/**
\brief 有限域Fp上多项式在Fp中的根(不含重数)
\param f Fp[x]中多项式
\param p 阶数
\return 根的集合
\note 利用因子分解算法求解
*/
void UniZpRootZp(std::vector<mpz_ptr> & rootlist,const poly_z & f,mpz_ptr p)
{
resize_z_list(rootlist,0);
poly_z h0,h;
h0.resize(2);
mpz_set_ui(h0[0],0);
mpz_set_ui(h0[1],1);
copy_poly_z(h,h0);
PowerMod(h,p,f,p);
mpz_sub_ui(h[1],h[1],1);
UniGcdZp(h0,h,f,p);
if(h0.size()==1)
{
h0.resize(0);
h.resize(0);
return ;
}
std::vector<poly_z> faclist;
UniEqlDegFacZp(faclist,h0,p,1);
for(uint i=0; i<faclist.size(); i++)
{
resize_z_list(rootlist,i+1);
mpz_neg(rootlist[i],faclist[i][0]);
}
clear_poly_z_list(faclist);
h0.resize(0);
h.resize(0);
std::sort(rootlist.begin(),rootlist.end(),mpz_ptr_less);
return ;
}
void UniEqlDegFacZp(std::vector<poly_z> & eqlfactorlist,const poly_z & f,mpz_ptr p,uint d,uint & current)
{
uint n=f.size()-1;
if(n==d)
{
copy_poly_z(eqlfactorlist[current],f);
current++;
return ;
}
poly_z g,h;
while(1)
{
UniEqlDegFacZp_Odd(g,f,p,d);
if(g.size()>=d)break;
}
UniEqlDegFacZp(eqlfactorlist,g,p,d,current);
UniDivZp(h,f,g,p);
UniEqlDegFacZp(eqlfactorlist,h,p,d,current);
g.resize(0);h.resize(0);
return ;
}