mirror of https://github.com/CGAL/cgal
51 lines
1.4 KiB
C++
51 lines
1.4 KiB
C++
#include <CGAL/Polynomial.h>
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#include <CGAL/Polynomial_traits_d.h>
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#include <CGAL/Polynomial_type_generator.h>
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#include <CGAL/Exact_integer.h>
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int main(){
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CGAL::IO::set_pretty_mode(std::cout);
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typedef CGAL::Exact_integer Int;
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typedef CGAL::Polynomial_type_generator<Int,1>::Type Poly_1;
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typedef CGAL::Polynomial_traits_d<Poly_1> PT_1;
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//construction using shift
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Poly_1 x = PT_1::Shift()(Poly_1(1),1); // x^1
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Poly_1 F // = (x+1)^2*(x-1)*(2x-1)=2x^4+x^3-3x^2-x+1
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= 2 * CGAL::ipower(x,4) + 1 * CGAL::ipower(x,3)
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- 3 * CGAL::ipower(x,2) - 1 * CGAL::ipower(x,1)
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+ 1 * CGAL::ipower(x,0);
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std::cout << "F=" << F << std::endl;
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Poly_1 G // = (x+1)*(x+3)=x^2+4*x+3
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= 1 * CGAL::ipower(x,2) + 4 * CGAL::ipower(x,1) + 3 * CGAL::ipower(x,0);
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std::cout << "G=" << G << std::endl;
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// Resultant computation:
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PT_1::Resultant resultant;
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std::cout << "The resultant of F and G is: " << resultant(F,G) << std::endl;
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// It is zero, because F and G have a common factor
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// Real root counting:
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PT_1::Principal_sturm_habicht_sequence stha;
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std::vector<Int> psc;
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stha(F,std::back_inserter(psc));
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int roots = CGAL::number_of_real_roots(psc.begin(),psc.end());
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std::cout << "The number of real roots of F is: " << roots << std::endl; // 3
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roots = CGAL::number_of_real_roots(G);
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std::cout << "The number of real roots of G is: " << roots << std::endl; // 2
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return 0;
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}
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