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cgal/Polynomial/test/Polynomial/sturm_habicht_sequence.cpp

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// TODO: Add licence
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL:$
// $Id: $
//
//
// Author(s) : Michael Kerber <mkerber@mpi-inf.mpg.de>
//
// ============================================================================
#include <CGAL/basic.h>
#include <vector>
#include <sstream>
#include <cstddef>
#include <CGAL/Polynomial/sturm_habicht_sequence.h>
#include <CGAL/Arithmetic_kernel.h>
template<typename ArithmeticKernel> void test_routine() {
// All results are computed with the sres_stha.mpl worksheet
typedef typename ArithmeticKernel::Integer NT;
typedef CGAL::Polynomial<NT> PNT_1;
typedef CGAL::Polynomial<PNT_1> PNT_2;
{ // test for the principal Sturm-Habicht sequence
// f=x^3*(x+1)*(x-1)*(x-2)^2
PNT_1 f(NT(0),NT(0),NT(0),NT(-4),NT(4),NT(3),NT(-4),NT(1));
std::vector<NT> stha;
CGAL::CGALi::principal_sturm_habicht_sequence(f,std::back_inserter(stha));
assert(stha.size()==8);
assert(stha[0] == NT(0));
assert(stha[1] == NT(0));
assert(stha[2] == NT(0));
assert(stha[3] == NT(864));
assert(stha[4] == NT(324));
assert(stha[5] == NT(54));
assert(stha[6] == NT(7));
assert(stha[7] == NT(1));
assert(CGAL::CGALi::stha_count_number_of_real_roots<NT>
(stha.begin(),stha.end()) == 4);
stha.clear();
CGAL::CGALi::prs_principal_sturm_habicht_sequence(f,std::back_inserter(stha));
assert(stha.size()==8);
assert(stha[0] == NT(0));
assert(stha[1] == NT(0));
assert(stha[2] == NT(0));
assert(stha[3] == NT(864));
assert(stha[4] == NT(324));
assert(stha[5] == NT(54));
assert(stha[6] == NT(7));
assert(stha[7] == NT(1));
assert(CGAL::CGALi::stha_count_number_of_real_roots<NT>
(stha.begin(),stha.end()) == 4);
stha.clear();
CGAL::CGALi::bezout_principal_sturm_habicht_sequence(f,std::back_inserter(stha));
assert(stha.size()==8);
assert(stha[0] == NT(0));
assert(stha[1] == NT(0));
assert(stha[2] == NT(0));
assert(stha[3] == NT(864));
assert(stha[4] == NT(324));
assert(stha[5] == NT(54));
assert(stha[6] == NT(7));
assert(stha[7] == NT(1));
assert(CGAL::CGALi::stha_count_number_of_real_roots<NT>
(stha.begin(),stha.end()) == 4);
stha.clear();
typename
CGAL::Polynomial_traits_d<PNT_1>::Principal_sturm_habicht_sequence()
(f,std::back_inserter(stha));
assert(stha.size()==8);
assert(stha[0] == NT(0));
assert(stha[1] == NT(0));
assert(stha[2] == NT(0));
assert(stha[3] == NT(864));
assert(stha[4] == NT(324));
assert(stha[5] == NT(54));
assert(stha[6] == NT(7));
assert(stha[7] == NT(1));
assert(CGAL::CGALi::stha_count_number_of_real_roots<NT>
(stha.begin(),stha.end()) == 4);
}
{ // Example for the defective case
// f:=x^8+x^2
PNT_1 f(NT(0),NT(0),NT(1),NT(0),NT(0),NT(0),NT(0),NT(0),NT(1));
std::vector<NT> stha;
CGAL::CGALi::principal_sturm_habicht_sequence (f,std::back_inserter(stha));
assert(stha.size()==9);
assert(stha[0] == NT(0));
assert(stha[1] == NT(-93312));
assert(stha[2] == NT(-62208));
assert(stha[3] == NT(0));
assert(stha[4] == NT(0));
assert(stha[5] == NT(0));
assert(stha[6] == NT(0));
assert(stha[7] == NT(8));
assert(stha[8] == NT(1));
assert(CGAL::CGALi::stha_count_number_of_real_roots<NT>(stha.begin(),stha.end()) == 1);
