Given a set of r-variale integral polynomials, a cylindrical algebraic decomposition (cad) of euclidean r-space E T partitions ET into connected subsets compatible with the zeros of the polynomials. Collins (1975) gave an algorithm for cad construction as part of a new decision procedure for real closed fields. This algorithm has since been implemented and applied to diverse problems (optimization, curve display). New applications of it have been proposed (program verification, motion planrnng), Part I of the present paper has several purposes, FirsL, it provides an exposition of the essential aspects of the algorithm. Second, it corrects mi.p.or errors in the 1975 paper, and develops certain concepts introduced there. Third. it provides a framework fOI" the adjacency algorithm presented in Part n. ]n addition. it surveys the applications of cad's und provides a detailed example of the operation of the algorithm.Key\'iO,'ds: polynomial zeros, computer .....lgebru. computational geometry, semi-algebraic geometry. real closed fields, decision procedures, real algebraic geometry.
Given a set of r-variale integral polynomials, a cylindrical algebraic decomposition (cad) of euclidean r-space E T partitions ET into connected subsets compatible with the zeros of the polynomials. Collins (1975) gave an algorithm for cad construction as part of a new decision procedure for real closed fields. This algorithm has since been implemented and applied to diverse problems (optimization, curve display). New applications of it have been proposed (program verification, motion planrnng), Part I of the present paper has several purposes, FirsL, it provides an exposition of the essential aspects of the algorithm. Second, it corrects mi.p.or errors in the 1975 paper, and develops certain concepts introduced there. Third. it provides a framework fOI" the adjacency algorithm presented in Part n. ]n addition. it surveys the applications of cad's und provides a detailed example of the operation of the algorithm.Key\'iO,'ds: polynomial zeros, computer .....lgebru. computational geometry, semi-algebraic geometry. real closed fields, decision procedures, real algebraic geometry.
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