=Paper=
{{Paper
|id=Vol-1186/paper-21
|storemode=property
|title=The SymbolicData Project – Towards a Computer Algebra Social Network.
|pdfUrl=https://ceur-ws.org/Vol-1186/paper-21.pdf
|volume=Vol-1186
|dblpUrl=https://dblp.org/rec/conf/mkm/GraebeNJ14
}}
==The SymbolicData Project – Towards a Computer Algebra Social Network. ==
https://ceur-ws.org/Vol-1186/paper-21.pdf
The SymbolicData Project – Towards a
Computer Algebra Social Network
Hans-Gert Gräbe, Andreas Nareike, and Simon Johanning
Universität Leipzig, Germany
(graebe|nareike|johanning)@informatik.uni-leipzig.de
Abstract. We report about a complete redesign of the tools and data of
the SymbolicData project according to RDF technologies and Linked
Data principles that proved to be powerful within modern semantic web
approaches. During that redesign the focus of the project changed from a
mere data store towards the vision of a Computer Algebra Social Network
(CASN) to support technically intercommunity communication between
Computer Algebra subcommunities. In the last part of the paper we
describe ongoing efforts to implement a technical basis for a Distributed
Semantic Social Network infrastructure to run such a CASN.
1 Introduction
The SymbolicData project grew up from the Special Session on Benchmarking
at the 1998 ISSAC conference to continue the efforts started by the PoSSo [11]
an FRISCO [5] projects. It aimed at building a reliable and sustainably avail-
able collection of Polynomial Systems that were reported in the literature for
benchmarking and profiling of CA software, to extend and update it, to collect
meta information about the records, and also to develop tools to manage the
data and to set up and run reliable tests and benchmark computations on the
data. A first prototype was developed during 1999–2002 by Olaf Bachmann and
Hans-Gert Gräbe with data from Polynomial Systems Solving and Geometry
Theorem Proving.
There was almost no advance during 2002–2005. In a second phase around
2006 the project matured again and extended its scope. Data was supplied
by the CoCoA group (F. Cioffi), the Singular group (M. Dengel, M. Bricken-
stein, S. Steidel, M. Wenk), V. Levandovskyy (non commutative polynomial
systems, G-Algebras) and R. Hemmecke (Test sets from Integer Programming).
In 2005 the German Fachgruppe Computeralgebra launched the Web site http:
//www.symbolicdata.org. During the Special Semester on Gröbner Bases (GB)
in March 2006 we tried to join forces with the GB-Bibliography project (B. Buch-
berger, A. Zapletal) and the GB-Facilities project (V. Levandovskyy).
In 2009 we started to refactor the data along standard Semantic Web concepts
based on the Resource Description Framework (RDF). We completed a redesign
of the data along RDF based semantic technologies, set up a Virtuoso [20] based
RDF triple store and SPARQL endpoint at http://www.symbolicdata.org as
an Open Data service along Linked Data standards [7], and started both con-
ceptual and practical work towards a semantic-aware Computer Algebra Social
Network. The new SymbolicData data and tools were released as version 3 in
September 2013.
One of the main decisions within that redesign process was a non-technical
one – leave the focus on data storage and the “roots” within the Polynomial
Systems Solving CA subcommunity in favour of stronger social interlinking. We
reshaped the SymbolicData Project as intercommunity project, that addresses
needs of subcommunities within the Symbolic Computation community to pro-
file, test and benchmark implementations as a cross cutting activity 1 , and started
to develop links to other intercommunity activities as sagemath [13], lmonade
[8] or swmath [16].
In section 2 and 3 we describe the current SymbolicData infrastructure in
more detail. The rest of this paper addresses conceptual and practical problems,
experiences and solutions towards a semantic-aware Computer Algebra Social
Network as an intercommunity project.
Acknowledgement: This and ongoing work was realised within a project
Benchmarking in Symbolic Computations and Web 3.0 supported by the Sax-
onian E-Science Initiative [3] with a 12 months grant for Andreas Nareike in
2012/13 and a five months grant for Simon Johanning in 2014.
2 The SymbolicData Infrastructure
Our basic resources (examples for testing, profiling and benchmarking software
and algorithms from different areas of symbolic computation) are publicly avail-
able in XML markup, meta data in RDF notation both from a public git repo,
hosted at http://github.org/symbolicdata, and from our remote RDF triple
store at http://symbolicdata.org/Data. Moreover, we offer a SPARQL end-
point [18] to explore the data by standard Linked Data methods.
The website operates on a standardized installation using an Apache web
server to deliver the data, the Virtuoso RDF data store [20] as data backend, a
SPARQL endpoint and (optionally) OntoWiki [10] to explore, display and edit
the data. This installation can easily be rolled out on a local site2 to support
local testing, profiling and benchmarking.
