1zef(1)                           User Commands                          zef(1)
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NAME

6       zef - convert a matrix to echelon form
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SYNOPSIS

9       zef [OPTIONS] <Inp> <Out>
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DESCRIPTION

12       This  program reads in a matrix, performs a Gaussian elimination to put
13       the matrix into semi-echelon form, and writes out the result.
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15       A matrix is in semi-echelon form, if the first non-zero entry  in  each
16       row  entry  is a 1, and all entries exactly below that 1 are zero. Here
17       is an example:
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19         000112312312342412123
20         012012312312231231233
21         000000001345121223233
22         102012330332333312212
23         001021230333323123123
24         000001230311212112121
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26       A matrix is in (full) echelon form if the rows are further permuted  so
27       that  the first non-zero entry in each row is later than the first non-
28       zero entry in all previous rows.  There is no real need to do this  row
29       permutation  in  the MeatAxe system, and the permutation is not done by
30       this program.
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32       At the end, the matrix may have fewer rows than it started with,  since
33       the  rows  may  have  been  linearly dependent.  The rows of the output
34       matrix are always linearly independent and span the same space  as  the
35       rows of the input matrix.  A message:
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37         RANK nnn
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39       is  printed at the end of the run to notify the operator of the size of
40       the output matrix.  This program may  be  used  to  find  the  rank  of
41       matrix, being faster than the null-space program.  There is no need for
42       the input matrix to be square, and the output may also not be square.
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OPTIONS

45       -Q     Quiet, no messages.
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47       -V     Verbose, more messages.
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49       -T <MaxTime>
50              Set CPU time limit
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52       -G     Produce output in GAP format.  This option implies -Q.
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INPUT FILES

55       Inp    The matrix.
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OUTPUT FILES

58       Out    The reduced matrix.
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62MeatAxe                             2.4.24                              zef(1)