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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  */
37 BOOLEAN 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  */
47 BOOLEAN 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  */
57 BOOLEAN 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: ***
Class used for (list of) interpreter objects.
Definition: subexpr.h:82
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:4877
BOOLEAN loSimplex(leftv res, leftv args)
Implementation of the Simplex Algorithm.
Definition: ipshell.cc:4538
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:4647
BOOLEAN nuMPResMat(leftv res, leftv arg1, leftv arg2)
returns module representing the multipolynomial resultant matrix Arguments 2: ideal i,...
Definition: ipshell.cc:4624
CanonicalForm res
Definition: facAbsFact.cc:64
int BOOLEAN
Definition: auxiliary.h:85
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:4776
BOOLEAN loNewtonP(leftv res, leftv arg1)
compute Newton Polytopes of input polynomials
Definition: ipshell.cc:4532