Step by Step solution about How to resolve the algorithm AKS test for primes step by step in the Mathematica / Wolfram Language programming language

Explanation:

Part 1: Powers of (x-1)

• Print["powers of (x-1)"]: Prints the title "powers of (x-1)".
• (x - 1)^( Range[0, 7]): Calculates the powers of (x-1) from 0 to 7 and stores the results in a list.
• Expand simplifies the expressions.
• TableForm: Displays the results in a tabular format.

Part 2: Primes under 50

• poly[p_] := (x - 1)^p - (x^p - 1) // Expand;: Defines a function poly that calculates the polynomial (x - 1)^p - (x^p - 1) for a given integer p.
• coefflist[p_Integer] := Coefficient[poly[p], x, #] & /@ Range[0, p - 1];: Defines a function coefflist that extracts the coefficients of the polynomial poly for a given p.
• AKSPrimeQ[p_Integer] := (Mod[coefflist[p] , p] // Union) == {0};: Defines a function AKSPrimeQ that checks if a given integer p is prime. It does this by calculating the coefficients of the polynomial poly for p and checking if all non-zero coefficients are divisible by p. If they are, then p is prime.
• Select[Range[1, 50], AKSPrimeQ]: Uses the function Select to find all primes under 50.

Print["powers of (x-1)"]
(x - 1)^( Range[0, 7]) // Expand // TableForm   
Print["primes under 50"]
poly[p_] := (x - 1)^p - (x^p - 1) // Expand;
coefflist[p_Integer] := Coefficient[poly[p], x, #] & /@ Range[0, p - 1];
AKSPrimeQ[p_Integer] := (Mod[coefflist[p] , p] // Union) == {0};
Select[Range[1, 50], AKSPrimeQ]