libgivaro-dev 4.0.2-5 / usr / include / givaro / givpoly1factor.inl

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// ================================================================= //
// 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
// Irreducibily test
// Factorisations de  Polynomes dans Fp[X] :
//      Distinct Degree
//      Cantor-Zassenhaus
//      Berlekamp : in LinBox
// Time-stamp: <26 Feb 08 13:37:26 Jean-Guillaume.Dumas@imag.fr>
// ================================================================= //
#ifndef __GIVARO_poly1_facto_INL
#define __GIVARO_poly1_facto_INL
#include <givaro/givpower.h>
#include <givaro/givcaster.h>

//!@todo use NTL if available ?


namespace Givaro {

// ---------------------------------------------------------------
// Splits a polynomial into prime factors of same degree
// ---------------------------------------------------------------

template<class Domain, class Tag, class RandomIterator>
template< template<class, class> class Container, template <class> class Alloc >
inline void Poly1FactorDom<Domain,Tag, RandomIterator>::SplitFactor(
    Container< Rep, Alloc<Rep> > & L
    , const Rep& G
    , Degree d
    , Residu_t MOD) const
{
    Degree dG; this->degree(dG,G);
    if (dG == d)
        L.push_back(G);
    else {
        int splitted = 0;
        while (! splitted) {
            Rep G1, G2;
            this->gcd(G1, G, this->random(_g, G2, dG-1) );
            Degree dG1; this->degree(dG1,G1);
// write(std::cerr << "SF rd: ", G2) << std::endl;
// write(std::cerr << "SF G1: ", G1) << std::endl;
            if ( dG1 != dG) {
                if (dG1 > 0 ) {
                    splitted = 1;
                    SplitFactor ( L, G1, d, MOD) ;
                    this->div(G2, G, G1);
                    SplitFactor ( L, G2, d, MOD) ;
                    return ;
                }

                Integer iMOD; Caster(iMOD, MOD);
                Integer pp = (power(iMOD, d.value()) - 1)/2;
// std::cerr << "pp: " << pp << std::endl;
                Rep tp;
                this->gcd(G1, G,
                          this->subin( this->powmod(tp, G2, pp, G), 
                                       _domain.one) 
                          );

                this->degree(dG1,G1);
// write(std::cerr << "SF t2: ", tp2) << std::endl;
// write(std::cerr << "SF G1: ", G1) << std::endl;
                if ( ( dG1 != dG) && (dG1 > 0 ) ) {
                    splitted = 1 ;
                    SplitFactor ( L, G1, d, MOD) ;
                    this->div( G2, G, G1);
                    SplitFactor ( L, G2, d, MOD) ;
                }
            }
        }
    }
}


template<class Domain, class Tag, class RandomIterator>
inline typename Poly1FactorDom<Domain,Tag, RandomIterator>::Rep& Poly1FactorDom<Domain,Tag, RandomIterator>::SplitFactor(
    Rep& G1
    , const Rep& G
    , Degree d
    , Residu_t MOD)  const  {
    Degree dG;this->degree(dG,G);
    if (dG == d)
        return G1.copy(G) ;
    else {
        while (1) {
            Rep tmp;
            this->gcd(G1, G, this->random(_g, tmp, d));
// write(std::cerr << "SF rd: ", tmp) << std::endl;
// write(std::cerr << "SF G1: ", G1) << std::endl;
            Degree dG1; this->degree(dG1,G1);
            if ( dG1 != dG) {
                if (dG1 > 0 ) {
                    return G1;
                }
                Integer iMOD; Caster(iMOD, MOD);
                Integer pp = (power(iMOD, d.value()) - 1)/2;
                Rep tp, tp2, G2;
                this->gcd(G2,G, this->sub(tp2, this->powmod(tp, tmp, pp, G) , _domain.one) );
                Degree dG2; this->degree(dG2,G2);
// write(std::cerr << "SF t2: ", tp2) << std::endl;
// write(std::cerr << "SF G2: ", G2) << std::endl;
                if ( dG2 != dG) {
                   if ( dG2 > 0 ) {
                        return G1.copy(G2);
                    }
// UNNECESSARY : ANYTHING FOUND BY G3 WOULD HAVE THE COFACTOR IN G2
                     Rep G3; this->gcd(G3, G, this->add(tp2,tp,_domain.one) );
                     Degree dG3; this->degree(dG3,G3);
// write(std::cerr << "SF t3: ", tp2) << std::endl;
// write(std::cerr << "SF G3: ", G3) << std::endl;
                     if (( dG3 != dG) && (dG3 > 0 )) {
                         return G1.copy(G3);
                     }
                }
            }
        }
    }
}


// ---------------------------------------------------------------
// Splits a polynomial into divisors of homogenous prime factors
// ---------------------------------------------------------------

template<class Domain, class Tag, class RandomIterator>
template< template<class, class> class Container, template <class> class Alloc >
inline void Poly1FactorDom<Domain,Tag, RandomIterator>::DistinctDegreeFactor(
    Container< Rep, Alloc<Rep> > & L
    , const Rep& f
    , Residu_t MOD)  const  {

