00001 #ifndef _synaps_solve_Sturm_h_ 00002 #define _synaps_solve_Sturm_h_ 00003 00004 #include <synaps/init.h> 00005 #include <synaps/arithm/Interval.h> 00006 #include <synaps/arithm/traits.h> 00007 #include <synaps/upol/UPolDse.h> 00008 #include <synaps/usolve/Small_degree.h> 00009 #include <synaps/usolve/sturm/common.h> 00010 #include <synaps/usolve/sturm/solve_sturm.h> 00011 00012 __BEGIN_NAMESPACE_SYNAPS 00013 00014 00015 template < class NT > 00016 struct Sturm : public Small_degree<NT> 00017 { 00018 typedef Sturm self_t; 00019 }; 00020 00021 00024 template < class NT > inline 00025 Seq< typename Sturm<NT>::RO_t > 00026 solve( const typename Sturm<NT>::Poly& f, 00027 Sturm<NT>) 00028 { 00029 typedef Sturm<NT> K; 00030 typedef typename K::RO_t RO_t; 00031 00032 Seq<RO_t> sol; 00033 00034 ALGEBRAIC::solve_sturm(f, std::back_inserter(sol.rep()), K()); 00035 00036 std::stable_sort( sol.begin(), sol.end(), ALGEBRAIC::Refine_compare()); 00037 return sol; 00038 } 00039 00040 00041 template < class NT, 00042 class OutputIterator> inline 00043 OutputIterator 00044 solve( const typename Sturm<NT>::Poly& f, 00045 OutputIterator it, 00046 Sturm<NT>) 00047 { 00048 typedef Sturm<NT> K; 00049 00050 return ALGEBRAIC::solve_sturm(f, it, K()); 00051 } 00052 00053 00054 00055 template < class NT > inline 00056 typename Sturm<NT>::RO_t 00057 RootOf( const typename Sturm<NT>::Poly& f, unsigned i, Sturm<NT>) 00058 { 00059 typedef Sturm<NT> K; 00060 return solve( f, K())[i]; 00061 } 00062 00063 00064 00065 template < class NT > inline 00066 int 00067 Count_real_roots( const typename Sturm<NT>::Poly& f, Sturm<NT>) 00068 { 00069 typedef Sturm<NT> K; 00070 typedef typename K::RT RT; 00071 typedef typename K::FT FT; 00072 typedef typename K::FIT FIT; 00073 00074 SturmSeq<RT> sth( f, UPOLDAR::diff(f), SUBRES()); 00075 FT b = Bound( f, Cauchy()); 00076 FT a = -b; 00077 00078 return ( Var( sth, a) - Var( sth, b) ); 00079 } 00080 00081 00082 __END_NAMESPACE_SYNAPS 00083 00084 #endif // _SYNAPS_SOLVE_STURM_H_ 00085
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