**FinInG** (pronunciation: [fɪnɪŋ]) is a package for computation in Finite Incidence Geometry. It provides users with the basic tools to work in various areas of finite geometry from the realms of projective spaces to the flat lands of generalised polygons. The algebraic power of GAP is employed, particularly in its facility with matrix and permutation groups.

A sample making FinInG's pronunciation crystal clear can be found here.

The development group of **FinInG** welcomes contact with users. In case you have obtained the package as a deposited package part of archive during the installation of GAP, we call on your beneficence to register at http://www.fining.org when you use **FinInG** or to tell us by sending a message to council@fining.org.

Please tell us about the use of **FinInG** in your research or teaching. We are very interested in results obtained using **FinInG** and we might refer to your work in the future. If your work is published, we ask you to cite **FinInG** like a journal article or book.

If you are using BibTeX, you can use the following BibTeX entry for the current **FinInG** version:

@manual{fining, Author = {Bamberg, John and Betten, Anton and Cara, Philippe and De Beule, Jan and Lavrauw, Michel and Neunh\"offer, Max }, Key = {fining}, Title = {{FinInG -- Finite Incidence Geometry, Version 1.5.6}}, Url = {\verb+(http://www.fining.org)+}, Year = 2023}

Here is the bibliography entry produced by BibTeX (in bibliography style `alpha'), to be pasted directly inside the bibliography environment of your LaTeX document:

\bibitem[FinInG]{fining} J.~Bamberg, A.~Betten, {Ph}. Cara, J.~De~Beule, M.~Lavrauw, and M.~Neunh\"offer. \newblock {\em Finite Incidence Geometry}. \newblock FInInG -- a {GAP} package, version 1.5.6, 2023.

When linking to FinInG from a web page you can use the link

<a href="http://www.fining.org">FinInG</a>.

This chapter (section 1.4) describes the installation of the package. Chapter 2 contains some extended examples to introduce the user to the basic functionality and philosophy to get started. Chapter 3 contains a rigorous description of the basic structures. This chapter can be omitted at first reading, since the set of consequent chapters is also self contained. Chapters 4, 5 and 6 deal with projective spaces, projective semilinear groups and polarities of projective spaces, respectively. In Chapter 7 the functionality for classical polar spaces is treated and in Chapter 9 affine spaces and their groups are considered. *Geometry morphisms* between various geometries that are available in the package, are introduced and discussed in Chapter 10. The final three chapters, 11, 12, and 13 explain the basic functionality which is provided for algebraic varieties (in projective or affine spaces), generalised polygons, of which several models can be constructed, and finally coset geometries and diagrams.

Since version 4.7.8, the official **GAP** distribution includes the **FinInG** package. The **FinInG** package requires the GAP packages **GAPDoc**, version 1.6 or higher, **Forms**, version 1.2.3 or higher, **Orb**, version 4.7.6 or higher, **GenSS**, version 1.6.4 or higher, and **GRAPE**, version 4.7 or higher, and **cvec**, version 2.5.7 or higher. These required packages are all part of the standard **GAP** distribution. However, the packages **cvec**, **GRAPE**, **IO**, and **Orb** may require additional compilation (cfr. infra for detailed instructions). Note that the **IO** is a package required by **cvec** and **Orb**, and is also part of the standard **GAP** distribution. Shortly summarized, to get **FinInG** working, download and install **GAP** as explained in its installation instructions, and, under UNIX like systems (including MacOS), make sure that the compilation of the packages **cvec**, **GRAPE**, **IO**, and **Orb** is done. Note that the windows distribution of **GAP** contains precompiled binaries of these packages, so under Windows, no further steps are required after installing **GAP** according to its installation instructions. In the next section we summarize the installation procedure under UNIX like systems.

