static
void compute_a_vals(Vec<ZZ>& a, long p, long e)
// computes a[m] = a(m)/m! for m = p..(e-1)(p-1)+1,
// as defined by Chen and Han.
// a.length() is set to (e-1)(p-1)+2
{
ZZ p_to_e = power_ZZ(p, e);
ZZ p_to_2e = power_ZZ(p, 2*e);
long len = (e-1)*(p-1)+2;
ZZ_pPush push(p_to_2e);
ZZ_pX x_plus_1_to_p = power(ZZ_pX(INIT_MONO, 1) + 1, p);
ZZ_pX denom = InvTrunc(x_plus_1_to_p - ZZ_pX(INIT_MONO, p), len);
ZZ_pX poly = MulTrunc(x_plus_1_to_p, denom, len);
poly *= p;
a.SetLength(len);
ZZ m_fac(1);
for (long m = 2; m < p; m++) {
m_fac = MulMod(m_fac, m, p_to_2e);
}
for (long m = p; m < len; m++) {
m_fac = MulMod(m_fac, m, p_to_2e);
ZZ c = rep(coeff(poly, m));
ZZ d = GCD(m_fac, p_to_2e);
if (d == 0 || d > p_to_e || c % d != 0) Error("cannot divide");
ZZ m_fac_deflated = (m_fac / d) % p_to_e;
ZZ c_deflated = (c / d) % p_to_e;
a[m] = MulMod(c_deflated, InvMod(m_fac_deflated, p_to_e), p_to_e);
}
}
static CYTHON_INLINE struct ZZ_pX ZZ_pE_to_ZZ_pX(struct ZZ_pE x)
{
return ZZ_pX(rep(x));
}