5.6. Modular evaluation

Sometimes when working with large numbers, it might be faster if results are modded after each calculation. To use it you just add "mod <integer>" after the expression. Example:

2^(5!) * 3^(6!) mod 5

You can calculate the inverses of numbers mod some integer by just using rational numbers (of course the inverse has to exist). Examples:

10^-1 mod 101
1/10 mod 101

You can also do modular evaluation with matrices including taking inverses, powers and dividing. Example:

A = [1,2;3,4]
B = A^-1 mod 5
A*B mod 5

This should yield the identity matrix as B will be the inverse of A mod 5.

Some functions such as sqrt or log work in a different way when in modulo mode. These will then work like their discrete versions working within the ring of integers you selected. For example:

genius> sqrt(4) mod 7
=
[2      5]
genius> 2*2 mod 7
= 4

sqrt will actually return all the possible square roots.