middle|\; a b a^{3} b a^{2} b a = b a b a^{3}
+\right\rangle
+\)
+
+## Modified presentation
+
+\(
+\left\langle
+  a, b, c, d \;\middle|\; a c a^{2} c a c = c^{2} a^{2},\; c = b a,\; d = a b a
+\right\rangle
+\)
+
+## Complete rewriting system
+
+Using recursive path order (`RPOCmp`) with \(a < d < b < c\):
+
+\(
+\begin{aligned}
+  c &\rightarrow b a \\
+  a b a &\rightarrow d \\
+  b d a^{2} &\rightarrow d a d^{2} \\
+  b d a d &\rightarrow d a d^{2} b a \\
+  a b d &\rightarrow d b a \\
+  d b a^{2} d &\rightarrow a d a d^{2} b a \\
+  d b a^{3} &\rightarrow a d a d^{2}
+\end{aligned}
+\)
+
+<!-- Generated from examples-1-relation-000-049.cpp, test case 007. -->