LIST OF FILES ============= Symmetry classifications ------------------------ To solve the simple but relatively extensive linear systems resulting from the symmetry classification, a special solver for solving large linear systems was written in REDUCE. It is available as file streamsolve.red in the directory SymmetryClassification. For example, when computing for n=4 from the face formula that already has the symmetry -+++ and thus has 349 unknown coefficients a specialization which in addition has the SL2-symmetry then this program - reads 24556 equations from the 5.2MB file 4dsymm_case1222, - solves these equations, and - writes the solution into the file 4dsymm_case1222.out in a 80MB session of REDUCE 3.8 running under Linux on a 32bit 900MHz Pentium III laptop in 37 sec. The default REDUCE solver SOLVE was not able to solve this or similar systems. All the mentioned files are available in the directory SymmetryClassification. For more details about the solver see the top of the file streamsolve.red. To do a test run, start REDUCE in a directory with the 2 files streamsolve.red and 4dsymm_case1222 and input: in "streamsolve.red"$ read_and_solve()$ "4dsymm_case1222" q n Solutions of consistency conditions for n=3 ------------------------------------------- In the directory SolutionsOfConsistency the sub-directories case---, case-++ and case+++ hold files s1,s2,... which are the solutions of the algebraic systems for the unknowns q_i which remain to be solved after the symmetry considerations. For case--- only one unknown q27 was left, for case-++ 13 unknowns had been left and for case+++ 22 unknows had to be determined. For each solution si there is a file Qi with the complete face formula corresponding to the solution si. In Qi the face formula is given first in human readable form and then machine readable form. "Brute force" checking of 4d-consistency of the unique formula for the case (---) ----------------------------------------------- In the directory BruteForceCheck the subdirectory Case--- contains the files: Q---terms.log - the commented FORM logfile for the estimate of the number of terms to be generated if the 4d-consistency check would be done straightforwardly for the smallest face formula (5). Please see the comments inside the file. Q---.frm and Q---.log contain the FORM code and the logfile of the FORM run proving that this face formula (5) is in fact 4d-consistent. Simplification of the candidate formulas using SL_2 --------------------------------------------------- In the directory SL2-simplification, and its subdirectories Case+++/ and Case-++/ one can find the FORM files and their respective log-files for SL_2-simplification of the corresponding candidate cases found by CRACK. Sometimes one should treat subsubcases when one of the free parametric q's may be 0, these cases are run separately and the subsubcase specification is included in the file name, for example the file Q1-q6-0.frm contains simplification of the case "Q1" with q6=0. The file 3d222-all.frm is the common data source for all of the subcases treated in Case+++, it contains the general face formula for the case (+++). The files Q*-in.frm in the subdirectory Case-++ contain the respective face formulas for the corresponding subcases Q1, Q2, Q3. The most difficult subcase was Q2 in the subdirectory Case+++. It required two consequitive runs as well as investigation of two subcases, q3=0 and q7=0. The latter after a transformation coincides with the partially simplified general case, obtained after running Q2.frm. On the next stage, the code Q2-step2.frm finally gets the completely simplified form, as given by the formula (6) in the paper. Please look into the commented code in Q2-step2.frm.