power_direct()

ring_elem PolyRing::power_direct ( const ring_elem f, int n ) const

protected

Definition at line 868 of file poly.cpp.

{
    ring_elem result, g, rest, h, tmp;
    ring_elem coef1, coef2, coef3;
 
    Nterm *lead = ff;
    if (lead == nullptr) return ZERO_RINGELEM;
 
    rest = lead->next;
    g = from_long(1);
 
    // Start the result with the n th power of the lead term
    Nterm *t = new_term();
    t->coeff = K_->power(lead->coeff, n);
    M_->power(lead->monom, n, t->monom);
    t->next = nullptr;
    //  if (_base_ring != NULL) normal_form(t);  NOT NEEDED
    result = t;
 
    if (POLY(rest) == nullptr) return result;
    monomial m = M_->make_one();
 
    mpz_t bin_c;
 
    mpz_init_set_ui(bin_c, 1);
 
    for (int i = 1; i <= n; i++)
    {
        tmp = mult(g, rest);
        g = tmp;
 
        mpz_mul_ui(bin_c, bin_c, n - i + 1);
        mpz_fdiv_q_ui(bin_c, bin_c, i);
 
        coef1 = K_->from_int(bin_c);
 
        if (!K_->is_zero(coef1))
        {
            coef2 = K_->power(lead->coeff, n - i);
            coef3 = K_->mult(coef1, coef2);
            M_->power(lead->monom, n - i, m);
 
            h = mult_by_term(g, coef3, m);
            add_to(result, h);
        }
    }
    mpz_clear(bin_c);
    return result;
}

References Ring::add_to(), Nterm::coeff, from_long(), PolynomialRing::K_, PolynomialRing::M_, Nterm::monom, monomial, mult(), mult_by_term(), new_term(), Nterm::next, POLY, result(), and ZERO_RINGELEM.

Referenced by power().