Power in ℤ/pℤ and in ℤ/pℤ[x] : ^

### 5.36.9 Power in ℤ/pℤ and in ℤ/pℤ[x] : ^

To compute a to the power n in ℤ/pℤ, we use the operator `^`. Xcas implementation is the binary power algorithm.
Input :

(5%13)`^`2

Output :

-1%13

To compute A to the power n in ℤ/pℤ[x], we use the operator `^` and the normal command .
Input :

normal(((2*x+1)%13)`^`5)

Output :

(6%13)*x`^`5+(2%13)*x`^`4+(2%13)*x`^`3+(1%13)*x`^`2+(-3%13)*x+1%13

because 10=−3 (mod 13), 40=1 (mod 13), 80=2 (mod 13), 32=6 (mod 13).