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Unformatted text preview: Geometric Constraint Lecture(Feb 14–23) Instructor: Meera Sitharam, Recorded by Heping Gao Thuresday, Feb 23, 2006 1 Combinatorial Property of PointLine Ma trix(Feb 14th) Conjecture on the combinatorial property of PointLine matrix. p9 p8 p7 p6 p5 p4 p3 p2 p1 Figure 1: Point Lince example 1 The following matrix is for Figure 1 1 P 1  1 1 0 0 0 0 1 0 0 P 2  0 0 1 1 0 0 1 0 0 P 3  0 0 0 0 1 1 1 0 0 P 4  0 0 1 0 1 0 0 1 0 P 5  1 0 0 0 0 1 0 1 0 P 6  0 1 0 1 0 0 0 1 0 P 7  1 0 1 0 0 0 0 0 1 P 8  0 1 0 0 1 0 0 0 1 P 9  0 0 0 1 0 1 0 0 1 p9 p8 p7 p6 p5 p4 p3 p2 p1 Figure 2: Point Line example 2 The following matrix is for Figure 2 P 1  1 1 0 0 0 0 0 1 0 P 2  1 0 1 0 0 0 0 0 1 P 3  0 0 0 1 0 0 0 1 1 P 4  1 0 0 0 1 0 1 0 0 P 5  0 0 0 0 1 1 0 1 0 P 6  0 0 0 0 0 1 1 0 1 P 7  0 1 1 0 1 0 0 0 0 P 8  0 1 0 1 0 1 0 0 0 P 9  0 0 1 1 0 0 1 0 0 For more details, please refer to the homework. 2 2 Feb 16th Question :when viewed as incidence equations between points and lines in R 2 , does it have dependence? Can this question be answered using purely combinatorial properity( ∈ P ) I ? I.e. should not require solution of any system S m (number of variables, number of equations or degree depending on m) of equations over R,N,Q...
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