modTable 2.0.1

Prints addition and multiplication tables for Z mod n*Z

About mod-table

mod-table prints the addition and multiplication tables for the ring of integers modulo n, denoted ℤ/nℤ - and ℤ/nℤ is a field if and only if n is prime.

Installing mod-table

    python3 -m pip install modTable --upgrade

It's recommended to install into a local venv, or if installing systemwide as the super-user to make a venv in /usr/local/venv, and install it there. For some helpful hints about how to do this see the addendum in the lsseq repo.

Testing mod-table

Running mod-table on the command line should show you this.

$ mod-table 5
ℤ/5ℤ
 + |  0  1  2  3  4 
--------------------
 0 |  0  1  2  3  4 
 1 |  1  2  3  4  0 
 2 |  2  3  4  0  1 
 3 |  3  4  0  1  2 
 4 |  4  0  1  2  3 

 * |  0  1  2  3  4 
--------------------
 0 |  0  0  0  0  0 
 1 |  0  1  2  3  4 
 2 |  0  2  4  1  3 
 3 |  0  3  1  4  2 
 4 |  0  4  3  2  1 

$ mod-table 6
ℤ/6ℤ
 + |  0  1  2  3  4  5 
-----------------------
 0 |  0  1  2  3  4  5 
 1 |  1  2  3  4  5  0 
 2 |  2  3  4  5  0  1 
 3 |  3  4  5  0  1  2 
 4 |  4  5  0  1  2  3 
 5 |  5  0  1  2  3  4 

 * |  0  1  2  3  4  5 
-----------------------
 0 |  0  0  0  0  0  0 
 1 |  0  1  2  3  4  5 
 2 |  0  2  4  0  2  4 
 3 |  0  3  0  3  0  3 
 4 |  0  4  2  0  4  2 
 5 |  0  5  4  3  2  1 

See how ℤ/6ℤ can't be a field because 2, 3 and 4 don't have multiplicative inverses. That is, there's no other number that when multiplied by 2, 3 or 4 gives 1.

But in ℤ/5ℤ all the non-zero numbers have multiplicative inverses, so it is a field!

Time to play - Enjoy!