The distribution contains also tools and prototypical solutions for a local
compute environment as, e.g., provided by Sagemath [13]. The Python based
SDEval package [6] by Albert Heinle offers a JUnit like framework to set up,
run, log, monitor and interrupt testing and benchmarking computations. The
SDSage package [9] by Andreas Nareike provides a showcase for SymbolicData
integration with the Sagemath [13] compute environment.
1
See http://en.wikipedia.org/wiki/Cross-cutting_concern.
2
Tested with Linux Debian and Ubuntu 12.04 LTS standard distributions; a more
detailed description can be found in the SymbolicData wiki [17].
We follow a development process along the Integration-Manager-Workflow
Model3 . This makes it easy to join forces with the SymbolicData team: Fork
the repo to your github account, start development and send a pull request
to the Integration Manager if you think you produced something worth to be
integrated into the upstream master branch. Even if your contribution is not
pulled to the upstream, people can use it, since they can pull it from your
github repo to their github repo. This allows even for agile common small feature
development – a widely practised way to advance projects hosted at github.com.
You are encouraged to start a discussion about your plans early in the process
and regularly report your progress on the SymbolicData mailing list.
Currently the SymbolicData data collection contains resources from Poly-
nomial Systems Solving (390 records, 633 configurations), Free Algebras (83
records), G-Algebras (8 records), GeoProofSchemes (297 records) and Test Sets
from Integer Programming (28 records). These resources are stored in a flat
XSchema based XML syntax developed within SymbolicData version 2 that
uses well established intracommunity syntaxes for the internal data.
3 Towards a Decentralized Infrastructure of Resources
Note that RDF provides a strong conceptual distinction between resources (basic
information) and resource descriptions (meta information) and with Symbolic-
Data version 3 we use XML representations more concisely to focus on the basic
information structure itself.
Since the basic information is provided by different CA subcommunities it is
a good advice to use the (textual) syntactical notations well established within
a subcommunity to store data. In most cases such syntactical notations are not
XML based, so one cannot use a standard XML parser to parse the internal
textual representations “out of the box”.
Since the subcommunity has plenty of parsers and tools at hand to input
textual representations into their semantic-aware tools this is not a real obsta-
cle in practise. In particular, in the early times of SymbolicData we had a
dispute about representation of polynomials – use the well established operator
syntax as, e.g., x^3+5*x-2, or provide polynomials in XML-based OpenMath
or MathML syntax. We decided to store polynomials in the compact human
readable operator syntax, as in the PoSSo project.
In the SymbolicData data structure concept we use XML markup mainly
to compile heterogeneously structured data into a single resource in such a way
that the different parts of this data can be extracted by a standard XML parser
and passed to appropriate semantic-aware tools for further processing. To start a
new data collection within SymbolicData you have to decide about the parts of
data that have to be bundled for a single resource, to decide about the syntactical
representation of these parts according to the standards of your scientific sub-
community, to develop a XSchema based XML representation for the bundling,
3
See http://git-scm.com/book/en/Distributed-Git-Distributed-Workflows.
and provide data along that standard. The main point about the resources is
the reliable and sustainable availability of the data through a permanent web
address, a Unique Resource Identifier (URI). We provide access to our centrally
managed resources via http://symbolicdata.org/XMLResources/.
Such a concept is not restricted to centrally managed resources, but can
easily be extended to other data stores on the web that are operated by diffe-
rent CA subcommunities and offer a minimum of Linked Data facilities. There
are draft versions of resource descriptions about Fano Polytopes (8630 records)
and Birkhoff Polytopes (5399 records) hosted by Andreas Paffenholz and about
Transitive Groups (3605 records) from the Database for Number Fields of Jürgen
Klüners and Gunter Malle that point to such external resources.
4 Resources and Resource Descriptions
Preparing SymbolicData version 3 we decided to strengthen the part of inter-
community communication aspects. From this point of view resources are owned
and maintained by different CA subcommunities, and meta data or resource de-
scriptions are important for technically supported interchange of data between
such subcommunities and for intercommunity communication, and hence should
be managed and maintained within a cooperative intercommunity process.
A first question to be solved was about data representation for resources and
resource descriptions. XML based design principles mainly distinguish between
information (XML records) and information structure (described with XSchema)
and are well suited for data representation of (basic) resources but proved to be
not expressive enough to represent interrelations between different resources in
a flexible way.
