Function kBucketPolyRed

libpolys/polys/kbuckets.cc:1071–1186

//

number kBucketPolyRed(kBucket_pt bucket,
                      poly p1, int l1,
                      poly spNoether)
{
  ring r=bucket->bucket_ring;
  assume((!rIsPluralRing(r))||p_LmEqual(p1,kBucketGetLm(bucket), r));
  assume(p1 != NULL &&
         p_DivisibleBy(p1,  kBucketGetLm(bucket), r));
  assume(pLength(p1) == l1);

  poly a1 = pNext(p1), lm = kBucketExtractLm(bucket);
  BOOLEAN reset_vec=FALSE;
  number rn;

  /* we shall reduce bucket=bn*lm+... by p1=an*t+a1 where t=lm(p1)
     and an,bn shall be defined further down only if lc(p1)!=1
     we already know: an|bn and t|lm */
  if(a1==NULL)
  {
    p_LmDelete(&lm, r);
    return n_Init(1,r->cf);
  }

  if (! n_IsOne(pGetCoeff(p1),r->cf))
  {
    number an = pGetCoeff(p1), bn = pGetCoeff(lm);
    /* ksCheckCoeff: divide out gcd from an and bn: */
    int ct = ksCheckCoeff(&an, &bn,r->cf);
    /* the previous command returns ct=0 or ct=2 iff an!=1
       note: an is now 1 or -1 */

    /* setup factor for p1 which cancels leading terms */
    p_SetCoeff(lm, bn, r);
    if ((ct == 0) || (ct == 2))
    {
      /* correct factor for cancelation by changing sign if an=-1 */
      if (rField_is_Ring(r))
        lm = __p_Mult_nn(lm, an, r);
      else
        kBucket_Mult_n(bucket, an);
    }
    rn = an;
  }
  else
  {
    rn = n_Init(1,r->cf);
  }

  if (p_GetComp(p1, r) != p_GetComp(lm, r))
  {
    p_SetCompP(a1, p_GetComp(lm, r), r);
    reset_vec = TRUE;
    p_SetComp(lm, p_GetComp(p1, r), r);
    p_Setm(lm, r);
  }

  p_ExpVectorSub(lm, p1, r);
  l1--;