The installation of **GAP** itself is generic for each UNIX like system, including the different flavours of Mac OS. You only need a terminal application, and you need access to the standard unix tools gunzip and tar, and the make tools. Detailed information on how to install **GAP**, can be found in the documentation of **GAP**. The installation procedure for **FinInG**, a standard GAP package, does *not* require compilation, however the packages **cvec**, **GRAPE**, **IO**, and **Orb** do. First install **GAP** according to the installation instructions. If you start **GAP** the output might look like in the example below. Note that **IO** is not listed as loaded package (see line starting with 'Packages' in the example output). This means that **IO** has not been compiled. Trying to load the **IO** will result in an error message.

jdebeule ~ $ gap4r8 +-------+ GAP 4.8.8, 20-Aug-2017, build of 2017-09-04 15:17:33 (CEST) | GAP | https://www.gap-system.org +-------+ Architecture: x86_64-apple-darwin16.7.0-gcc-default64 Libs used: gmp Loading the library and packages ... Components: trans 1.0, prim 2.1, small* 1.0, id* 1.0 Packages: AClib 1.2, Alnuth 3.0.0, AtlasRep 1.5.1, AutPGrp 1.8, CRISP 1.4.4, Cryst 4.1.12, CrystCat 1.1.6, CTblLib 1.2.2, FactInt 1.5.4, FGA 1.3.1, GAPDoc 1.6, IRREDSOL 1.4, LAGUNA 3.7.0, Polenta 1.3.7, Polycyclic 2.11, RadiRoot 2.7, ResClasses 4.6.0, Sophus 1.23, SpinSym 1.5, TomLib 1.2.6, Utils 0.46 Try '??help' for help. See also '?copyright', '?cite' and '?authors' gap> LoadPackage("io"); #I IO package is not available. To see further details, enter #I SetInfoLevel(InfoPackageLoading,4); and try to load the package again. fail

In this subsection it is explained how to compile the necessary packages in case this is not yet done for your **GAP** installation. We assume that you have write access to the **GAP** installation on your computer. If this is not the case, you should ask your system administrator to do this for you. Locate your **GAP** installation. The examples below are generated using a GAP4.8.8 installation residing in "/opt/gap4r8". Clearly, subsequent versions of gap will reside in a differently named directory, e.g. "/opt/gap4r9". Another commonly used directory under UNIX like systems to install software is "/usr/local", so gap might reside in "/usr/local/gap4r8" too. In all examples in this section, we assume your **GAP** installation resides in "/opt/gap4r8". Therefore, replace any occurrence of "/opt/gap4r8" with the actual directory of your **GAP** installation when executing the installation steps. Three steps will be necessary to compile the **IO** package: go into the correct directory, and issue the 'configure' command and then issue the 'make' command. Note that the directory name of the package is dependent on its version number. The correct name can be found as follows:

jdebeule ~ $ ls /opt/gap4r8/pkg/ |grep io- io-4.4.6

From this output, it can be determined that the **IO** resides in "/opt/gap4r8/pkg/io-4.4.6/". The three steps to be taken to compile **io** are demonstrated in the example below.

root ~ $ cd /opt/gap4r8/pkg/io-4.4.6/ root /opt/gap4r8/pkg/io-4.4.6 $ ./configure checking for a BSD-compatible install... /usr/bin/install -c checking whether build environment is sane... yes checking for a thread-safe mkdir -p... cnf/install-sh -c -d ... ...lots of output ... config.status: creating Makefile config.status: creating src/pkgconfig.h config.status: src/pkgconfig.h is unchanged config.status: executing depfiles commands config.status: executing libtool commands root /opt/gap4r8/pkg/io-4.4.6 $ make CC src/io_la-io.lo CCLD io.la cnf/install-sh -c -d ./bin/x86_64-apple-darwin16.7.0-gcc-default64 cp .libs/io.so bin/x86_64-apple-darwin16.7.0-gcc-default64/io.so

Now starting **GAP** should produce the following output, notice the presence of "IO 4.4.6" as one of the loaded packages.

