USAGE: change_cost [options] groebner_file new_cost_file DESCRIPTION: change_cost is a program for recomputing the reduced Groebner basis of a toric ideal with respect to a term ordering with modified weights. This can be used for varying the cost function in integer programming (see the help for solve_IP for more information). The program simply restarts Buchberger´s algorithm on an already computed toric ideal using the modified term ordering. FILE FORMAT: The first input file has to be a GROEBNER file; the second input file should to be a NEW_COST file. For convenience, also MATRIX files are accepted as second input files. For their format see the help for the solve_IP or the toric_ideal program. change_cost writes the new Groebner basis into a GROEBNER file named like the second input file with extensions replaced by .GB. where GB stands for GROEBNER and is the abbreviation of the algorithm used for computing the input GROEBNER file (see the help for solve_IP or toric_ideal for an explanation). A GROEBNER file looks as follows: GROEBNER computed with algorithm: (* abbreviations as above *) from file(s): (* the following four lines are optional *) computation time: term ordering: elimination block variables >0 *) weighted block should always be >0 *) size: Groebner basis: (* optional *) The Groebner basis consists always of binomials of the form x^a - x^b where x^a and x^b are relatively prime. Such a binomial can be represented by the vector a-b. The basis elements in the GROEBNER file are given by the coefficients of this vector representation. The settings for Buchberger´s algorithm and the compiler flags are produced when the GROEBNER file is generated by a call of solve_IP with the verbose output option -v, --verbose Example: GROEBNER computed with algorithm: du term ordering: elimination block: 0 weighted block: 3 W_LEX 1 2 3 size: 1 Groebner basis: 2 3 -2 (* x^2 * y^3 - z^2 *) A NEW_COST file should look as follows: NEW_COST variables: cost vector: OPTIONS: -p percentage of new generators to cause an autoreduction during Buchberger´s algorithm; may be an arbitrary float, a negative value allows no intermediate autoreductions default is -p 12.0 -S [RP] [M] [B] [M] [2] criteria to use in Buchberger´s algorithm for discarding unnecessary S-pairs RP relatively prime leading terms M Gebauer-Moeller criterion M F Gebauer-Moeller criterion F B Gebauer-Moeller criterion B 2 Buchberger´s second criterion default is -S RP M B -v, --verbose verbose output mode; writes the settings for Buchberger´s algorithm and the compiler flags into the output GROEBNER file -V , --version version of Buchberger´s algorithm to use; may be 1, 1a, 2 or 3 default is -V 1