[6ba162] | 1 | USAGE: change_cost [options] groebner_file new_cost_file |
---|
| 2 | |
---|
| 3 | |
---|
| 4 | |
---|
| 5 | DESCRIPTION: |
---|
| 6 | |
---|
| 7 | change_cost is a program for recomputing the reduced Groebner basis of |
---|
| 8 | a toric ideal with respect to a term ordering with modified |
---|
| 9 | weights. This can be used for varying the cost function in integer |
---|
| 10 | programming (see the help for solve_IP for more information). |
---|
| 11 | The program simply restarts BuchbergerŽs algorithm on an already |
---|
| 12 | computed toric ideal using the modified term ordering. |
---|
| 13 | |
---|
| 14 | |
---|
| 15 | |
---|
| 16 | FILE FORMAT: |
---|
| 17 | |
---|
| 18 | The first input file has to be a GROEBNER file; the second input file |
---|
| 19 | should to be a NEW_COST file. For convenience, also MATRIX files are |
---|
| 20 | accepted as second input files. For their format see the help for the |
---|
| 21 | solve_IP or the toric_ideal program. |
---|
| 22 | |
---|
| 23 | change_cost writes the new Groebner basis into a GROEBNER file named |
---|
| 24 | like the second input file with extensions replaced by |
---|
| 25 | |
---|
| 26 | .GB.<alg> |
---|
| 27 | |
---|
| 28 | where GB stands for GROEBNER and <alg> is the abbreviation of the |
---|
| 29 | algorithm used for computing the input GROEBNER file (see the help for |
---|
| 30 | solve_IP or toric_ideal for an explaination). |
---|
| 31 | |
---|
| 32 | A GROEBNER file looks as follows: |
---|
| 33 | |
---|
| 34 | |
---|
| 35 | GROEBNER |
---|
| 36 | |
---|
| 37 | computed with algorithm: |
---|
| 38 | <algorithm name abbreviation> (* abbreviations as above *) |
---|
| 39 | from file(s): (* the following four lines are |
---|
| 40 | <name of respective MATRIX file> optional *) |
---|
| 41 | computation time: |
---|
| 42 | <computation time in seconds> |
---|
| 43 | |
---|
| 44 | term ordering: |
---|
| 45 | elimination block |
---|
| 46 | <number of elimination variables> |
---|
| 47 | <LEX / DEG_LEX (* only if number of elimination |
---|
| 48 | / DEG_REV_LEX> variables >0 *) |
---|
| 49 | weighted block |
---|
| 50 | <number of weighted variables> |
---|
| 51 | <W_LEX / W_REV_LEX (* number of weighted variables |
---|
| 52 | / W_DEG_LEX / W_DEG_REV_LEX> should always be >0 *) |
---|
| 53 | <weight_vector> |
---|
| 54 | |
---|
| 55 | size: |
---|
| 56 | <number of elements> |
---|
| 57 | |
---|
| 58 | Groebner basis: |
---|
| 59 | <basis elements> |
---|
| 60 | |
---|
| 61 | <settings for the Buchberger |
---|
| 62 | algorithm and compiler settings> (* optional *) |
---|
| 63 | |
---|
| 64 | |
---|
| 65 | The Groebner basis consists always of binomials of the form x^a - x^b |
---|
| 66 | where x^a and x^b are relatively prime. Such a binomial can be |
---|
| 67 | represented by the vector a-b. The basis elements in the GROEBNER file |
---|
| 68 | are given by the coefficients of this vector representation. |
---|
| 69 | The settings for BuchbergerŽs algorithm and the compiler flags are |
---|
| 70 | produced when the GROEBNER file is generated by a call of solve_IP |
---|
| 71 | with the verbose output option |
---|
| 72 | |
---|
| 73 | -v, --verbose |
---|
| 74 | |
---|
| 75 | Example: |
---|
| 76 | |
---|
| 77 | |
---|
| 78 | GROEBNER |
---|
| 79 | |
---|
| 80 | computed with algorithm: |
---|
| 81 | du |
---|
| 82 | |
---|
| 83 | term ordering: |
---|
| 84 | elimination block: |
---|
| 85 | 0 |
---|
| 86 | weighted block: |
---|
| 87 | 3 |
---|
| 88 | W_LEX |
---|
| 89 | 1 2 3 |
---|
| 90 | |
---|
| 91 | size: |
---|
| 92 | 1 |
---|
| 93 | |
---|
| 94 | Groebner basis: |
---|
| 95 | 2 3 -2 (* x^2 * y^3 - z^2 *) |
---|
| 96 | |
---|
| 97 | |
---|
| 98 | A NEW_COST file should look as follows: |
---|
| 99 | |
---|
| 100 | |
---|
| 101 | NEW_COST |
---|
| 102 | |
---|
| 103 | variables: |
---|
| 104 | <number of weighted variables> |
---|
| 105 | |
---|
| 106 | cost vector: |
---|
| 107 | <coefficients of the new weight vector> |
---|
| 108 | |
---|
| 109 | |
---|
| 110 | |
---|
| 111 | OPTIONS: |
---|
| 112 | |
---|
| 113 | -p <number> percentage of new generators to cause an |
---|
| 114 | autoreduction during BuchbergerŽs algorithm; |
---|
| 115 | <number> may be an arbitrary float, a |
---|
| 116 | negative value allows no intermediate |
---|
| 117 | autoreductions |
---|
| 118 | default is |
---|
| 119 | -p 12.0 |
---|
| 120 | |
---|
| 121 | -S [RP] [M] [B] [M] [2] criteria to use in BuchbergerŽs algorithm |
---|
| 122 | for discarding unneccessary S-pairs |
---|
| 123 | RP relatively prime leading terms |
---|
| 124 | M Gebauer-Moeller criterion M |
---|
| 125 | F Gebauer-Moeller criterion F |
---|
| 126 | B Gebauer-Moeller criterion B |
---|
| 127 | 2 BuchbergerŽs second criterion |
---|
| 128 | default is |
---|
| 129 | -S RP M B |
---|
| 130 | |
---|
| 131 | -v, |
---|
| 132 | --verbose verbose output mode; writes the settings for |
---|
| 133 | BuchbergerŽs algorithm and the compiler |
---|
| 134 | flags into the output GROEBNER file |
---|
| 135 | |
---|
| 136 | -V <number>, |
---|
| 137 | --version <number> version of BuchbergerŽs algorithm to use; |
---|
| 138 | <number> may be 1, 1a, 2 or 3 |
---|
| 139 | default is |
---|
| 140 | -V 1 |
---|
| 141 | |
---|