1 | #ifndef MPR_H |
---|
2 | #define MPR_H |
---|
3 | /**************************************** |
---|
4 | * Computer Algebra System SINGULAR * |
---|
5 | ****************************************/ |
---|
6 | |
---|
7 | /* $Id: mpr_inout.h,v 1.4 1999-07-08 10:18:13 wenk Exp $ */ |
---|
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 pVariables == 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 | */ |
---|
31 | BOOLEAN 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 | */ |
---|
38 | BOOLEAN 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 | */ |
---|
48 | BOOLEAN 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 | */ |
---|
58 | BOOLEAN nuVanderSys( leftv res, leftv arg1, leftv arg2, leftv arg3 ); |
---|
59 | |
---|
60 | #endif |
---|
61 | |
---|
62 | // local Variables: *** |
---|
63 | // folded-file: t *** |
---|
64 | // compile-command-1: "make installg" *** |
---|
65 | // compile-command-2: "make install" *** |
---|
66 | // End: *** |
---|