1 | /*****************************************************************************\ |
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2 | * Computer Algebra System SINGULAR |
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3 | \*****************************************************************************/ |
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4 | /** @file cfNewtonPolygon.h |
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5 | * |
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6 | * This file provides functions to compute the Newton polygon of a bivariate |
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7 | * polynomial |
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8 | * |
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9 | * @author Martin Lee |
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10 | * |
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11 | * @internal |
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12 | * @version \$Id$ |
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13 | * |
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14 | **/ |
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15 | /*****************************************************************************/ |
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16 | |
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17 | #ifndef CF_NEWTON_POLYGON_H |
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18 | #define CF_NEWTON_POLYGON_H |
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19 | |
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20 | #include <config.h> |
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21 | |
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22 | #ifdef HAVE_NTL |
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23 | #include "NTLconvert.h" |
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24 | #endif |
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25 | |
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26 | /// compute a polygon |
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27 | /// |
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28 | /// @return an integer n such that the first n entries of @a points are the |
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29 | /// vertices of the convex hull of @a points |
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30 | int polygon (int** points, ///< [in,out] an array of points in the plane |
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31 | int sizePoints///< [in] number of elements in @a points |
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32 | ); |
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33 | |
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34 | /// compute the Newton polygon of a bivariate polynomial |
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35 | /// |
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36 | /// @return an array of points in the plane which are the vertices of the Newton |
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37 | /// polygon of F |
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38 | int ** newtonPolygon (const CanonicalForm& F,///< [in] a bivariate polynomial |
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39 | int& sizeOfNewtonPoly ///< [in, out] size of the result |
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40 | ); |
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41 | |
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42 | /// check if @a point is inside a polygon described by points |
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43 | /// |
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44 | /// @return true if @a point is inside a polygon described by points |
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45 | bool isInPolygon (int ** points, ///< [in] an array of points in the |
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46 | ///< plane describing a polygon |
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47 | int sizePoints,///< [in] size of @a points |
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48 | int* point ///< [in] a point in the plane |
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49 | ); |
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50 | |
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51 | #ifdef HAVE_NTL |
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52 | /// Algorithm 5 as described in Convex-Dense Bivariate Polynomial Factorization |
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53 | /// by Berthomieu, Lecerf |
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54 | void convexDense (int** points, ///< [in, out] a set of points in Z^2, returns |
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55 | ///< M (points)+A |
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56 | int sizePoints,///< [in] size of points |
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57 | mat_ZZ& M, ///< [in,out] returns an invertible matrix |
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58 | vec_ZZ& A ///< [in,out] returns translation |
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59 | ); |
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60 | |
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61 | /// compress a bivariate poly |
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62 | /// |
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63 | /// @return @a compress returns a compressed bivariate poly |
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64 | /// @sa convexDense, decompress |
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65 | CanonicalForm |
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66 | compress (const CanonicalForm& F, ///< [in] compressed, i.e. F.level()==2, |
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67 | ///< bivariate poly |
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68 | mat_ZZ& inverseM, ///< [in,out] returns the inverse of M |
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69 | vec_ZZ& A ///< [in,out] returns translation |
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70 | ); |
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71 | |
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72 | /// decompress a bivariate poly |
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73 | /// |
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74 | /// @return @a decompress returns a decompressed bivariate poly |
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75 | /// @sa convexDense, decompress |
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76 | CanonicalForm |
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77 | decompress (const CanonicalForm& F,///< [in] compressed, i.e. F.level()<= 2, |
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78 | ///< uni- or bivariate poly |
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79 | const mat_ZZ& M, ///< [in] matrix M obtained from compress |
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80 | const vec_ZZ& A ///< [in] vector A obtained from compress |
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81 | ); |
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82 | #endif |
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83 | |
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84 | #endif |
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85 | |
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