\\ SLIDE 5 H = hgminit([5]); hgmparams(H) hgmalpha(H) hgmcyclo(H) hgmgamma(H) \\ SLIDE 6 H2 = hgminit([2,3,4],[1,5]); hgmparams(H2) hgmalpha(H2) hgmgamma(H2) \\ SLIDE 9 hgmeulerfactor(H, -1, 3) \\ good prime hgmeulerfactor(H, -1, 2) \\ tame prime hgmeulerfactor(H, -1, 5) \\ wild primes not implemented hgmeulerfactor(H, 1/3, 3) \\ tame prime hgmeulerfactor(H, 1/3, 2) \\ good prime hgmeulerfactor(H, 1/3, 5) \\ wild primes not implemented \\ For H2: 2,3,5 are wild hgmeulerfactor(H2, 2, 7) \\ good prime hgmeulerfactor(H2, 1/8, 7) \\ tame prime \\ SLIDE 11 lfunhgm(H, 1/2); [N] = lfunparams(L); N \\ the conductor factor(N) lfuneuler(L,2) lfuneuler(L,3) lfuneuler(L,5) lfuneuler(L,7) L = lfunhgm(H, 1/64); \\ more complicated [N] = lfunparams(L); N factor(N) lfuneuler(L,2) lfuneuler(L,3) lfuneuler(L,5) lfuneuler(L,7) \\ SLIDE 12 hgmcoefs(H,1/64,7^6)[7^6] \\ slow ! hgmcoef(H,1/64,7^6) hgmcoef(H, 1/64, 10)