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2.31.9  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).


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