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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6 | |
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7 | /* $Id: mpr_inout.h,v 1.1.1.1 2003-10-06 12:15:58 Singular Exp $ */ |
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8 | |
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9 | /* |
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10 | * ABSTRACT - multipolynomial resultants - interface to Singular |
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11 | * |
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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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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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23 | * (Gelfand, Kapranov, Zelevinsky). |
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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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29 | * Returns a list containing the roots of the system. |
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30 | */ |
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31 | BOOLEAN nuUResSolve( leftv res, leftv args ); |
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32 | |
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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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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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41 | * Determines the roots of an univariate polynomial using Laguerres' |
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42 | * root-solver. Good for polynomials with low and middle degree (<40). |
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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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47 | */ |
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48 | BOOLEAN nuLagSolve( leftv res, leftv arg1, leftv arg2, leftv arg3 ); |
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49 | |
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50 | /** |
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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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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 | /** compute Newton Polytopes of input polynomials |
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61 | */ |
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62 | BOOLEAN loNewtonP( leftv res, leftv arg1 ); |
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63 | |
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64 | /** Implementation of the Simplex Algorithm. |
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65 | * For args, see class simplex. |
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66 | */ |
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67 | BOOLEAN loSimplex( leftv res, leftv args ); |
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68 | |
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69 | #endif |
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70 | |
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71 | // local Variables: *** |
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72 | // folded-file: t *** |
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73 | // compile-command-1: "make installg" *** |
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74 | // compile-command-2: "make install" *** |
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75 | // End: *** |
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