// write(std::cerr << "DD in: ", f) << std::endl;
    Rep W, D, P = f;
    Degree dP;
    Rep Unit, G1;
    this->init(Unit, Degree(1));
    W.copy(Unit);
    this->degree(dP,P); Degree dPo = (dP/2);
    for(Degree dp = 1; dp <= dPo; ++dp) {
// std::cerr << "DD degree: " << dp << std::endl;
        this->powmod(W, D.copy(W), MOD, P);
        this->gcd (G1,this->sub(D,W,Unit), P) ;
        Degree dG1; this->degree(dG1,G1);
// write(std::cerr << "DD found: ", G1) << ", of degree " << dG1 << std::endl;
        if ( dG1 > 0 ) {
            SplitFactor (L, G1, dp, MOD);
            this->divin(P,G1);
        }
    }
    this->degree(dP,P);
    if (dP > 0)
        L.push_back(P);
// write(std::cerr << "DD: ", P) << std::endl;
}

// ---------------------------------------------------------------
// Cantor-Zassenhaus Polynomial factorization over Z/pZ
// ---------------------------------------------------------------

template<class Domain, class Tag, class RandomIterator>
template< template<class, class> class Container, template <class> class Alloc>
inline void
Poly1FactorDom<Domain,Tag, RandomIterator>::CZfactor( Container< Rep, Alloc<Rep> > & Lf,
			   Container< uint64_t, Alloc<uint64_t> > & Le,
	       const Rep& P,
	       Residu_t MOD)  const
{
// write(std::cerr << "CZ in: ", P) << std::endl;
    Degree dp;
    this->degree(dp,P);
    size_t nb=(size_t)dp.value()+1;
    Rep * g = new Rep[nb];
    this->sqrfree(nb,g,P);
// std::cerr << "CZ sqrfree: " << nb << std::endl;
    for(size_t i = 0; i<nb;++i) {
        size_t this_multiplicity = Lf.size();
        DistinctDegreeFactor(Lf, g[i], MOD) ;
        Le.resize(Lf.size());
        for( ; this_multiplicity < Lf.size(); ++this_multiplicity)
            Le[this_multiplicity] = i+1;
// std::cerr << "multiplicities";
// for (typename Container< uint64_t, Alloc<uint64_t> >::const_iterator e=Le.begin(); e!=Le.end(); ++e)
// std::cerr << " " << *e;
// std::cerr << std::endl;

    }
    ::delete [] g;
}



// ---------------------------------------------------------------
// Irreducibility tests
// ---------------------------------------------------------------

template<class Domain, class Tag, class RandomIterator>
inline bool Poly1FactorDom<Domain,Tag, RandomIterator>::is_irreducible( const Rep& P
								  , Residu_t MOD ) const
{
	Rep W,D;
	this->gcd(W,this->diff(D,P),P);
	Degree d, dP;
	if (this->degree(d,W) > 0) return 0;
	// Distinct degree free ?
	Rep Unit, G1;
	this->init(Unit, Degree(1));
	W.copy(Unit);
	this->degree(dP,P); Degree dPo = (dP/2);
	for(Degree dp = 1; dp <= dPo; ++dp) {
		this->powmod(W, D.copy(W), MOD, P);
		this->gcd (G1, this->sub(D,W,Unit), P) ;
		if ( this->degree(d,G1) > 0 ) return 0;
	}
	return 1;
}


// ---------------------------------------------------------------
// Gives one non-trivial factor of P if P is reducible
// returns P otherwise
// ---------------------------------------------------------------

template<class Domain, class Tag, class RandomIterator>
inline typename Poly1FactorDom<Domain,Tag, RandomIterator>::Rep& Poly1FactorDom<Domain,Tag, RandomIterator>::factor(
    Rep& W
    , const Rep& P
    , Residu_t MOD)  const
{
// write(cerr << "In factor P:", P) << endl;
        // Square free ?
    Rep D; this->gcd(W,diff(D,P),P);
    Degree d, dP;
// write(cerr << "In factor P':", D) << "(deg: " << degree(d,D) << ")" << endl;
// write(cerr << "In factor P^P':", W) << "(deg: " << degree(d,W) << ")" << endl;

    if (this->degree(d,W) > 0) return W;
        // Distinct degree free ?
    Rep Unit, G1; init(Unit, Degree(1));
// write(cerr << "In factor U:", Unit) << endl;
    W.copy(Unit);
    this->degree(dP,P); Degree dPo = (dP/2);
    for(Degree dp = 1; dp <= dPo; ++dp) {
// write(cerr << "In factor W:(deg: " << degree(d,W) << "):", W) << endl;
        this->powmod(W, D.copy(W), MOD, P);
        this->gcd (G1, sub(D,W,Unit), P) ;
        Degree dG1; this->degree(dG1,G1);
        if ( dG1 > 0 ) {
            if (dG1 < dP)
                return W.copy(G1);
            else
                return SplitFactor(W,G1,dp,MOD);
        }
    }
    return W.copy(P);
}

} // Givaro


#endif // __GIVARO_poly1_facto_INL

/* -*- mode: C++; tab-width: 8; indent-tabs-mode: t; c-basic-offset: 8 -*- */
// vim:sts=8:sw=8:ts=8:noet:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s

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