4.1 Why RDF?
We decided to switch to RDF as basic representation for resource descriptions by
several reasons. First, we could join forces with the Agile Knowledge Engineering
and Semantic Web (AKSW) Group at Leipzig University4 , a leading research
group in semantic technologies, and exploit their experience about concepts and
tools in that area. Second, RDF gets established more and more for exchange of
meta information not only within the Linked Open Data world [7], but also for
the big projects on standardization of scientific communication as the Dublin
Core DCMI Metadata Terms Initiative [2] or the Joint Steering Committee for
Development of Resource Description and Access [12]. Third, there are well
elaborated concepts and tools how to exchange RDF based information by a
protocol as simple and widely spread as HTTP Get and how to manage that
within a standard web server infrastructure.
4
See http://aksw.org/About.html.
4.2 RDF Basics
RDF – the Resource Description Framework – is about description of resources,
represented by (globally unique) resource identifiers (URIs). RDF provides a
unified scheme to represent relational information as triples. There are several
notational standards (ntriples, turtle, rdf/xml, json) for triples and plenty of
tools to manage sets of triples, i.e., RDF graphs.
Each such triple can be considered as a sentence of a story that consists
of a subject s, a predicate p and an object o, but different to real stories the
semantics of an RDF graph is that of a set, i.e., the order of the sentences does not
matter. Hence the expressiveness of RDF stories is very restricted compared to
natural languages. The main advantage however, is a separation between data
and search algorithms on data patterns as in rule based programming. RDF
comes with the standardized pattern based query language SPARQL to operate
such search queries on RDF data stores. For SymbolicData we use Virtuoso
[20] as RDF data store and SPARQL endpoint.
RDF has another advantage compared to classical database approaches –
one can express descriptions of descriptions, i.e., database design, within the
same language concepts, and thus share not only descriptions of data but also
descriptions of data descriptions, i.e., information about the semantics of the
data in a machine readable way.
Subjects and predicates have to be URIs while objects (or ‘values’) can be ei-
ther URIs or (plain or typed) literals in lexical form (a string included in quotes).
There are some predefined common types (e.g., xsd:integer) but custom types
can be defined as well.
A set of triples can be interpreted as a directed graph (RDF graph) with
subjects and objects as nodes (replacing literals by labelled blank nodes) and
predicates as labelled edges between nodes. On the opposite, a directed graph
can be written as a set of triples (and is commonly represented in such a way as
internal data structure of graph programs). Another representation uses sets of
key-value pairs p → o assigned to the different subjects s. Note that, different
to database columns, a key p can have multiple values.
RDF uses some more basic concepts – character sets to compose URIs and
literals and name spaces to structure information spaces and to resolve conflicts
within URI creation. There are more elaborated concepts as OWL, RDFS etc.
on top of RDF as explained in the Semantic Web Stack [15], but not yet used
within SymbolicData. Note that nowadays the syntax layer below the RDF
data interchange layer in the Semantic Web Stack is no more bound solely to
XML as [15] might suggest – the most widespread syntax representation is in
Turtle format5 .
4.3 Linked Data Principles
The real power of RDF does not originate in an alleged superiority of concepts
but in the practical availability of data stores all over the world that are orga-
5
See http://en.wikipedia.org/wiki/Turtle_(syntax).
nized on RDF based principles. Whereas the (traditional) Web 2.0 is build upon
interlinked dynamical HTML web pages based on private databases, the Seman-
tic Web as part of Web 3.0 [14] focuses on interlinking these private databases
themselves into a single big distributed data store.
RDF supports both ways of data dissemination – by file transfer as in Web
2.0 and by remote access to RDF triple stores as in Web 3.0 –, and so does
SymbolicData: You can download whole RDF graphs as data files from our
remote host, upload this data into your local data store and process it locally,
but you can also directly access our remote RDF data store. RDF data stores
operate on the HTTP protocol and hence are best deployed within a webserver
infrastructure, either remote or local. The only difference between remote and
local approaches are the stronger web security requirements for a remote loca-
tion.
To achieve web access of RDF data on a remote host, URIs should be available
as URLs, i.e., a HTTP Get request to an URI should deliver a valuable portion
of RDF information about that subject. This is the core of the Linked Data
Principle [7] and realised for the http://symbolicdata.org/Data/ name space
within the SymbolicData project.
5 SymbolicData Resource Descriptions
RDF resource descriptions are the main part of the meta information collected
within the SymbolicData project. We offer resource descriptions for several
purposes – resource fingerprints to navigate within the examples, relational in-
formation to, e.g., bibliographical references or CA software descriptions, and
information about activities of people involved with CA research.
5.1 Resource Fingerprints
Semantically equivalent data usually can be given in different syntactical form.
For example, the same Polynomial System can be given with different variable
names, in different polynomial orderings and even in different forms as, e.g.,
expanded or factorized polynomials.
To navigate within such data, to prestructure data for efficient search or
to identify a given example within the database it is helpful to precompile fin-
gerprints, i.e., (semantically sound) invariants of the different examples. For
example, the set of degree lists (in standard grading) or the set of the lengths
of polynomials in distributive normal form are such invariants for Polynomial
Systems.
