// =============================================================== //
// Copyright(c)'1994-2009 by The Givaro group
// This file is part of Givaro.
// Givaro is governed by the CeCILL-B license under French law
// and abiding by the rules of distribution of free software.
// see the COPYRIGHT file for more details.
// Givaro / Athapascan-1
// Cyclotomic polynomials
// Time-stamp: <15 Jul 08 10:40:47 Jean-Guillaume.Dumas@imag.fr>
// =============================================================== //
#ifndef __GIVARO_poly1_cyclo_INL
#define __GIVARO_poly1_cyclo_INL
#include <givaro/givintfactor.h>

namespace Givaro {

// ---------------------------------------------------------------
// Composition by a power of X
// ---------------------------------------------------------------
template<class Domain>
inline typename Poly1Dom<Domain,Dense>::Rep& Poly1Dom<Domain,Dense>::power_compose(Rep& W, const Rep& P, long b) const
{
  Degree dp; degree(dp, P);
  Type_t lc;
  leadcoef(lc, P);
  assign( W, b*dp.value(), lc); // all coeffs to zero, except leading ...
  for(long i=0;i<dp.value();++i) {
      _domain.assign(W[i*b], P[i]);
  }
  return setdegree(W);
}




// ---------------------------------------------------------------
// n th Cyclotomic polynomial
// ---------------------------------------------------------------
template<class Domain>
inline typename Poly1Dom<Domain,Dense>::Rep& Poly1Dom<Domain,Dense>::cyclotomic( Rep& P, long n) const
{
  // P must provide an indeterminate
//   Integer In(n);
    IntFactorDom<> IF;
    if (n <= 1) {
        init(P, Degree(1));
        _domain.assign(P[0], _domain.one);
        _domain.negin(P[0]);
        return setdegree(P);
    } else if (IF.isprime(n)) {
        init(P, Degree(n-1));
        for(size_t i=(size_t)n-1;--i;)
            _domain.assign(P[i], _domain.one);
        return setdegree(P);
    }
    else {
        long q,f;
        q = n / 2;
        f = n % 2;
        if (f) {
            IntFactorDom<>::Rep If, Iq;
            IF.divexact(Iq, n, IF.factor(If,n) );
            IF.convert(f, If);
            IF.convert(q, Iq);
            Rep inter;
            cyclotomic(inter,q);
            if (q % f) {
                Rep res;
                power_compose(res, inter, f);
                return div(P, res, inter);
            } else
                return power_compose(P,inter,f);
        } else {
            if (q%2) {
                    // q odd
                cyclotomic(P,q);
                Degree di;
                degree(di, P);
                for(int i=1;i<=di.value();i+=2)
                    _domain.negin(P[i]);
                return setdegree(P);
            } else {
                    // q even
                Rep inter;
                cyclotomic(inter,q);
                Degree di;
                degree(di, inter);
                return power_compose(P, inter, 2);
            }
        }
    }
}

} // Givaro

#endif // __GIVARO_poly1_cyclo_INL
