1 | USAGE: change_cost [options] groebner_file new_cost_file |
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2 | |
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3 | |
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4 | |
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5 | DESCRIPTION: |
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6 | |
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7 | change_cost is a program for recomputing the reduced Groebner basis of |
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8 | a toric ideal with respect to a term ordering with modified |
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9 | weights. This can be used for varying the cost function in integer |
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10 | programming (see the help for solve_IP for more information). |
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11 | The program simply restarts BuchbergerŽs algorithm on an already |
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12 | computed toric ideal using the modified term ordering. |
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13 | |
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14 | |
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15 | |
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16 | FILE FORMAT: |
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17 | |
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18 | The first input file has to be a GROEBNER file; the second input file |
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19 | should to be a NEW_COST file. For convenience, also MATRIX files are |
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20 | accepted as second input files. For their format see the help for the |
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21 | solve_IP or the toric_ideal program. |
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22 | |
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23 | change_cost writes the new Groebner basis into a GROEBNER file named |
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24 | like the second input file with extensions replaced by |
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25 | |
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26 | .GB.<alg> |
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27 | |
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28 | where GB stands for GROEBNER and <alg> is the abbreviation of the |
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29 | algorithm used for computing the input GROEBNER file (see the help for |
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30 | solve_IP or toric_ideal for an explaination). |
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31 | |
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32 | A GROEBNER file looks as follows: |
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33 | |
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34 | |
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35 | GROEBNER |
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36 | |
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37 | computed with algorithm: |
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38 | <algorithm name abbreviation> (* abbreviations as above *) |
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39 | from file(s): (* the following four lines are |
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40 | <name of respective MATRIX file> optional *) |
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41 | computation time: |
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42 | <computation time in seconds> |
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43 | |
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44 | term ordering: |
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45 | elimination block |
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46 | <number of elimination variables> |
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47 | <LEX / DEG_LEX (* only if number of elimination |
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48 | / DEG_REV_LEX> variables >0 *) |
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49 | weighted block |
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50 | <number of weighted variables> |
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51 | <W_LEX / W_REV_LEX (* number of weighted variables |
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52 | / W_DEG_LEX / W_DEG_REV_LEX> should always be >0 *) |
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53 | <weight_vector> |
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54 | |
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55 | size: |
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56 | <number of elements> |
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57 | |
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58 | Groebner basis: |
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59 | <basis elements> |
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60 | |
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61 | <settings for the Buchberger |
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62 | algorithm and compiler settings> (* optional *) |
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63 | |
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64 | |
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65 | The Groebner basis consists always of binomials of the form x^a - x^b |
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66 | where x^a and x^b are relatively prime. Such a binomial can be |
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67 | represented by the vector a-b. The basis elements in the GROEBNER file |
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68 | are given by the coefficients of this vector representation. |
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69 | The settings for BuchbergerŽs algorithm and the compiler flags are |
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70 | produced when the GROEBNER file is generated by a call of solve_IP |
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71 | with the verbose output option |
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72 | |
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73 | -v, --verbose |
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74 | |
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75 | Example: |
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76 | |
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77 | |
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78 | GROEBNER |
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79 | |
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80 | computed with algorithm: |
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81 | du |
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82 | |
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83 | term ordering: |
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84 | elimination block: |
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85 | 0 |
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86 | weighted block: |
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87 | 3 |
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88 | W_LEX |
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89 | 1 2 3 |
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90 | |
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91 | size: |
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92 | 1 |
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93 | |
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94 | Groebner basis: |
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95 | 2 3 -2 (* x^2 * y^3 - z^2 *) |
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96 | |
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97 | |
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98 | A NEW_COST file should look as follows: |
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99 | |
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100 | |
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101 | NEW_COST |
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102 | |
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103 | variables: |
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104 | <number of weighted variables> |
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105 | |
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106 | cost vector: |
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107 | <coefficients of the new weight vector> |
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108 | |
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109 | |
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110 | |
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111 | OPTIONS: |
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112 | |
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113 | -p <number> percentage of new generators to cause an |
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114 | autoreduction during BuchbergerŽs algorithm; |
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115 | <number> may be an arbitrary float, a |
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116 | negative value allows no intermediate |
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117 | autoreductions |
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118 | default is |
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119 | -p 12.0 |
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120 | |
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121 | -S [RP] [M] [B] [M] [2] criteria to use in BuchbergerŽs algorithm |
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122 | for discarding unneccessary S-pairs |
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123 | RP relatively prime leading terms |
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124 | M Gebauer-Moeller criterion M |
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125 | F Gebauer-Moeller criterion F |
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126 | B Gebauer-Moeller criterion B |
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127 | 2 BuchbergerŽs second criterion |
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128 | default is |
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129 | -S RP M B |
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130 | |
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131 | -v, |
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132 | --verbose verbose output mode; writes the settings for |
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133 | BuchbergerŽs algorithm and the compiler |
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134 | flags into the output GROEBNER file |
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135 | |
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136 | -V <number>, |
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137 | --version <number> version of BuchbergerŽs algorithm to use; |
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138 | <number> may be 1, 1a, 2 or 3 |
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139 | default is |
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140 | -V 1 |
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141 | |
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