One way to work conveniently with the data is to put all .tbl files in a single directory. In my case I have a directory formlib of which the content is shown in this file. Be aware though that these files together use more than 27 Gbytes! If you do not have that much space try to make a selection of the files you may need.
In my .cshrc file I have the statement setenv FORMPATH .:/user/t68/lst/formlib It is important that the directory formlib is on the local disk. One does not want to move Gbytes across networks. It would make things very slow.
I have FORM installed in such a way that the directory in which it resides is in my path variable. Hence all I have to do is type form -l modbas19 to execute the file modbas19.frm. This file contains a program that uses one of the .tbl files to study the basis of the MZVs at weight 19 as embedded in the Euler sums. There is quite an amount of commentary in the file.
If you become a bit braver there are also the files modbas21.frm for the same at weight 21 (and with hardly any commentary) and rebas3.frm which rewrites MZVs in the Euler databases up to weight 17 depth 5 into the pushdown basis. It also studies the `climbers'.
A second example is the verification of a set of formulas discovered by M. Hoffman. The formulas are
H(2,1,2,3)-H(2,2,2,2)-2*H(2,3,3) = 0 H(2,1,2,2,3)-H(2,2,2,2,2)-2*H(2,2,3,3) = 0 H(2,1,2,2,2,3)-H(2,2,2,2,2,2)-2*H(2,2,2,3,3) = 0 H(2,1,2,2,2,2,3)-H(2,2,2,2,2,2,2)-2*H(2,2,2,2,3,3) = 0The first three are given in his homepage (actually a subpage of it) and can be tested there. The last one is also given, but the testing program can apparently not handle it. The program apply.frm works it out up to weight 22. Again it assumes that the corresponding tablebases (mzv12.tbl to mzv22.tbl) can be found by FORM. If you are just curious about the result, but do not want to go through the hassle of installing all those files you can cheat and look at the output.