[35aab3] | 1 | #ifndef MPR_H |
---|
| 2 | #define MPR_H |
---|
| 3 | /**************************************** |
---|
| 4 | * Computer Algebra System SINGULAR * |
---|
| 5 | ****************************************/ |
---|
| 6 | |
---|
| 7 | /* $Id: mpr_inout.h,v 1.1.1.1 2003-10-06 12:15:58 Singular 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 | /** compute Newton Polytopes of input polynomials |
---|
| 61 | */ |
---|
| 62 | BOOLEAN loNewtonP( leftv res, leftv arg1 ); |
---|
| 63 | |
---|
| 64 | /** Implementation of the Simplex Algorithm. |
---|
| 65 | * For args, see class simplex. |
---|
| 66 | */ |
---|
| 67 | BOOLEAN 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: *** |
---|