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Let

Def[ termP | termA, termB, ... ]

be a statement defining the mathematical term "termP" by means of those "termA" , "termB" , ...

As example:

Def[ magma | set, binary operation ]

Def[ semigroup | magma, associative binary operation ]

Def[ monoid | semigroup, identy element ]

Def[ quasigroup | magma, division ]

...

Such entities naturally fit in a graph structure having (1) as vertex each of them and (2) as directed edges the relations among them.

I have been meditating on for a while about the possibility to store mathematical definitions in a database shaped around the above considerations (that's the reason why I wrote "graph oriented", in the title).

Please, can you point at : - previous attempts, if any (may be, I'm reinventing the wheel ...) - what I should to learn, about graphs, before digging further

Here are mentioned many graph database projects but no one seems to be relevant to mathematical definitions storage: http://en.wikipedia.org/wiki/Graph_database

Thanks !!

moonray
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1 Answers1

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My personal notebook, AxiomsOfChoice.org, is organized this way. It's a Doku-Wiki of formal definitions and comments about those entities, and I read out the entries and can plot them in a graph showing requirements for the definitions and subset relations.

For example, here is the (short) entry on semigroups. At the bottom it specifies that the Magma entry points at it, and the Monid entry in turn points at Semigroup. What a "subset" is might depend on the context. E.g. here is the entry on the category theoretical limit, and at at the bottom you learn that in its definition I require the notion of a Functor category, a Diagonal functor, and that it's a Terminal morphism.

A friend helped me to set up a visualization using the free software graph-viz. When I have time, I'll write my own more dynamics version, because at about 70 vertices, the edges starting in an unpractical way, and at 200 vertices, I stopped using it.

I gave an answer on what I found out is already out there in this thread. Please comment here/tell me when you find out more about these kinds of things, my project is also always under construction.

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Community
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Nikolaj-K
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  • Thanks for your reply; I'm browsing your interesting site and I will keep you updated. At present moment I'm evaluating the opportunity to develop a sketchy database in Mathematica. I'm a newcomer in stackexchange.com community: may I ask what's the appropriate way to debate an issue in terms not immediately answering the question I asked ? – moonray Feb 03 '15 at 14:53
  • @user281912: In fact I stated out to generate the graph in Mathematica too, see http://i.imgur.com/GpNymt6.png, but it's not really the appropriate software for either the graph nor the data content behind it. StackExchange isn't really suited for discussions, but you can open up a chat (search for the keyword on the front page) and call people by writing @ and then their name. – Nikolaj-K Feb 03 '15 at 15:29