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<TitlePage>
<Title>
homalg
</Title>
<Subtitle>
A homological algebra meta-package for computable Abelian categories
</Subtitle>
<
Version>
2024.
01-
01
</
Version>
<Author>
Mohamed Barakat<Alt Only=
"LaTeX"><Br/></Alt>
<Address>
Walter-Flex-Str.
3<Br/>
57072 Siegen<Br/>
Germany<Br/>
</Address>
<Email>mohamed.barakat@uni-siegen.de</Email>
<Homepage>
https://mohamed-barakat.github.io</Homepage>
</Author>
<Author>
Sebastian Gutsche<Alt Only=
"LaTeX"><Br/></Alt>
<Address>
Department Mathematik<Br/>
Universität Siegen<Br/>
Walter-Flex-Straße
3<Br/>
57072 Siegen<Br/>
Germany<Br/>
</Address>
<Email>gutsche@mathematik.uni-siegen.de</Email>
<Homepage>
https://sebasguts.github.io</Homepage>
</Author>
<Author>
Markus Lange-Hegermann<Alt Only=
"LaTeX"><Br/></Alt>
<Address>
Markus Lange-Hegermann<Br/>
Hochschule Ostwestfalen-Lippe<Br/>
Liebigstraße
87<Br/>
32657 Lemgo<Br/>
Germany<Br/>
</Address>
<Email>markus.lange-hegermann@hs-owl.de</Email>
<Homepage>
https://www.th-owl.de/eecs/fachbereich/team/markus-lange-hegermann/</Home
page>
</Author>
<Date>
10 January 2024
</Date>
<Copyright>
©right; 2007-2015 by Mohamed Barakat and Markus Lange-Hegermann
This package may be distributed under the terms and conditions of the GNU Public License Version 2 or (at your option) any later version.
</Copyright>
<Acknowledgements>
<Alt Not="Text"><URL Text="Max Neunhöffer">https://www.arangodb.com/speakers/max-neunhoeffer/</URL></Alt>
<Alt Only="Text">Max Neunhöffer</Alt> not only taught me the
philosophy of object-oriented programming in &GAP4;, but also to
what extent this philosophy is still unique among programming
languages (&see; <Ref Sect="WhyGAP4" Text="Why GAP4?"/>).
He, <Alt Not="Text"><URL Text="Frank
Lübeck">http://www.math.rwth-aachen.de/~Frank.Luebeck/</URL></Alt><Alt Only="Text">Frank
Lübeck</Alt>, and
<Alt Not="Text"><URL Text="Thomas
Breuer">http://www.math.rwth-aachen.de/~Thomas.Breuer/</URL></Alt>
<Alt Only="Text">Thomas Breuer</Alt> patiently answered trillions of
specific questions, even those I was too lazy to look up in the
excellent <Alt Only="HTML"><Ref Chap="Preface" Text="reference manual"
BookName="Reference"/></Alt><Alt Only="Text">
programming tutorial</Alt><Alt Only="LaTeX"><URL Text="reference manual">http://www.gap-system.org/Manuals/doc/ref/chap0.html</URL></Alt>.
Without their continuous and tireless help and advice, not only this
package but the <Alt Only="Text">&homalg; project</Alt> as a whole
<Alt Not="Text"><URL Text="homalg
project">https://homalg-project.github.io/homalg_project/</URL></Alt> would
have remained on my todo list. <P/>
A lot of <Alt Only="HTML"><Ref Text="ideas" Label="intro"/></Alt>
<Alt Not="HTML">ideas</Alt> that make up this package and the whole
&homalg; project came out of intensive discussions
with <Alt Only="Text">Daniel Robertz</Alt>
<Alt Not="Text"><URL Text="Daniel
Robertz">https://www.plymouth.ac.uk/staff/daniel-robertz</URL></Alt> during
our early collaboration, where we developed our philosophy of a meta
package for homological algebra and <Alt Only="Text">implemented</Alt>
<Alt Not="Text"><URL Text="implemented">https://algebra.mathematik.uni-siegen.de/barakat/homalg_in_maple/</URL></Alt>
it in &Maple;.