stha.clear();
CGAL::CGALi::prs_principal_sturm_habicht_sequence (f,std::back_inserter(stha));
assert(stha.size()==9);
assert(stha[0] == NT(0));
assert(stha[1] == NT(-93312));
assert(stha[2] == NT(-62208));
assert(stha[3] == NT(0));
assert(stha[4] == NT(0));
assert(stha[5] == NT(0));
assert(stha[6] == NT(0));
assert(stha[7] == NT(8));
assert(stha[8] == NT(1));
assert(CGAL::CGALi::stha_count_number_of_real_roots<NT>(stha.begin(),stha.end()) == 1);
stha.clear();
CGAL::CGALi::bezout_principal_sturm_habicht_sequence (f,std::back_inserter(stha));
assert(stha.size()==9);
assert(stha[0] == NT(0));
assert(stha[1] == NT(-93312));
assert(stha[2] == NT(-62208));
assert(stha[3] == NT(0));
assert(stha[4] == NT(0));
assert(stha[5] == NT(0));
assert(stha[6] == NT(0));
assert(stha[7] == NT(8));
assert(stha[8] == NT(1));
assert(CGAL::CGALi::stha_count_number_of_real_roots<NT>(stha.begin(),stha.end()) == 1);
}
{ // test for the complete Sturm-Habicht sequence
// f:=(2*x+1)^3*(x+1)*(x-1)
PNT_1 f(NT(-1),NT(-6),NT(-11),NT(-2),NT(12),NT(8));
PNT_1 fx(f);
fx.diff();
std::vector<PNT_1> stha;
CGAL::CGALi::sturm_habicht_sequence(f,std::back_inserter(stha));
assert(stha.size()==6);
assert(stha[5]==f);
assert(stha[4]==fx);
assert(stha[3]==PNT_1(NT(1024),NT(5568),NT(9984),NT(5888)));
assert(stha[2]==PNT_1(NT(55296),NT(221184),NT(221184)));
assert(stha[1].is_zero());
assert(stha[0].is_zero());
stha.clear();
typename CGAL::Polynomial_traits_d<PNT_1>::Sturm_habicht_sequence()
(f,std::back_inserter(stha));
assert(stha.size()==6);
assert(stha[5]==f);
assert(stha[4]==fx);
assert(stha[3]==PNT_1(NT(1024),NT(5568),NT(9984),NT(5888)));
assert(stha[2]==PNT_1(NT(55296),NT(221184),NT(221184)));
assert(stha[1].is_zero());
assert(stha[0].is_zero());
}
{ // test for cofactors
// f:=(2*x+1)^3*(x+1)*(x-1)
PNT_1 f(NT(-1),NT(-6),NT(-11),NT(-2),NT(12),NT(8));
PNT_1 fx = CGAL::diff(f);
std::vector<PNT_1> stha_check,stha,co_f,co_fx;
CGAL::CGALi::sturm_habicht_sequence(f,std::back_inserter(stha_check));
CGAL::CGALi::sturm_habicht_sequence_with_cofactors(f,
std::back_inserter(stha),
std::back_inserter(co_f),
std::back_inserter(co_fx)
);
int n = static_cast<int>(stha.size());
assert(n == static_cast<int>(stha_check.size()));
for(int i = 0; i < n; i++) {
assert(stha[i]==stha_check[i]);
assert(stha[i]==co_f[i]*f + co_fx[i]*fx);
}
stha.clear();
co_f.clear();
co_fx.clear();
typename CGAL::Polynomial_traits_d<PNT_1>
::Sturm_habicht_sequence_with_cofactors()(f,
std::back_inserter(stha),
std::back_inserter(co_f),
std::back_inserter(co_fx)
);
n = static_cast<int>(stha.size());
assert(n == static_cast<int>(stha_check.size()));
for(int i = 0; i < n; i++) {
assert(stha[i]==stha_check[i]);
assert(stha[i]==co_f[i]*f + co_fx[i]*fx);
}
}
{ // Cofactors, defective case
// f:=x^8+x^2
PNT_1 f(NT(0),NT(0),NT(1),NT(0),NT(0),NT(0),NT(0),NT(0),NT(1));
PNT_1 fx = CGAL::diff(f);
std::vector<PNT_1> stha_check,stha,co_f,co_fx;
CGAL::CGALi::sturm_habicht_sequence(f,std::back_inserter(stha_check));
CGAL::CGALi::sturm_habicht_sequence_with_cofactors(f,
std::back_inserter(stha),
std::back_inserter(co_f),
std::back_inserter(co_fx)
);
int n = static_cast<int>(stha.size());
assert(n == static_cast<int>(stha_check.size()));