jdebeule ~ $ gap4r8 +-------+ GAP 4.8.8, 20-Aug-2017, build of 2017-09-04 15:17:33 (CEST) | GAP | https://www.gap-system.org +-------+ Architecture: x86_64-apple-darwin16.7.0-gcc-default64 Libs used: gmp Loading the library and packages ... Components: trans 1.0, prim 2.1, small* 1.0, id* 1.0 Packages: AClib 1.2, Alnuth 3.0.0, AtlasRep 1.5.1, AutPGrp 1.8, CRISP 1.4.4, Cryst 4.1.12, CrystCat 1.1.6, CTblLib 1.2.2, FactInt 1.5.4, FGA 1.3.1, GAPDoc 1.6, IO 4.4.6, IRREDSOL 1.4, LAGUNA 3.7.0, Polenta 1.3.7, Polycyclic 2.11, RadiRoot 2.7, ResClasses 4.6.0, Sophus 1.23, SpinSym 1.5, TomLib 1.2.6, Utils 0.46 Try '??help' for help. See also '?copyright', '?cite' and '?authors' gap>

Similar steps are now necessary to compile the package **cvec**, **Orb**, and **grape**: go into the correct directory, and issue the 'configure' and 'make' command. In the example below, we include the determination of the correct directory names. Note that the directory name of the **grape** package is not dependent on its version number, so it resides in "/opt/gap4r8/pkg/grape".

root /opt/gap4r8/pkg/cvec-2.5.7 $ cd root ~ $ ls /opt/gap4r8/pkg/ |grep cvec- cvec-2.5.7 root ~ $ cd /opt/gap4r8/pkg/cvec-2.5.7/ root /opt/gap4r8/pkg/cvec-2.5.7 $ ./configure ... ...lots of output ... config.status: executing libtool commands root /opt/gap4r8/pkg/cvec-2.5.7 $ make CC src/cvec_la-cvec.lo CCLD cvec.la cnf/install-sh -c -d ./bin/x86_64-apple-darwin16.7.0-gcc-default64 cp .libs/cvec.so bin/x86_64-apple-darwin16.7.0-gcc-default64/cvec.so root ~ $ ls /opt/gap4r8/pkg/ |grep orb- orb-4.7.6 root ~ $ cd /opt/gap4r8/pkg/orb-4.7.6/ root /opt/gap4r8/pkg/orb-4.7.6 $ ./configure ... ...lots of output ... config.status: executing libtool commands root /opt/gap4r8/pkg/orb-4.7.6 $ make ...some output cp .libs/orb.so bin/x86_64-apple-darwin16.7.0-gcc-default64/orb.so root ~ $ cd /opt/gap4r8/pkg/grape root /opt/gap4r8/pkg/grape $ ./configure root /opt/gap4r8/pkg/grape $ make ...lots of output root /opt/gap4r8/pkg/grape $

Note that warnings may occur during the compilation process, which can all be ignored. If compilation of these packages has been successful, restart **GAP** and load **FinInG** using "LoadPackage("fining")". The output should look as follows.

