[a5f15a] | 1 | #ifndef MPR_H |
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| 2 | #define MPR_H |
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| 3 | /**************************************** |
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| 4 | * Computer Algebra System SINGULAR * |
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| 5 | ****************************************/ |
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[9a6c4a] | 6 | |
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[416465] | 7 | /* $Id: mpr_inout.h,v 1.5 1999-11-15 17:20:31 obachman Exp $ */ |
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[a5f15a] | 8 | |
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[e858e7] | 9 | /* |
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[a5f15a] | 10 | * ABSTRACT - multipolynomial resultants - interface to Singular |
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[e858e7] | 11 | * |
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[a5f15a] | 12 | */ |
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| 13 | |
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| 14 | #define DEFAULT_DIGITS 30 |
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| 15 | |
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| 16 | #define MPR_DENSE 1 |
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| 17 | #define MPR_SPARSE 2 |
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| 18 | |
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| 19 | /** solve a multipolynomial system using the u-resultant |
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| 20 | * Input ideal must be 0-dimensional and pVariables == IDELEMS(ideal). |
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[e858e7] | 21 | * Resultant method can be MPR_DENSE, which uses Macaulay Resultant (good for |
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| 22 | * dense homogeneous polynoms) or MPR_SPARSE, which uses Sparse Resultant |
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[a5f15a] | 23 | * (Gelfand, Kapranov, Zelevinsky). |
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[da408f] | 24 | * Arguments 4: ideal i, int k, int l, int m |
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| 25 | * k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky |
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| 26 | * k=1: use resultant matrix of Macaulay (k=0 is default) |
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| 27 | * l>0: defines precision of fractional part if ground field is Q |
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| 28 | * m=0,1,2: number of iterations for approximation of roots (default=2) |
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[a5f15a] | 29 | * Returns a list containing the roots of the system. |
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| 30 | */ |
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[da408f] | 31 | BOOLEAN nuUResSolve( leftv res, leftv args ); |
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[a5f15a] | 32 | |
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[da408f] | 33 | /** returns module representing the multipolynomial resultant matrix |
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| 34 | * Arguments 2: ideal i, int k |
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| 35 | * k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky |
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| 36 | * k=1: use resultant matrix of Macaulay (k=0 is default) |
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[a5f15a] | 37 | */ |
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| 38 | BOOLEAN nuMPResMat( leftv res, leftv arg1, leftv arg2 ); |
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| 39 | |
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| 40 | /** find the (complex) roots an univariate polynomial |
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[e858e7] | 41 | * Determines the roots of an univariate polynomial using Laguerres' |
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[a5f15a] | 42 | * root-solver. Good for polynomials with low and middle degree (<40). |
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[da408f] | 43 | * Arguments 3: poly arg1 , int arg2 , int arg3 |
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| 44 | * arg2>0: defines precision of fractional part if ground field is Q |
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| 45 | * arg3: number of iterations for approximation of roots (default=2) |
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| 46 | * Returns a list of all (complex) roots of the polynomial arg1 |
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[a5f15a] | 47 | */ |
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[da408f] | 48 | BOOLEAN nuLagSolve( leftv res, leftv arg1, leftv arg2, leftv arg3 ); |
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[a5f15a] | 49 | |
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| 50 | /** |
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[da408f] | 51 | * COMPUTE: polynomial p with values given by v at points p1,..,pN derived |
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| 52 | * from p; more precisely: consider p as point in K^n and v as N elements in K, |
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| 53 | * let p1,..,pN be the points in K^n obtained by evaluating all monomials |
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| 54 | * of degree 0,1,...,N at p in lexicographical order, then the procedure |
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| 55 | * computes the polynomial f satisfying f(pi) = v[i] |
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| 56 | * RETURN: polynomial f of degree d |
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[a5f15a] | 57 | */ |
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| 58 | BOOLEAN nuVanderSys( leftv res, leftv arg1, leftv arg2, leftv arg3 ); |
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| 59 | |
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| 60 | #endif |
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| 61 | |
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| 62 | // local Variables: *** |
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| 63 | // folded-file: t *** |
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| 64 | // compile-command-1: "make installg" *** |
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| 65 | // compile-command-2: "make install" *** |
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[e858e7] | 66 | // End: *** |
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