mirror of https://github.com/CGAL/cgal
58 lines
2.1 KiB
C++
58 lines
2.1 KiB
C++
#include <CGAL/config.h>
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#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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int main(){
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CGAL::set_pretty_mode(std::cout);
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typedef CGAL::Polynomial_type_generator<int,2>::Type Poly_2;
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typedef CGAL::Polynomial_traits_d<Poly_2> PT_2;
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//construction using shift
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Poly_2 x = PT_2::Shift()(Poly_2(1),1,0); // x^1
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Poly_2 y = PT_2::Shift()(Poly_2(1),1,1); // y^1
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Poly_2 F = 2*x*y + 3*CGAL::ipower(y,3);
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std::cout << "The bivariate polynomial F: " << F // = 3*y^3 + (2*x)*y
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<< std::endl << std::endl;
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PT_2::Evaluate evaluate;
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PT_2::Evaluate_homogeneous hevaluate;
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// Evaluation considers a polynomials as univariate:
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std::cout << "F(5): " << evaluate(F,5) // = 10*x + 375
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<< std::endl;
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// Evaluate_homogeneous considers F as a homogeneous polynomial in
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// the outermost variable only, that is, F is interpreted as
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// F(u,v) = 2*x*u*v^2 + 3 * u^3
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std::cout << "F(5,7): " << hevaluate(F,5,7) // = 490*x + 375
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<< std::endl << std::endl;
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PT_2::Substitute substitute;
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PT_2::Substitute_homogeneous hsubstitute;
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// Substitute considers a polynomials as multivariate, that is, the
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// new values for the variables are given by an iterator range
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// Note that the value type only has to be interoperable with the innermost
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// coefficient
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std::list<Poly_2> replacements;
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replacements.push_back(x-1); // replace x by x-1
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replacements.push_back(y); // replace y by y, i.e., do nothing
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std::cout << "The bivariate polynomial F: " << F // = 3*y^3 + (2*x)*y
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<< std::endl;
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std::cout << "F(x-1,y): " // = 3*y^3 + (2*x + (-2))*y
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<< substitute(F,replacements.begin(),replacements.end())
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<< std::endl;
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// Substitute_homogeneous considers F as a homogeneous polynomial in
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// all variable, that is, F is interpreted as
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// F(x,y,w) = 2*x*y*w + 3 * y^3
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replacements.push_back(y); // replace z by y
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std::cout << "F(x-1,y,y): " // = 3*y^3 + (2*x + (-2))*y^2
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<< hsubstitute(F,replacements.begin(),replacements.end())
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<< std::endl;
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}
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