jdebeule ~ $ gap4r8 +-------+ GAP 4.8.8, 20-Aug-2017, build of 2017-09-04 15:17:33 (CEST) | GAP | https://www.gap-system.org +-------+ Architecture: x86_64-apple-darwin16.7.0-gcc-default64 Libs used: gmp Loading the library and packages ... Components: trans 1.0, prim 2.1, small* 1.0, id* 1.0 Packages: AClib 1.2, Alnuth 3.0.0, AtlasRep 1.5.1, AutPGrp 1.8, CRISP 1.4.4, Cryst 4.1.12, CrystCat 1.1.6, CTblLib 1.2.2, FactInt 1.5.4, FGA 1.3.1, GAPDoc 1.6, IO 4.4.6, IRREDSOL 1.4, LAGUNA 3.7.0, Polenta 1.3.7, Polycyclic 2.11, RadiRoot 2.7, ResClasses 4.6.0, Sophus 1.23, SpinSym 1.5, TomLib 1.2.6, Utils 0.46 Try '??help' for help. See also '?copyright', '?cite' and '?authors' gap> LoadPackage("fining"); --------------------------------------------------------------------- Loading 'Forms' 1.2.5 (21/09/2017) by John Bamberg (http://school.maths.uwa.edu.au/~bamberg/) Jan De Beule (http://www.debeule.eu) For help, type: ?Forms --------------------------------------------------------------------- --------------------------------------------------------------------- Loading orb 4.7.6 (Methods to enumerate orbits) by Juergen Mueller (http://www.math.rwth-aachen.de/~Juergen.Mueller), Max Neunhöffer (http://www-groups.mcs.st-and.ac.uk/~neunhoef), and Felix Noeske (http://www.math.rwth-aachen.de/~Felix.Noeske). Homepage: https://gap-packages.github.io/orb --------------------------------------------------------------------- --------------------------------------------------------------------- Loading cvec 2.5.7 (Compact vectors over finite fields) by Max Neunhöffer (http://www-groups.mcs.st-and.ac.uk/~neunhoef). Homepage: https://gap-packages.github.io/cvec --------------------------------------------------------------------- --------------------------------------------------------------------- Loading genss 1.6.4 (Generic Schreier-Sims) by Max Neunhöffer (http://www-groups.mcs.st-and.ac.uk/~neunhoef) and Felix Noeske (http://www.math.rwth-aachen.de/~Felix.Noeske). Homepage: https://gap-packages.github.io/genss --------------------------------------------------------------------- --------------------------------------------------------------------- Loading GRAPE 4.7 (GRaph Algorithms using PErmutation groups) by Leonard H. Soicher (http://www.maths.qmul.ac.uk/~leonard/). Homepage: http://www.maths.qmul.ac.uk/~leonard/grape/ --------------------------------------------------------------------- ------------------------------------------------------------------------------- ______________ ________ _________ __________ __ ___ ____/__(_)__________ _/________ ____/ __< /_ // / __ /_ __ /__ __ __ / __ __ / __ __ /_ // /_ _ __/ _ / _ / / /_/ / _ / / / /_/ / _ /_/__ __/ /_/ /_/ /_/ /_//___/ /_/ /_/____/ /_/_(_)/_/ ------------------------------------------------------------------------------- Loading FinInG 1.4.1 (Finite Incidence Geometry) by John Bamberg (http://school.maths.uwa.edu.au/~bamberg/) Anton Betten (http://www.math.colostate.edu/~betten) Jan De Beule (http://www.debeule.eu) Philippe Cara (http://homepages.vub.ac.be/~pcara) Michel Lavrauw (http://people.sabanciuniv.edu/~mlavrauw/) Max Neunhoeffer (http://www-groups.mcs.st-and.ac.uk/~neunhoef/) For help, type: ?FinInG --------------------------------------------------------------------- true gap>

New releases of **FinInG** will be distributed automatically with new releases of **GAP**. However, it is possible easily to update **FinInG** in an existing installation of **GAP**, provided the new version of **FinInG** does not require newer versions of existing packages in the installation. It is also possible to have different versions of **FinInG** installed on one system. To update **FinInG** it is sufficient to download and unpack the archive containing the new release. First find the location of your existing **GAP** installation. We assume in the example below that it is

/opt/gap4r8/

Make sure you have write permission on this location. If this is not the case, you must ask your system administrator to do this. Download the **FinInG** archive "fining-....tgz" to this location, and unpack the archive. This can be done by issuing

gunzip fining-....tgz

which yields a file "fining-....tar", in the pkg directory, after which issuing the command

tar -xf fining-....tar

Unpack the archive in a subdirectory fining. Starting **GAP** and loading **FinInG** the usual way should give you the newly installed version. Please notice that you can unpack your archive in your favorite local "./pkg" directory, e.g. "/home/yourself/pkg/", in case you are using **GAP** on a server on which you have only a restricted access. In this case, i.e. if you installed **FinInG** in your local pkg directory, e.g. "/home/yourself/pkg/", then move to "/home/yourself", and issue the command

gap -l "/opt/gap4r8;./"

This will cause gap to startup and use as pkg directory both its own central pkg directory, i.e. "/opt/gap4r8/pkg/", as well as your local pkg directory, i.e. "/home/yourself/pkg/". You should see something like the following output.

