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Power in $ \mathbb {Z}$/p$ \mathbb {Z}$ and in $ \mathbb {Z}$/p$ \mathbb {Z}$[x] : ^

To compute a to the power n in $ \mathbb {Z}$/p$ \mathbb {Z}$, 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 $ \mathbb {Z}$/p$ \mathbb {Z}$[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).



giac documentation written by Renée De Graeve and Bernard Parisse