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65 lines
2.6 KiB
65 lines
2.6 KiB
// Special procedures for the ``generic'' algorithm, i.e. going through the param
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// of a quadric of inertia (2,2)
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#ifndef _qi_inter_with_22_
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#define _qi_inter_with_22_
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/** QI */
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#include <libqi/kernel/QIHompoly.h>
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#include <libqi/kernel/QIQsicStruct.h>
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using namespace std;
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using namespace rpl;
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// Enter namespace QI
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namespace QI {
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// Input : initial quadrics q1, q2
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// determinental equation of the pencil : det_p
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// a quadric 22 : q
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// case_flag = 0 if the intersection is a smooth quartic, 2 real affinely finite
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// = 1 " 1 real affinely finite
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// = 2 " 2 real affinely infinite
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// = 3 if intersection is a cubic and a line secant
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// = 4 " non-secant
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// = 5 if intersection is two real skew lines
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// Output : Compute the Parameterization s1 + sqrt(xi) s2 of a quadric 22 in the pencil
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// and the Associated biquadratic equation poly1 + sqrt(xi) poly2 = 0
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// Call smooth_quartic(...) or cubic_line(...) for computing the intersection curve
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quad_inter <bigint> intersection_with_quadric22(const bigint_matrix &q1,
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const bigint_matrix &q2,
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const hom_polynomial <bigint> &det_p,
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const bigint_matrix &q,
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const unsigned int case_flag,
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const int opt_level,
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ostream &s);
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// Input : initial quadrics q1, q2
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// determinental equation of the pencil : det_p
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// a quadric 22 q
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// Output : a quadric 22 quadric_sol and a point on it point_sol
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// the determinant a^2.b of the quadric 22 in the form [a,b]
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void find_quadric_22_and_point(const bigint_matrix &q1, const bigint_matrix &q2,
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const hom_polynomial <bigint> &det_p,
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const bigint_matrix &q_cp,
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bigint_matrix &quadric_sol,
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math_vector <bigint> &point_sol,
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bigint &det_R,
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math_vector <bigint> &det_sol,
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const int opt_level, ostream &s);
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// Input: a matrix q of inertia 2,2
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// a point on it and the determinant of q in the form [a,b] such that det(q)=a^2. b
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// Output : Parameterization of the quadric : s1 + sqrt(det_q[1]) s2
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// If det_q[1]=1 then s2=[0,0,0,0]
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void find_parameterization_quadric_22(const math_matrix <bigint> &q_cp,
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const math_vector <bigint> &point_on_q,
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const math_vector <bigint> &det_q_cp,
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const bigint &det_R,
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surface_param <bigint> &s1,
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surface_param <bigint> &s2,
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const int opt_level, ostream &s);
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} // end of namespace QI
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#endif
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