Hypergeometric templates (3/4) : example
To such a hypergeometric template is associated a number of additional parameters: the
degree d, the (motivic) weight w, a Hodge polynomial P, a Tate twist T, and a normalizing
M-factor M =
Q
n nnγn . The hgmparams function returns
[d, w, [P, T], M] .
Example with cyclotomic parameters [5], [1, 1, 1, 1]:
? H = hgminit([5]);
? hgmparams(H)
%2 = [4, 3, [x^3+x^2+x+1,0], 3125]
? hgmalpha(H)
%3 = [[1/5, 2/5, 3/5, 4/5], [0, 0, 0, 0]]
? hgmcyclo(H)
%4 = [Vecsmall([5]), Vecsmall([1, 1, 1, 1])]
? hgmgamma(H)
%5 = Vecsmall([-5,0,0,0,1]) \\ A/B = (x^5-1) / (x-1)^5
Atelier 2022 (13/01/2022) – p. 5/12