# Singular/Sources

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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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