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mpr_inout.h
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1#ifndef MPR_H
2#define MPR_H
3/****************************************
4* Computer Algebra System SINGULAR *
5****************************************/
6
7
8/*
9* ABSTRACT - multipolynomial resultants - interface to Singular
10*
11*/
12
13#define DEFAULT_DIGITS 30
14
15#define MPR_DENSE 1
16#define MPR_SPARSE 2
17
18/** solve a multipolynomial system using the u-resultant
19 * Input ideal must be 0-dimensional and (currRing->N) == IDELEMS(ideal).
20 * Resultant method can be MPR_DENSE, which uses Macaulay Resultant (good for
21 * dense homogeneous polynoms) or MPR_SPARSE, which uses Sparse Resultant
22 * (Gelfand, Kapranov, Zelevinsky).
23 * Arguments 4: ideal i, int k, int l, int m
24 * k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky
25 * k=1: use resultant matrix of Macaulay (k=0 is default)
26 * l>0: defines precision of fractional part if ground field is Q
27 * m=0,1,2: number of iterations for approximation of roots (default=2)
28 * Returns a list containing the roots of the system.
29 */
31
32/** returns module representing the multipolynomial resultant matrix
33 * Arguments 2: ideal i, int k
34 * k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky
35 * k=1: use resultant matrix of Macaulay (k=0 is default)
36 */
37BOOLEAN nuMPResMat( leftv res, leftv arg1, leftv arg2 );
38
39/** find the (complex) roots an univariate polynomial
40 * Determines the roots of an univariate polynomial using Laguerres'
41 * root-solver. Good for polynomials with low and middle degree (<40).
42 * Arguments 3: poly arg1 , int arg2 , int arg3
43 * arg2>0: defines precision of fractional part if ground field is Q
44 * arg3: number of iterations for approximation of roots (default=2)
45 * Returns a list of all (complex) roots of the polynomial arg1
46 */
47BOOLEAN nuLagSolve( leftv res, leftv arg1, leftv arg2, leftv arg3 );
48
49/**
50 * COMPUTE: polynomial p with values given by v at points p1,..,pN derived
51 * from p; more precisely: consider p as point in K^n and v as N elements in K,
52 * let p1,..,pN be the points in K^n obtained by evaluating all monomials
53 * of degree 0,1,...,N at p in lexicographical order, then the procedure
54 * computes the polynomial f satisfying f(pi) = v[i]
55 * RETURN: polynomial f of degree d
56 */
57BOOLEAN nuVanderSys( leftv res, leftv arg1, leftv arg2, leftv arg3 );
58
59/** compute Newton Polytopes of input polynomials
60 */
62
63/** Implementation of the Simplex Algorithm.
64 * For args, see class simplex.
65 */
67
68#endif
69
70// local Variables: ***
71// folded-file: t ***
72// compile-command-1: "make installg" ***
73// compile-command-2: "make install" ***
74// End: ***
int BOOLEAN
Definition: auxiliary.h:87
Class used for (list of) interpreter objects.
Definition: subexpr.h:83
CanonicalForm res
Definition: facAbsFact.cc:60
BOOLEAN nuLagSolve(leftv res, leftv arg1, leftv arg2, leftv arg3)
find the (complex) roots an univariate polynomial Determines the roots of an univariate polynomial us...
Definition: ipshell.cc:4678
BOOLEAN nuVanderSys(leftv res, leftv arg1, leftv arg2, leftv arg3)
COMPUTE: polynomial p with values given by v at points p1,..,pN derived from p; more precisely: consi...
Definition: ipshell.cc:4821
BOOLEAN nuMPResMat(leftv res, leftv arg1, leftv arg2)
returns module representing the multipolynomial resultant matrix Arguments 2: ideal i,...
Definition: ipshell.cc:4655
BOOLEAN loSimplex(leftv res, leftv args)
Implementation of the Simplex Algorithm.
Definition: ipshell.cc:4569
BOOLEAN loNewtonP(leftv res, leftv arg1)
compute Newton Polytopes of input polynomials
Definition: ipshell.cc:4563
BOOLEAN nuUResSolve(leftv res, leftv args)
solve a multipolynomial system using the u-resultant Input ideal must be 0-dimensional and (currRing-...
Definition: ipshell.cc:4922