| 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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