for(int i = 0; i < n; i++) {
assert(stha[i]==stha_check[i]);
assert(stha[i]==co_f[i]*f + co_fx[i]*fx);
}
}
{ // Test for bivariate polynomials
// f:=y^4 + 6*y^3 + 9*y^2 + (9*x^3 + 3*x^2 + 2*x + 5)*y + (2*x^2 + 5*x + 7)
std::stringstream ss("P[4(0,P[2(0,7)(1,5)(2,2)])(1,P[3(0,5)(1,2)(2,3)(3,9)])(2,P[0(0,9)])(3,P[0(0,6)])(4,P[0(0,1)])]");
PNT_2 f;
ss >> f;
{
std::vector<PNT_1> stha,costha;
CGAL::CGALi::first_two_sturm_habicht_coefficients(f,std::back_inserter(stha),
std::back_inserter(costha));
assert(stha.size()==5);
assert(costha.size()==4);
NT c1[13] = { NT(-81383),NT(-113448),NT(-123840),NT(-223936),NT(-272142),
NT(-14700),NT(419954),NT(156816),NT(-247131),NT(-498636),
NT(-275562),NT(-236196),NT(-177147) };
PNT_1 p1(c1,c1+13);
assert(stha[0] == p1);
assert(stha[1] == PNT_1(NT(-828),NT(-1008),NT(-864),NT(-1728),NT(-1620),
NT(-1944),NT(-2916)) );
assert(stha[2] == PNT_1(NT(36)) );
assert(stha[3] == PNT_1(NT(4)) );
assert(stha[4] == PNT_1(NT(1)) );
assert(costha[0] == PNT_1(NT(-2742),NT(-2592),NT(-1788),NT(-2100),
NT(-1638),NT(108),NT(1458)) );
assert(costha[1] == PNT_1(NT(48),NT(-24),NT(-36),NT(-108)) );
assert(costha[2] == PNT_1(NT(18)) );
assert(costha[3] == PNT_1(NT(6)) );
}
{
std::vector<PNT_1> stha,costha;
CGAL::CGALi::prs_first_two_sturm_habicht_coefficients(f,std::back_inserter(stha),
std::back_inserter(costha));
assert(stha.size()==5);
assert(costha.size()==4);
NT c1[13] = { NT(-81383),NT(-113448),NT(-123840),NT(-223936),NT(-272142),
NT(-14700),NT(419954),NT(156816),NT(-247131),NT(-498636),
NT(-275562),NT(-236196),NT(-177147) };
PNT_1 p1(c1,c1+13);
assert(stha[0] == p1);
assert(stha[1] == PNT_1(NT(-828),NT(-1008),NT(-864),NT(-1728),NT(-1620),
NT(-1944),NT(-2916)) );
assert(stha[2] == PNT_1(NT(36)) );
assert(stha[3] == PNT_1(NT(4)) );
assert(stha[4] == PNT_1(NT(1)) );
assert(costha[0] == PNT_1(NT(-2742),NT(-2592),NT(-1788),NT(-2100),
NT(-1638),NT(108),NT(1458)) );
assert(costha[1] == PNT_1(NT(48),NT(-24),NT(-36),NT(-108)) );
assert(costha[2] == PNT_1(NT(18)) );
assert(costha[3] == PNT_1(NT(6)) );
}
{
std::vector<PNT_1> stha,costha;
CGAL::CGALi::bezout_first_two_sturm_habicht_coefficients
(f,std::back_inserter(stha),
std::back_inserter(costha));
assert(stha.size()==5);
assert(costha.size()==4);
NT c1[13] = { NT(-81383),NT(-113448),NT(-123840),NT(-223936),NT(-272142),
NT(-14700),NT(419954),NT(156816),NT(-247131),NT(-498636),
NT(-275562),NT(-236196),NT(-177147) };
PNT_1 p1(c1,c1+13);
assert(stha[0] == p1);
assert(stha[1] == PNT_1(NT(-828),NT(-1008),NT(-864),NT(-1728),NT(-1620),
NT(-1944),NT(-2916)) );
assert(stha[2] == PNT_1(NT(36)) );
assert(stha[3] == PNT_1(NT(4)) );
assert(stha[4] == PNT_1(NT(1)) );
assert(costha[0] == PNT_1(NT(-2742),NT(-2592),NT(-1788),NT(-2100),
NT(-1638),NT(108),NT(1458)) );
assert(costha[1] == PNT_1(NT(48),NT(-24),NT(-36),NT(-108)) );
assert(costha[2] == PNT_1(NT(18)) );
assert(costha[3] == PNT_1(NT(6)) );
}
}
}
int main() {
#ifdef CGAL_USE_LEDA
test_routine<CGAL::LEDA_arithmetic_kernel>();
#else
std::cout << "LEDA tests skipped" << std::endl;
#endif
#ifdef CGAL_USE_CORE
test_routine<CGAL::CORE_arithmetic_kernel>();
#else
std::cout << "CORE tests skipped" << std::endl;
#endif
return 0;
}
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