This &Maple; package &homalg; is <Alt Only="Text">now part of</Alt><Alt Not="Text">
<URL Text="now part of">https://github.com/homalg-project/homalg_project/tree/master/RingsForHomalg/maple</URL></Alt> the GAP package &RingsForHomalg;. <P/>
In the fall of 2007 I began collaborating
with <Alt Only="Text">Simon Görtzen</Alt>
<Alt Not="Text"><URL Text="Simon
Görtzen">https://www.linkedin.com/in/simongoertzen/</URL></Alt> to
further pursue and extend these <Alt Only="HTML"><Ref Text="ideas"
Sect="Ring dictionaries" BookName="Modules"/></Alt>
<Alt Not="HTML">ideas</Alt> preparing the transition to &GAP4;. With
his help &homalg; became an extendable multi-package project. <P/>
Max Neunhöffer convinced me to use his wonderful &IO; package to
start communicating with external computer algebra systems. This was
crucial to remedy the yet missing support for important rings in
&GAP;. Max provided the first piece of code to access the computer
algebra system &Singular;. This was the starting point of the
packages &HomalgToCAS; and &IO_ForHomalg;, which were further abstracted
by Simon and myself enabling &homalg; to communicate with virtually any external
(computer algebra) system. <P/>
<Alt Not="Text"><URL Text="Thomas
Bächler">https://www.researchgate.net/scientific-contributions/50557632_Thomas_Baechler</URL></Alt>
<Alt Only="Text">Thomas Bächler</Alt> wrote the package
&MapleForHomalg; to directly access &Maple; via its
&C;-interface. It offers an alternative to the package
&IO_ForHomalg;, which requires &Maple;'s terminal
interface <C>cmaple</C>. <P/>
The basic support for &Sage; was added by Simon, and the support for
&Singular; was initiated by
<Alt Only="Text">Markus Lange-Hegermann</Alt>
<Alt Not="Text"><URL Text="Markus
Lange-Hegermann">https://www.th-owl.de/eecs/fachbereich/team/markus-lange-hegermann/</URL></Alt>
and continued by him and Simon, while
<Alt Only="Text">Markus Kirschmer</Alt>
<Alt Not="Text"><URL Text="Markus
Kirschmer">http://www.math.rwth-aachen.de/~Markus.Kirschmer/</URL></Alt>
contributed the complete support for &MAGMA;. This formed the
beginning of the &RingsForHomalg; package. Recently, Daniel added
the support for &Macaulay2;. <P/>
My concerns about how to handle the garbage collection in the
external computer algebra systems were evaporated with the idea of
Thomas Breuer using the so-called <Alt Only="Text">weak
pointers</Alt><Alt Only="LaTeX"><URL Text="weak
pointers">http://www.gap-system.org/Manuals/doc/ref/chap86.html</URL></Alt>
<Alt Only="HTML"><Ref Chap="Weak Pointers" Text="weak pointers"
BookName="Reference"/></Alt> in &GAP4; to keep track of all the
external objects that became obsolete for &homalg;. This idea took
shape in a discussion with him and Frank Lübeck and finally found
its way into the package &HomalgToCAS;. <P/>
My gratitude to all with whom I worked together to develop extension
packages and those who developed their own packages within the
&homalg; project (&see; Appendix <Ref Sect="homalg-Project"/>).
Without their contributions the package &homalg; would have remained
a core without a body:
<List>
<Item><URL Text="Thomas Bächler">https://www.researchgate.net/scientific-contributions/50557632_Thomas_Baechler</URL></Item>
<Item>Barbara Bremer</Item>
<Item><URL Text="Thomas Breuer">http://www.math.rwth-aachen.de/~Thomas.Breuer/</URL></Item>
<Item>Anna Fabiańska</Item>
<Item><URL Text="Simon Görtzen">https://www.linkedin.com/in/simongoertzen/</URL></Item>
<Item><URL Text="Markus Kirschmer">http://www.math.rwth-aachen.de/~Markus.Kirschmer/</URL></Item>
<Item><URL Text="Markus Lange-Hegermann">https://www.th-owl.de/eecs/fachbereich/team/markus-lange-hegermann/</URL></Item>
<Item><URL Text="Frank Lübeck">http://www.math.rwth-aachen.de/~Frank.Luebeck/</URL></Item>
<Item><URL Text="Max Neunhöffer">https://www.arangodb.com/speakers/max-neunhoeffer/</URL></Item>
<Item><URL Text="Daniel Robertz">https://www.plymouth.ac.uk/staff/daniel-robertz</URL></Item>
</List>
I would also like to thank <Alt Only="Text">Alban Quadrat</Alt>
<Alt Not="Text"><URL Text="Alban
Quadrat">https://who.rocq.inria.fr/Alban.Quadrat/</URL></Alt>
for supporting the &homalg; project and for all the wonderful
discussions we had. At several places in the code I was happy to add
the comment: <Q>I learned this from Alban</Q>.
<Par></Par>
My teacher <Alt Not="Text"><URL Text="Wilhelm
Plesken">https://www.researchgate.net/profile/Wilhelm_Plesken</URL></Alt>
<Alt Only="Text">Wilhelm Plesken</Alt> remains an inexhaustible source of
extremely broad and deep knowledge. Thank you for being such a
magnificent person. <P/>
This manual was created using the GAPDoc package of Max Neunhöffer
and Frank Lübeck. <P/>
Last but not least, thanks
to <E>Miriam</E>, <E>Josef</E>, <E>Jonas</E>, and <E>Irene</E> for
the endless love and support.
<P/>
<P/>
Mohamed Barakat
</Acknowledgements>
</TitlePage>
