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MeatAxe 2.4
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zbl [Options] Input Output
This program reads in a matrix, zeroizes all entries above the main diagonal, and writes out the result. For example:
Mat Result
12100201201212212122 10000000000000000000
21000000000000001111 21000000000000000000
12212120101201201201 12200000000000000000
01020010020102012012 01020000000000000000
12100012101201012012 12100000000000000000
12120212121012012012 12120200000000000000
Notice that the input matrix need not be square, and the output matrix has always the same dimensions as the input matrix.
If file names are omitted, the matrix is read from G1 and output goes to P2.
The purpose of this program is to enable the MeatAxe to check if an irreducible representation in characteristic 2 fixes a quadratic form. This job is not particularly simple -- in many ways it is just a bodge, but it is possible:
for each generator
, and checking that the diagonal is still the same as it was before (the symplectic form should have been checked before starting). The check can be done by adding the form to the result, then doing zbl, ztr and zbl again --- the result will be the zero matrix (use znu) iff the form was fixed (given that the symplectic one was).