Rebuild a fraction from it’s value modulo p : fracmod

### 2.31.12 Rebuild a fraction from it’s value modulo p : `fracmod`

`fracmod` takes two arguments, an integer n (representing a fraction) and an integer p (the modulus).
If possible, `fracmod` returns a fraction a/b such that

− |
√ |
p
2
| < a ≤ |
√ |
p
2
| , 0 ≤ b < |
√ |
p
2
| , n × b =a (mod p )

In other words n=a/b(mod p ).
Input :

`fracmod(3,13)`

Output :

`-1/4`

Indeed : 3*−4=−12=1 (mod 13), hence 3=−1/4%13.
Input :

`fracmod(13,121)`

Output :

`-4/9`

Indeed : 13×−9=−117=4 (mod 121) hence 13=−4/9%13.