Basil
Basil (for BASIs List) enumerates bases of hyperplane arrangements up to symmetries. It depends on David Avis' LRS library to represent the hyperplane arrangements and Thomas Rehn's permlib for the permutation calculations.
Building
Run make basil
Dependencies
- Boost (including program_options)
- GMP
- doxygen (for documentation generation)
Documentation
Program Options
--arrangement-pivot Makes Basil pivot as if the input was an
arrangement.
--assume-no-symmetry Forces Basil to assume there is no symmetry in the
input.
--generate-symmetry Forces Basil to generate a new symmetry group
--show-all-dicts Show all intermediate dictionaries in the search
tree.
--no-fixed-plane Do not fix the x_0 = 1 plane for automorphism
calculations. This may result in spurious
automorphisms for certain instances (notably those
which have rows where x_0 = 0).
--fund-domain-lim arg Maximum number of constraints to include in the
fundamental domain [default 0]
--gram arg Gram matrix generation to use: 'begin' to use the
gram matrix from the input file, 'Q' to use the
Q-matrix metric for Gram hashing [default],
'no-augment' to use the Q-matrix metric without
row-augmenting the input first (only works for input
matrices of full rank), 'Euclidean' to use the
Euclidean metric for Gram matrix generation, or
'no-norm' to use the Euclidean metric without
normalizing the row vectors of the matrix to the
same norm (saves expensive normalization
calculations, at the possible expense of not finding
all symmetries)
--no-gram Deactivates Gram matrix hashing.
--debug-gram Print gram vectors for vertices/rays/cobases that
are printed
--stab-search Activate cobasis stabilizer search (not
reccommended, stabilizer computation costs more than
it saves)
--print-basis arg Print the number of cobases found and running time
every n cobases.
--print-new Print the added {cobasis,vertex,ray} when printing a
status message
--print-ray arg Print the number of cobases found and running time
every n cobases.
--print-vertex arg Print the number of cobases found and running time
every n cobases.
--print-each arg Convenience for print-{basis,ray,vertex} with the
given parameter. If any of the others are given,
they take precedence
--print-trace Print the full trace of the DFS (warning: very
verbose).
-p [ --preprocess ] Do not DFS, simply do preprocessing work, and print
normalized input file to output stream
-v [ --verbose ] Shorthand for --print-interval=1, --print-new. Those
settings, if supplied, will take precedence.
-i [ --input-file ] arg Input file name. Standard input if none supplied;
may also be supplied as first positional argument.
-m [ --matrix-file ] arg Matrix file name. Alias for --input-file.
-g [ --group-file ] arg File to read symmetry group from - overrides any
supplied in the input file.
-o [ --output-file ] arg Output file name. Standard output if none supplied;
may also be supplied as second positional argument.
-h [ --help ] Produce help message.
Input Format
(based on LRS)
[name]
[(H|V|A)-representation]
[linearity <k> < k linearity indices >]
[< other lrs options >]
begin
<n> <d> rational
< n * d whitespace-delimited data values >
end
[symmetry begin
{<comma-delimeted cycles of whitespace delimeted elements>}
symmetry end]
[gram auto
|gram Q
|gram augmented
|gram Euclid
|gram inexact
|gram begin
< n * n whitespace-delimited integers >
gram end]
[< other lrs options >]
Class Documentation
Run make doc (requires doxygen)