# source:git/factory/cfNewtonPolygon.h

spielwiese Release-4-3-2p1
Last change on this file was 34636b, checked in by Martin Lee <martinlee84@…>, 10 years ago
chg: rewrote convex dense compression with mpz_t
• Property mode set to `100644`
File size: 5.5 KB
Line
1/*****************************************************************************\
2 * Computer Algebra System SINGULAR
3\*****************************************************************************/
4/** @file cfNewtonPolygon.h
5 *
6 * This file provides functions to compute the Newton polygon of a bivariate
7 * polynomial
8 *
9 * @author Martin Lee
10 *
11 **/
12/*****************************************************************************/
13
14#ifndef CF_NEWTON_POLYGON_H
15#define CF_NEWTON_POLYGON_H
16
17// #include "config.h"
18
19/// compute a polygon
20///
21/// @return an integer n such that the first n entries of @a points are the
22///         vertices of the convex hull of @a points
23int polygon (int** points, ///< [in,out] an array of points in the plane
24             int sizePoints///< [in] number of elements in @a points
25            );
26
27/// compute the Newton polygon of a bivariate polynomial
28///
29/// @return an array of points in the plane which are the vertices of the Newton
30///         polygon of F
31int ** newtonPolygon (const CanonicalForm& F,///< [in] a bivariate polynomial
32                      int& sizeOfNewtonPoly  ///< [in, out] size of the result
33                     );
34
35/// compute the convex hull of the support of two bivariate polynomials
36///
37/// @return an array of points in the plane which are the vertices of the convex
38///         hull of the support of F and G
39int ** newtonPolygon (const CanonicalForm& F,///< [in] a bivariate polynomial
40                      const CanonicalForm& G,///< [in] a bivariate polynomial
41                      int& sizeOfNewtonPoly  ///< [in, out] size of the result
42                     );
43
44/// check if @a point is inside a polygon described by points
45///
46/// @return true if @a point is inside a polygon described by points
47bool isInPolygon (int ** points, ///< [in] an array of points in the
48                                 ///< plane describing a polygon
49                  int sizePoints,///< [in] size of @a points
50                  int* point     ///< [in] a point in the plane
51                 );
52
53/// get the y-direction slopes of all edges with positive slope in y-direction
54/// of a convex polygon with at least one point of the polygon lying on the
55/// x-axis and one lying on the y-axis
56///
57/// @return an array containing the slopes as described above
58int* getRightSide (int** polygon,     ///<[in] vertices of a polygon
59                   int sizeOfPolygon, ///<[in] number of vertices
60                   int& sizeOfOutput  ///<[in,out] size of the output
61                  );
62
63/// computes the Newton polygon of F and checks if it satisfies the
64/// irreducibility criterion from S.Gao "Absolute irreducibility of polynomials
65/// via polytopes", Example 1
66///
67/// @return true if it satisfies the above criterion, false otherwise
68bool
69irreducibilityTest (const CanonicalForm& F ///<[in] a bivariate polynomial
70                   );
71
72/// absolute irreducibility test as described in "Modular Las Vegas Algorithms
73/// for Polynomial Absolute Factorization" by C. Bertone, G. Cheze, A. Galligo
74///
75/// @return true if F satisfies condition (C) from the above paper and thus
76/// is absolutely irreducible, false otherwise
77bool
78absIrredTest (const CanonicalForm& F ///< [in] a bivariate polynomial
79                                     ///< irreducible over ground field
80             );
81
82/// modular absolute irreducibility test as described in "Modular Las Vegas
83/// Algorithms for Polynomial Absolute Factorization" by C. Bertone, G. Cheze,
84/// A. Galligo
85///
86/// @return true if F is absolutely irreducible, false otherwise
87bool
88modularIrredTest (const CanonicalForm& F ///< [in] a bivariate polynomial
89                                         ///< irreducible over Z
90                 );
91
92/// modular absolute irreducibility test with shift as described in "Modular Las
93/// Vegas Algorithms for Polynomial Absolute Factorization" by C. Bertone,
94/// G. Cheze, A. Galligo
95///
96/// @return true if F is absolutely irreducible, false otherwise
97bool
98modularIrredTestWithShift (const CanonicalForm& F ///< [in] a bivariate polynomial
99                                                  ///< irreducible over Z
100                          );
101
102/// Algorithm 5 as described in Convex-Dense Bivariate Polynomial Factorization
103/// by Berthomieu, Lecerf
104void convexDense (int** points,  ///< [in, out] a set of points in Z^2, returns
105                                 ///< M (points)+A
106                  int sizePoints,///< [in] size of points
107                  mpz_t*& M,     ///< [in,out] returns an invertible 2x2 matrix
108                  mpz_t*& A      ///< [in,out] returns translation
109                 );
110
111/// compress a bivariate poly
112///
113/// @return @a compress returns a compressed bivariate poly
114/// @sa convexDense, decompress
115CanonicalForm
116compress (const CanonicalForm& F, ///< [in] compressed, i.e. F.level()==2,
117                                  ///< bivariate poly
118          mpz_t*& inverseM,       ///< [in,out] returns the inverse of M,
119                                  ///< if computeMA==true, M otherwise
120          mpz_t*& A,              ///< [in,out] returns translation
121          bool computeMA= true    ///< [in] whether to compute M and A
122         );
123
124/// decompress a bivariate poly
125///
126/// @return @a decompress returns a decompressed bivariate poly
127/// @sa convexDense, decompress
128CanonicalForm
129decompress (const CanonicalForm& F,///< [in] compressed, i.e. F.level()<= 2,
130                                   ///< uni- or bivariate poly
131            const mpz_t* M,       ///< [in] matrix M obtained from compress
132            const mpz_t* A        ///< [in] vector A obtained from compress
133           );
134
135#endif
136
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