added partial substitutions

Polynomial/include/CGAL/Polynomial/polynomial_functions.h

@@ -34,10 +34,16 @@
 #define CGAL_POLYNOMIAL_FUNCTIONS_H
 
 #include <CGAL/config.h>
+
+#include <vector>
+
 #include <CGAL/Polynomial.h>
 
 CGAL_BEGIN_NAMESPACE
 
+// leading coefficient
+//////////////////////
+
 namespace CGALi {
 
 template <class NT>
@@ -76,6 +82,97 @@ bool check_leadcoeff(const CGAL::Polynomial< CGAL::Polynomial< NT > > &p) {
     return CGALi::_check_leadcoeff(0, p.degree(), p);
 }
 
+// partial substitutions
+////////////////////////
+
+/*!\brief substitute innermost variable
+ *
+ *  The substituted number \e x may have a more general number type
+ *  NTX than the coefficient type NT, provided there is an explicit
+ *  conversion NTX(NT).
+ */
+template < class NT, class NTX >
+typename CGAL::Polynomial< typename CGAL::Coercion_traits< NT, NTX >::Type >  
+substitute_x(CGAL::Polynomial< CGAL::Polynomial< NT > > p, const NTX& x) {
+    
+    typedef CGAL::Polynomial_traits_d< 
+    CGAL::Polynomial < CGAL::Polynomial< NT > > > PT_d;
+    
+    const int d = PT_d::d;
+
+    CGAL_precondition(d >= 1);
+    
+    typedef typename CGAL::Coercion_traits< CGAL::Polynomial< NT >,NTX > CT;
+    typedef typename CT::Type Coercion;
+    typedef typename CGAL::Coercion_traits< NT, NTX > CTi;
+    typedef typename CTi::Type Coercion_i;
+    typedef CGAL::Polynomial_traits_d< Coercion > PT_d1;
+
+    std::vector< Coercion > replacements;
+    replacements.push_back(typename CT::Cast()(x));
+    for (int i = 0; i < d-1; i++) {
+        Coercion repl(Coercion_i(0), Coercion_i(1));
+        typename PT_d1::Move move;
+        repl = move(repl, d-2,i);
+        replacements.push_back(repl);
+    }
+    
+    typename PT_d::Substitute substitute;
+    Coercion sub = 
+        substitute(p, replacements.begin(), replacements.end());
+
+    //typename PT_d::Get_coefficient coeff;
+    //Coercion ret = coeff(sub,0,d-1);
+    
+    return sub;
+}
+
+/*!\brief substitute two innermost variables
+ *
+ *  The substituted numbers \e x and \e y may have a more general number type
+ *  NTX than the coefficient type NT, provided there is an explicit
+ *  conversion NTX(NT).
+ */
+template <class NT, class NTX>
+typename CGAL::Polynomial< typename CGAL::Coercion_traits< NT, NTX >::Type >  
+substitute_xy(
+    const CGAL::Polynomial< CGAL::Polynomial< CGAL::Polynomial< NT > > >& p, 
+    const NTX& x, const NTX& y
+) {
+
+    typedef CGAL::Polynomial_traits_d< 
+    CGAL::Polynomial< CGAL::Polynomial < CGAL::Polynomial< NT > > > > PT_d;
+    
+    const int d = PT_d::d;
+
+    CGAL_precondition(d >= 2);
+    
+    typedef typename CGAL::Coercion_traits< CGAL::Polynomial< NT >, NTX > CT;
+    typedef typename CT::Type Coercion;
+    typedef typename CGAL::Coercion_traits< NT, NTX > CTi;
+    typedef typename CT::Type Coercion_i;
+    typedef CGAL::Polynomial_traits_d < Coercion > PT_dc;
+    
+    std::vector< Coercion > replacements;
+    replacements.push_back(typename CT::Cast()(x));
+    replacements.push_back(typename CT::Cast()(y));
+    for (int i = 0; i < d-2; i++) {
+        Coercion repl(typename PT_dc::Coefficient_type(0), 
+                      typename PT_dc::Coefficient_type(1));
+        typename PT_dc::Move move;
+        repl = move(repl, d-3,i);
+        replacements.push_back(repl);
+    }
+
+    typename PT_d::Substitute substitute;
+    Coercion sub = 
+        substitute(p, replacements.begin(), replacements.end());
+
+    return sub;
+}
+
+
+
 CGAL_END_NAMESPACE
 
 #endif // CGAL_POLYNOMIAL_FUNCTIONS_H