Integer Modulo n

[muratcankilic96]

Are there any future plans to add integer modulo n?

I mean features such as multiplicative/additive inverses modulo n, order a modulo n, primitive roots modulo n, quadratic residues etc.

[markrogoyski]

Hi @muratcankilic96,

Thank you for your interest in MathPHP. And thank you for your feature request.

We can consider modular arithmetic for upcoming feature development. What kinds of things are you looking to do? And what specific functions do you consider "must haves" vs "nice to have?"

And are there any reference libraries with similar functionality that you think have good interfaces/APIs (or bad interfaces/APIs)?

Thanks, Mark

[muratcankilic96]

Hello @markrogoyski

Thanks for replying.

Must have features are:

• Find x mod n
• Find a^b mod n
• Find a! mod n
• Whether a and b are congruent mod n
• Additive and multiplicative inverses mod n
• Order of a mod n
• Primitive roots mod n
  • Whether the congruence system has primitive roots or not mod n
  • Count of primitive roots (if exists) mod n
  • List of primitive roots mod n
  • Whether r is a primitive root or not
  • Index base r of a mod n

Nice to have:

• Solve linear congruences of the form ax ≡ b (mod n)
• Quadratic residue: Legendre and Jacobi symbols

For reference, I have implemented several modular arithmetic features myself in C#. We need Euler totient function and MathPHP already supports that.

[Beakerboy]

If you have already implemented several of these in another language, please translate them into PHP, add some unit tests, and submit the work in a merge request. That would be the fastest way to see these features in this library.