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#ifndef MPR_H
#define MPR_H
/****************************************
* Computer Algebra System SINGULAR *
****************************************/
/*
* ABSTRACT - multipolynomial resultants - interface to Singular
*
*/
#define DEFAULT_DIGITS 30
#define MPR_DENSE 1
#define MPR_SPARSE 2
/** solve a multipolynomial system using the u-resultant
* Input ideal must be 0-dimensional and (currRing->N) == IDELEMS(ideal).
* Resultant method can be MPR_DENSE, which uses Macaulay Resultant (good for
* dense homogeneous polynoms) or MPR_SPARSE, which uses Sparse Resultant
* (Gelfand, Kapranov, Zelevinsky).
* Arguments 4: ideal i, int k, int l, int m
* k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky
* k=1: use resultant matrix of Macaulay (k=0 is default)
* l>0: defines precision of fractional part if ground field is Q
* m=0,1,2: number of iterations for approximation of roots (default=2)
* Returns a list containing the roots of the system.
*/
BOOLEAN nuUResSolve( leftv res, leftv args );
/** returns module representing the multipolynomial resultant matrix
* Arguments 2: ideal i, int k
* k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky
* k=1: use resultant matrix of Macaulay (k=0 is default)
*/
BOOLEAN nuMPResMat( leftv res, leftv arg1, leftv arg2 );
/** find the (complex) roots an univariate polynomial
* Determines the roots of an univariate polynomial using Laguerres'
* root-solver. Good for polynomials with low and middle degree (<40).
* Arguments 3: poly arg1 , int arg2 , int arg3
* arg2>0: defines precision of fractional part if ground field is Q
* arg3: number of iterations for approximation of roots (default=2)
* Returns a list of all (complex) roots of the polynomial arg1
*/
BOOLEAN nuLagSolve( 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: consider p as point in K^n and v as N elements in K,
* let p1,..,pN be the points in K^n obtained by evaluating all monomials
* of degree 0,1,...,N at p in lexicographical order, then the procedure
* computes the polynomial f satisfying f(pi) = v[i]
* RETURN: polynomial f of degree d
*/
BOOLEAN nuVanderSys( leftv res, leftv arg1, leftv arg2, leftv arg3 );
/** compute Newton Polytopes of input polynomials
*/
BOOLEAN loNewtonP( leftv res, leftv arg1 );
/** Implementation of the Simplex Algorithm.
* For args, see class simplex.
*/
BOOLEAN loSimplex( leftv res, leftv args );
#endif
// local Variables: ***
// folded-file: t ***
// compile-command-1: "make installg" ***
// compile-command-2: "make install" ***
// End: ***
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