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petersonfree is a collection of programs for comparing Peterson translation and freeness of hyperplane arrangements, in support of the following papers: W. Slofstra. Rationally smooth Schubert varieties and inversion hyperplane arrangements. http://arxiv.org/abs/1312.7540. 2013. W. Slofstra. A pattern avoidance criterion for free inversion arrangements. http://arxiv.org/abs/1409.7299. 2014. Note: The code has a lot of rough edges, and probably shouldn't be used for anything other than verifying the claims in the above papers. Use at your own peril. For more information see <http://www.math.ucdavis.edu/~wslofstra>. Currently the collection contains 3 programs: - indfree: check inductive freeness of hyperplane arrangements over the integers. - freepattern: find minimally non-free convex/coconvex/biconvex subsets of rootsystems. - petersonfree: generate Peterson translation graphs, and check freeness of the vertices. To make any of these programs from source: cd src make program_name cd .. cp src/program_name . There is also a certificate checker to verify the output of indfree. To make the certificate checker: cd check_certificate make cd .. cp check_certificate/checkcert . To see a summary of commandline options for any of these programs: ./program_name -h Also included: - maple_src: similar programs implemented in Maple. - sage_src: a certficate checking program in sage. - scripts: directory for related shell scripts. - input: directory for input files. - output: directory for output files. - certs: directory for certificates generated by indfree. ------------------------------------------------------------------------------------------------- indfree is a program for checking inductive freeness of hyperplane arrangements. 1. To generate a certificate of a inductive freeness for a file: ./indfree cert cert_filename < input_filename Some default files are in the "input" directory. So to get a certificate of freeness for D4, run ./indfree cert certs/D4.cert < input/D4 2. To check the certificate: ./checkcert cert_filename < input_filename So for D4: ./checkcert certs/D4.cert < input/D4 One of the reasons for the certificate checker is that indfree (as well as the other programs in this collection use long long ints (effectively working mod 2^64), whereas the certificate checker can handle integers of arbitrary size (via gmp). 3. To check the certificate in sage: ./indfree sage cert_filename.sage < input/input_filename sage %load cert_filename.sage %load sage_src/check_certificate.sage check_certificate(M,C) So for D4, generate the sage certificate: ./indfree sage D4.sage < input/D4 And verify: sage %load certs/D4.sage %load sage_src/check_certificate.sage check_certificate(M,C) ------------------------------------------------------------------------------------------------- freepattern is a program for finding the minimal non-free convex/coconvex/biconvex sets in a root system. Currently the program cannot generate the rootsystems; these must be given as input. 1. To generate all coconvex sets: ./freepattern coconvex < input/rootsystem So for instance to generate all coconvex sets for D4: ./freepattern coconvex < input/D4 2. A set is minimally non-free if it is not free, and no flattening of the set is non-free. To generate all minimally non-free coconvex sets: ./freepattern comin < input/rootsystem Run ./freepattern to see other options. ------------------------------------------------------------------------------------------------- petersonfree is a program to generate the Peterson translation graph associated with a root system. 1. To generate the Peterson translation graph: ./petersonfree < input/rootsystem Note that the vertices of this graph are coconvex subsets of the root system, specified as a column set. Each vertex is assigned an identification number, and edges are specified as n (l) where n is the target edge, and l is the column of the original input matrix labelling the edge. 2. To test freeness of each vertex: ./petersonfree 0 < input/rootsystem Run ./petersonfree help to see other options and information.