The GAP package latinsquare

latinsquare: A package for counting and generating Latin squares in GAP.

Using

Loading:

gap> LoadPackage("latinsquare");
──────────────────────────────────────────────────────────────────────────────────────────────────────────────
Loading latinsquare 0.1 (A package for counting and generating Latin squares in GAP.)
by Seyyed Ali Mohammadiyeh (https://github.com/basemax).
Homepage: https://github.com/BaseMax/LatinSquareGAP/
Report issues at https://github.com/BaseMax/LatinSquareGAP/issues
──────────────────────────────────────────────────────────────────────────────────────────────────────────────
true

Listing:

gap> LatinSquareList(1);
[[[1]]]
gap> Length(LatinSquareList(1));
1
gap> LatinSquareList(2);
[[[1, 2], [2, 1]], [[2, 1], [1, 2]]]
gap> Length(LatinSquareList(2));
2
gap> LatinSquareList(3);
[[[1, 2, 3], [2, 3, 1], [3, 1, 2]], [[1, 2, 3], [3, 1, 2], [2, 3, 1]],
[[1, 3, 2], [2, 1, 3], [3, 2, 1]], [[1, 3, 2], [3, 2, 1], [2, 1, 3]],
[[2, 1, 3], [1, 3, 2], [3, 2, 1]], [[2, 1, 3], [3, 2, 1], [1, 3, 2]],
[[2, 3, 1], [1, 2, 3], [3, 1, 2]], [[2, 3, 1], [3, 1, 2], [1, 2, 3]],
[[3, 1, 2], [1, 2, 3], [2, 3, 1]], [[3, 1, 2], [2, 3, 1], [1, 2, 3]],
[[3, 2, 1], [1, 3, 2], [2, 1, 3]], [[3, 2, 1], [2, 1, 3], [1, 3, 2]]]
gap> Length(LatinSquareList(3));
12
gap> LatinSquareList(4);
[[[1, 2, 3, 4], [2, 1, 4, 3], [3, 4, 1, 2], [4, 3, 2, 1]],
[[1, 2, 3, 4], [2, 1, 4, 3], [3, 4, 2, 1], [4, 3, 1, 2]],
[[1, 2, 3, 4], [2, 1, 4, 3], [4, 3, 1, 2], [3, 4, 2, 1]],
[[1, 2, 3, 4], [2, 1, 4, 3], [4, 3, 2, 1], [3, 4, 1, 2]],
....[[4, 3, 2, 1], [3, 4, 1, 2], [2, 1, 4, 3], [1, 2, 3, 4]]]
gap> Length(LatinSquareList(4));
576

Counting:

gap> LatinSquareCount(1);
1
gap> LatinSquareCount(2);
2
gap> LatinSquareCount(3);
12
gap> LatinSquareCount(4);
576
gap> LatinSquareCount(5);
161280

Tests

$ gap -A testall.g
┌───────┐ GAP 4.15dev built on 2025-04-07 18:12:09+0330
│ GAP │ https://www.gap-system.org
└───────┘ Architecture: x86_64-pc-linux-gnu-default64-kv10
Configuration: gmp 6.3.0, GASMAN, readline
Loading the library and packages ...
Packages: GAPDoc 1.6.7, PrimGrp 3.4.4, SmallGrp 1.5.4, TransGrp 3.6.5
Try '??help'for help. See also '?copyright', '?cite' and '?authors'
───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Loading latinsquare 0.1 (A package forcounting and generating Latin squaresin GAP.)
by Seyyed Ali Mohammadiyeh (https://github.com/basemax).
Homepage: https://github.com/BaseMax/LatinSquareGAP/blob/main/
Report issues at https://github.com/BaseMax/LatinSquareGAP/issues
───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Architecture: x86_64-pc-linux-gnu-default64-kv10
testing: /home/ali/.gap/pkg/latinsquare/tst/count.tst
6189 ms (360 ms GC) and 734MB allocated for count.tst
testing: /home/ali/.gap/pkg/latinsquare/tst/list.tst
7716 ms (993 ms GC) and 980MB allocated for list.tst
-----------------------------------
total 13905 ms (1353 ms GC) and 1.67GB allocated
0 failures in 2 files
#I No errors detected while testing

Contact

Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-53153, I. R. Iran

alim@kashanu.ac.ir

max@std.kashanu.ac.ir

maxbasecode@gmail.com

License

GPL-2.0-or-later

Copyright 2025, Seyyed Ali Mohammadiyeh (Max Base)