How to use the program for computing Grobner fans.

Put the file "toric.tar" in a separate dir and use "tar -x < toric.tar" to extract. Run "make". This will produce two executable files "main" and "tester". Following is a list of examples on how to use the program:

EXAMPLE 1: Computing a reduced Grobner basis of the ideal I_A where A=[1,2,3,4].

Run the program "main".
Type "3" to select [Sturmfels] algorithm 12.3.
Type "1" ... yes we want the output LaTeXed to a dvi-file
Type "0" since we do not want a random matrix
Type "{(1)(2)(3)(4)}" which is the ASCII-representation of the matrix A

Now the program starts computing and produces the file "ud.tex" and if latex is available in the path it also produces the "ud.dvi" file. View this file with xdvi: "xdvi ud.dvi&" to see each step in the algorithm.

EXAMPLE 2: Computing all reduced Grobner bases of the ideal I_A where A=[1,2,3,4] and list them.

Run the program "main".
Type "7" to select the exhaustive search method which is needed when listing all reduced Grobner bases.
Type "2" LaTeX the output and list the Grobner bases too
Type "0" since we do not want a random matrix
Type "{(1)(2)(3)(4)}" which is the ASCII-representation of matrix A

The program will now produce the "ud.dvi" file containing a list of the 20 reduced Grobner bases of I_A.

EXAMPLE 3: Computing all reduced Grobner bases of the ideal I_HA8

where HA8 is the 2x8 matrix:


1 1 1 1 1 1 1 1


 1 2 3 4 5 6 7 8

Run the program "main"
Type "8" to select the reverse search method
Type "1" to LaTeX the output. We do not want to list the bases in the output
Type "0" since we do not want a random matrix
Type "{(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(1,7)(1,8)}"

The program now traverses the graph. This will take a while. When finished we can see the number of vertices (40284) and the number of edges (147086) in the file "ud.dvi". These numbers are also written to the file "output".

EXAMPLE 4: Producing a table of timings for the built-in examples.

Make sure that the file "main" is in your path. (you could use "PATH=.:$PATH")
Run the program "tester"
Type "1" since we want to test the traversing algorithms
Wait several hours

The program produces the files "tableB.tex" and "tableB.dvi" containing the results.