p = 13(the order values appear to go: gamma, `*`(gamma, `*`(p)), `*`(`^`(p, 2)), `*`(gamma, `*`(`^`(p, 3))), `*`(`^`(p, 4)), `*`(gamma, `*`(`^`(p, 5))), () .. () 

 

 

 

>    p := 13:

bound := 4:

 for alpha to bound do

          GF||alpha := PI(p^alpha, 4, 1):
         ord||alpha := order(GF||alpha, p^alpha):
      
od: print(``);

print(array([

['p', ``, 'alpha', ``, ``, 'p^alpha', ``, ``, '(({p^alpha-1}/4))[p]!', ORDER],

seq([p, ``, alpha, ``, ``, ifactor(p^alpha), ``, ``, GF||alpha, ifactor(ord||alpha)],

alpha = 1..bound)])): print(``);
 

 

 

array( 1 .. 5, 1 .. 10, [( 1, 5 ) = (``), ( 2, 7 ) = (``), ( 3, 3 ) = (2), ( 3, 9 ) = (72), ( 1, 10 ) = (ORDER), ( 5, 8 ) = (``), ( 5, 1 ) = (13), ( 3, 2 ) = (``), ( 3, 4 ) = (``), ( 1, 3 ) = (alpha),...
(9.2.2.1)
 

> gamma, 2*gamma*p, gamma*p^2, 2*gamma*p^3, `...`;
 

gamma, `+`(`*`(2, `*`(gamma, `*`(p)))), `*`(gamma, `*`(`^`(p, 2))), `+`(`*`(2, `*`(gamma, `*`(`^`(p, 3))))), `...` (9.2.2.2)
 

>