fac_sqrfree.cc

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/* emacs edit mode for this file is -*- C++ -*- */
 
 
#include "config.h"
 
 
#include "cf_assert.h"
 
#include "cf_defs.h"
#include "canonicalform.h"
#include "cf_map.h"
#include "cf_algorithm.h"
 
#ifdef HAVE_FLINT
#include "FLINTconvert.h" // for __FLINT_RELEASE
#endif
 
static int
compareFactors( const CFFactor & f, const CFFactor & g )
{
    return f.exp() > g.exp();
}
 
CFFList
sortCFFList( CFFList & F )
{
    F.sort( compareFactors );
 
    int exp;
    CanonicalForm f;
    CFFListIterator I = F;
    CFFList result;
 
    // join elements with the same degree
    while ( I.hasItem() ) {
        f = I.getItem().factor();
        exp = I.getItem().exp();
        I++;
        while ( I.hasItem() && I.getItem().exp() == exp ) {
            f *= I.getItem().factor();
            I++;
        }
        result.append( CFFactor( f, exp ) );
    }
 
    return result;
}
 
CFFList sqrFreeZ ( const CanonicalForm & a )
{
    if ( a.inCoeffDomain() )
        return CFFactor( a, 1 );
    CanonicalForm aa, LcA;
    if (isOn (SW_RATIONAL))
    {
      LcA= bCommonDen (a);
      aa= a*LcA;
    }
    else
    {
      LcA= icontent (a);
      if (lc (a).sign() < 0)
        LcA= -LcA;
      aa= a/LcA;
    }
    CanonicalForm cont = content( aa );
    aa /= cont;
    CanonicalForm b = aa.deriv(), c = gcd( aa, b );
    CanonicalForm y, z, w = aa / c;
    int i = 1;
    CFFList F;
    Variable v = aa.mvar();
    CanonicalForm lcinv;
    while ( c.degree(v) != 0 )
    {
        y = gcd( w, c ); z = w / y;
        if ( degree( z, v ) > 0 )
        {
          if (isOn (SW_RATIONAL))
          {
            lcinv= 1/Lc (z);
            z *= lcinv;
            z *= bCommonDen (z);
          }
          if (lc (z).sign() < 0)
            z= -z;
          F.append( CFFactor( z, i ) );
        }
        i++;
        w = y; c = c / y;
    }
    if ( degree( w,v ) > 0 )
    {
      if (isOn (SW_RATIONAL))
      {
        lcinv= 1/Lc (w);
        w *= lcinv;
        w *= bCommonDen (w);
      }
      if (lc (w).sign() < 0)
        w= -w;
      F.append( CFFactor( w, i ) );
    }
    if ( ! cont.isOne() )
    {
        CFFList buf= sqrFreeZ (cont);
        buf.removeFirst();
        F = Union( F, buf );
    }
    F.insert (CFFactor (LcA, 1));
    return F;
}
 
CanonicalForm
sqrfPart (const CanonicalForm& F)
{
  if (F.inCoeffDomain())
    return F;
  CFMap M;
  CanonicalForm A= compress (F, M);
  CanonicalForm w, v, b;
  CanonicalForm result;
  int i= 1;
  for (; i <= A.level(); i++)
  {
    if (!deriv (A, Variable (i)).isZero())
      break;
  }
 
  w= gcd (A, deriv (A, Variable (i)));
  b= A/w;
  result= b;
  if (degree (w) < 1)
    return M (result);
  i++;
  for (; i <= A.level(); i++)
  {
    if (!deriv (w, Variable (i)).isZero())
    {
      b= w;
      w= gcd (w, deriv (w, Variable (i)));
      b /= w;
      if (degree (b) < 1)
        break;
      CanonicalForm g= gcd (b, result);
      if (degree (g) > 0)
        result *= b/g;
      if (degree (g) <= 0)
        result *= b;
    }
  }
  result= M (result);
  return result;
}
 
#if !defined(HAVE_NTL)
static int divexp = 1;
 
static void divexpfunc ( CanonicalForm &, int & e )
{
    e /= divexp;
}
 
CFFList sqrFreeFp ( const CanonicalForm & f )
{
    CanonicalForm t0 = f, t, v, w, h;
    CanonicalForm leadcf = t0.lc();
    Variable x = f.mvar();
    CFFList F;
    int p = getCharacteristic();
    int k, e = 1;
 
    if ( ! leadcf.isOne() )
        t0 /= leadcf;
 
    divexp = p;
    while ( t0.degree(x) > 0 )
    {
        t = gcd( t0, t0.deriv() );
        v = t0 / t;
        k = 0;
        while ( v.degree(x) > 0 )
        {
            k = k+1;
            if ( k % p == 0 )
            {
                t /= v;
                k = k+1;
            }
            w = gcd( t, v );
            h = v / w;
            v = w;
            t /= v;
            if ( h.degree(x) > 0 )
                F.append( CFFactor( h/h.lc(), e*k ) );
        }
        t0 = apply( t, divexpfunc );
        e = p * e;
    }
    if ( ! leadcf.isOne() )
    {
        if ( !F.isEmpty() && (F.getFirst().exp() == 1) )
        {
            leadcf = F.getFirst().factor() * leadcf;
            F.removeFirst();
        }
        F.insert( CFFactor( leadcf, 1 ) );
    }
    return F;
}
#endif