source: git/numeric/mpr_inout.h @ 08e15e7

spielwiese
Last change on this file since 08e15e7 was 08e15e7, checked in by Oleksandr Motsak <motsak@…>, 13 years ago
FIX: numeric/mpr_*
  • Property mode set to 100644
File size: 2.7 KB
Line 
1#ifndef MPR_H
2#define MPR_H
3/****************************************
4*  Computer Algebra System SINGULAR     *
5****************************************/
6
7/* $Id$ */
8
9/*
10* ABSTRACT - multipolynomial resultants - interface to Singular
11*
12*/
13
14#define DEFAULT_DIGITS 30
15
16#define MPR_DENSE  1
17#define MPR_SPARSE 2
18
19/** solve a multipolynomial system using the u-resultant
20 * Input ideal must be 0-dimensional and (currRing->N) == IDELEMS(ideal).
21 * Resultant method can be MPR_DENSE, which uses Macaulay Resultant (good for
22 * dense homogeneous polynoms) or MPR_SPARSE, which uses Sparse Resultant
23 * (Gelfand, Kapranov, Zelevinsky).
24 * Arguments 4: ideal i, int k, int l, int m
25 *   k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky
26 *   k=1: use resultant matrix of Macaulay (k=0 is default)
27 *   l>0: defines precision of fractional part if ground field is Q
28 *   m=0,1,2: number of iterations for approximation of roots (default=2)
29 * Returns a list containing the roots of the system.
30 */
31BOOLEAN nuUResSolve( leftv res, leftv args );
32
33/** returns module representing the multipolynomial resultant matrix
34 * Arguments 2: ideal i, int k
35 *   k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky
36 *   k=1: use resultant matrix of Macaulay (k=0 is default)
37 */
38BOOLEAN nuMPResMat( leftv res, leftv arg1, leftv arg2 );
39
40/** find the (complex) roots an univariate polynomial
41 * Determines the roots of an univariate polynomial using Laguerres'
42 * root-solver. Good for polynomials with low and middle degree (<40).
43 * Arguments 3: poly arg1 , int arg2 , int arg3
44 *  arg2>0: defines precision of fractional part if ground field is Q
45 *  arg3: number of iterations for approximation of roots (default=2)
46 * Returns a list of all (complex) roots of the polynomial arg1
47 */
48BOOLEAN nuLagSolve( leftv res, leftv arg1, leftv arg2, leftv arg3 );
49
50/**
51 * COMPUTE: polynomial p with values given by v at points p1,..,pN derived
52 * from p; more precisely: consider p as point in K^n and v as N elements in K,
53 * let p1,..,pN be the points in K^n obtained by evaluating all monomials
54 * of degree 0,1,...,N at p in lexicographical order, then the procedure
55 * computes the polynomial f satisfying f(pi) = v[i]
56 * RETURN:  polynomial f of degree d
57 */
58BOOLEAN nuVanderSys( leftv res, leftv arg1, leftv arg2, leftv arg3 );
59
60/** compute Newton Polytopes of input polynomials
61 */
62BOOLEAN loNewtonP( leftv res, leftv arg1 );
63
64/** Implementation of the Simplex Algorithm.
65 * For args, see class simplex.
66 */
67BOOLEAN loSimplex( leftv res, leftv args );
68
69#endif
70
71// local Variables: ***
72// folded-file: t ***
73// compile-command-1: "make installg" ***
74// compile-command-2: "make install" ***
75// End: ***
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