+-------+ GAP 4.8.8, 20-Aug-2017, build of 2017-09-04 15:17:33 (CEST) | GAP | https://www.gap-system.org +-------+ Architecture: x86_64-apple-darwin16.7.0-gcc-default64 Libs used: gmp Loading the library and packages ... Components: trans 1.0, prim 2.1, small* 1.0, id* 1.0 Packages: AClib 1.2, Alnuth 3.0.0, AtlasRep 1.5.0, AutPGrp 1.6, Browse 1.8.6, CRISP 1.3.8, Cryst 4.1.12, CrystCat 1.1.6, CTblLib 1.2.2, FactInt 1.5.3, FGA 1.2.0, GAPDoc 1.5.1, IO 4.4.4, IRREDSOL 1.2.4, LAGUNA 3.7.0, Polenta 1.3.2, Polycyclic 2.11, RadiRoot 2.7, ResClasses 3.4.0, Sophus 1.23, SpinSym 1.5, TomLib 1.2.5 Try '?help' for help. See also '?copyright' and '?authors' gap> LoadPackage("fining"); --------------------------------------------------------------------- Loading 'Forms' 1.2.5 (21/09/2017) by John Bamberg (http://school.maths.uwa.edu.au/~bamberg/) Jan De Beule (http://www.debeule.eu) For help, type: ?Forms --------------------------------------------------------------------- --------------------------------------------------------------------- Loading orb 4.7.6 (Methods to enumerate orbits) by Juergen Mueller (http://www.math.rwth-aachen.de/~Juergen.Mueller), Max Neunhöffer (http://www-groups.mcs.st-and.ac.uk/~neunhoef), and Felix Noeske (http://www.math.rwth-aachen.de/~Felix.Noeske). Homepage: https://gap-packages.github.io/orb --------------------------------------------------------------------- --------------------------------------------------------------------- Loading cvec 2.5.7 (Compact vectors over finite fields) by Max Neunhöffer (http://www-groups.mcs.st-and.ac.uk/~neunhoef). Homepage: https://gap-packages.github.io/cvec --------------------------------------------------------------------- --------------------------------------------------------------------- Loading genss 1.6.4 (Generic Schreier-Sims) by Max Neunhöffer (http://www-groups.mcs.st-and.ac.uk/~neunhoef) and Felix Noeske (http://www.math.rwth-aachen.de/~Felix.Noeske). Homepage: https://gap-packages.github.io/genss --------------------------------------------------------------------- --------------------------------------------------------------------- Loading GRAPE 4.7 (GRaph Algorithms using PErmutation groups) by Leonard H. Soicher (http://www.maths.qmul.ac.uk/~leonard/). Homepage: http://www.maths.qmul.ac.uk/~leonard/grape/ --------------------------------------------------------------------- ------------------------------------------------------------------------------- ______________ ________ _________ __________ __ ___ ____/__(_)__________ _/________ ____/ __< /_ // / __ /_ __ /__ __ __ / __ __ / __ __ /_ // /_ _ __/ _ / _ / / /_/ / _ / / / /_/ / _ /_/__ __/ /_/ /_/ /_/ /_//___/ /_/ /_/____/ /_/_(_)/_/ ------------------------------------------------------------------------------- Loading FinInG 1.4.1 (Finite Incidence Geometry) by John Bamberg (http://school.maths.uwa.edu.au/~bamberg/) Anton Betten (http://www.math.colostate.edu/~betten) Jan De Beule (http://www.debeule.eu) Philippe Cara (http://homepages.vub.ac.be/~pcara) Michel Lavrauw (http://people.sabanciuniv.edu/~mlavrauw/) Max Neunhoeffer (http://www-groups.mcs.st-and.ac.uk/~neunhoef/) For help, type: ?FinInG --------------------------------------------------------------------- true

This is the development team (without Anton), meeting in St. Andrews in September 2008, from left to right: Philippe Cara, Michel Lavrauw, Max Neunhöffer, Jan De Beule and John Bamberg.

The development team meeting again (without Anton and Max), now in Vicenza in april 2011. from left to right: Michel Lavrauw, John Bamberg, Philippe Cara, Jan De Beule.

Survivors of the first version of **FinInG**, enjoying a trip to Chioggia, december 2011.

The same survivors, staring at the destiny.

Anton Betten, during a milestone meeting at the finite geometries conference in Irsee, september 2014.

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