AssociativeOperationCounter-Cpp_port

In hopes of trying to make this program faster, I've ported this python variant to C++.

It will count and show all possible associative operations (semigroups) on a finite set of N elements, where N <= 4.

Compilation

To create a Makefile and run it using CMake:

• cmake -G "Unix Makefiles" -DCMAKE_BUILD_TYPE=Debug
• make
• ./AssociativeOperationCounter_Cpp_port

Notes:

To compile it under release mode in order to speed up running time use:

• cmake -G "Unix Makefiles" -DCMAKE_BUILD_TYPE=Release

This has only been tested on Linux.

Output files

The program will create a file output_<<N>>.txt with all generated semigroups.

The file will be located in the same directory as the executable, usually it will be in the parent directory. ( but, for example, when running the program in CLion, the output files will actually be stored in cmake-build-debug/ or cmake-build-release/)

Changing the cardinal of the set

To modify the cardinal of the set - on which you are generating semigroups -, please modify in main.cpp the line constexpr int CARDINAL_SET = <<Insert New Cardinal>>; and recompile the program.

Optimisation ideas:

Similarly to how I computed isomorphisms from one semigroup to another. I could do the same to the other non-associative grupoids. This way I refrain from checking associativity on a structure which is isomorphic to another non-associative structure.

The most obvious downside to this strategy would be heavy RAM/Heap usage