macaulay.hpp

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#include<vector>

#if 0
long long binom(int n, int m)
//C_m^n
{
  long long res=1;
  if(n>m || m<0 || n<0)
    return 0;
  for(int i=m;i>m-n;i--)
    res*=i;
  for(int i=1;i<=n;i++)
    res/=i;
  return res;
}
#endif

QQ binom(int n, int m)
//C_m^n
{
  QQ res=1;
  if(n>m || m<0 || n<0)
    return 0;
  for(int i=m;i>m-n;i--)
    res*=i;
  for(QQ i=1;i<=n;i+=1)
    res/=i;
  return res;
}


void Macaulay_dec(std::vector<int> &coeff_mac, int k, int dim)
{
  QQ mydim=dim;
  for(int kk=k;kk>0;kk--)
    {
      int tmp;
      for(tmp=kk;binom(kk,tmp)<=mydim;tmp++);
      tmp--;
      mydim-=binom(kk,tmp);
      coeff_mac.push_back(tmp);
    }
}

long nextdim(std::vector<int> &coeff_mac, int k)
{
  QQ res=0;
  for(std::vector<int>::iterator iter=coeff_mac.begin();
      iter!=coeff_mac.end();iter++)
    res+=binom(k--+1,*iter+1);
  int tmpres=0;
  for(tmpres=0;res>tmpres;tmpres++);
  return tmpres;
}