Examples with different fingerprints are surely different, examples with the
same fingerprint require more elaborated methods to be distinguished. In most
cases the latter is not worth to be automated since the “general nonsense” knowl-
edge of the experts (optionally added as rdfs:comment to the resource descrip-
tion) is a more powerful “tool” to resolve such disambiguities.
The computation of fingerprints requires semantic-aware tools and both the
definition of useful fingerprints and its computation are due to the CA subcom-
munity experts with the appropriate semantic knowledge and tools. To compare
user given examples with existing ones it is a good advice to have enough invari-
ants as fingerprints at hand that can be computed in polynomial time.
5.2 Relational Information
It was one of the great visions of the SymbolicData Project to collect not only
benchmark and testing data but also valuable background information about
the records in the database as, e.g., information about papers, people, history,
systems etc. concerned with the examples in our collection. It was the main
target of SymbolicData version 3 to redesign these data along RDF principles.
We provide a general concept of an RDF class sd:Annotation to store back-
ground information in a unified way. Instances of this class have predicates
– rdfs:label – a label,
– rdfs:comment – a text field for annotation,
– sd:relatesTo – a set of related URIs.
We use that concept in particular to relate bibliographical information of type
sd:Reference to different data records. The management of bibliographical re-
ferences was completely redesigned with SymbolicData version 3 exploiting
RDF and the established Dublin Core ontology [2] to represent bibliographical
information in a way that is queryable by standard means and tools. On the other
hand, we strongly reduced the part of information about bibliographical refe-
rences kept inside SymbolicData since there are comprehensive bibliographical
stores available on the web that provide all required information via permanent
URIs, although in most cases not yet in RDF format. At the moment we provide
links to three such bibliographical stores,
– the database of Zentralblatt Mathematik (predicate sd:hasZBentry),
– the Gröbner Bases Bibliography database (predicate sd:hasGBBentry) and
– the CiteSeer database (predicate sd:hasCSentry).
The same applies to information about and references to CA software that
is SymbolicData-internally stored as resource description of type sd:CAS but
points as far as possible to the relevant information within the swmath database
[16], even if swmath does not (yet) operate by Linked Open Data standards.
5.3 Publicly Tracking Personal Profiles
Bibliographical references, references to CA software and even references about
contributions to SymbolicData itself refer to people involved with CA research.
It is one of the challenges of big data stores about scientific publications to find
out all publications of a given author, since the same author may be listed in
different ways in the author list of different publications. The big identification
projects use elaborated evaluation algorithms of cross references to solve this
problem or – as the Zentralblatt Mathematik did for a long time – use simple
string pattern matching. Some time ago the Zentralblatt started a certain kind
of tracking of personal profiles6 to improve that alignment.
We argue that it is a good advise for scientific communities to support such
tracking activities since the benefits much exceed the drawbacks. Moreover, ac-
tive involvement of scientific communities allows to “track the trackers”, i.e.,
to start open discussions and to influence actively the settings of the tracking
process to maximize its benefits and minimize its drawbacks.
The sd:Person database (274 records) supports that process of disambigua-
tion on the level of references and authors evaluating different sources of informa-
tion about CA publications and relating authorship to sd:Person URIs that are
composed following well defined naming rules. This part of the project is under
heavy development with focus on activities within the German Fachgruppe.
6 Towards a Computer Algebra Social Network
From the five stars to be assigned to a Linked Data project according to Tim
Berners-Lee’s classification [1] SymbolicData earned four stars so far (for of-
fering data in interoperable RDF format on the web and providing a SPARQL
querable RDF triple store). For the fifth star one has to build up stable semantic
relations to foreign knowledge bases and thus become part of the Linked Open
Data Cloud [7].
Much of such interrelation, e.g., a list of interoperability references for people,
software and bibliographical data with Zentralblatt, is on the way. Moreover, we
joined forces with the efforts of the board of the German Fachgruppe to store
and provide information about people and groups working on CA topics at their
new Wordpress driven web site [4]. We developed a first prototype to store this
information in RDF format, to extract it by means of SPARQL queries and to
view it on the web site using the Wordpress shortcode mechanism7 via a special
Wordpress plugin. We apply the same technique to maintain information about
upcoming conferences, CA projects within the SPP 1489 priority program and
a list of dissertations in CA at this site.
The vision of a Computer Algebra Social Network (CASN) goes far beyond
that: Get people involved themselves on a regular basis, set up and run within
the CA community a semantic-aware Facebook like Social Network and con-
tribute to it about all topics around Computer Algebra using tools that express
your contributions in an RDF based vocabulary that the community agreed
upon. This sounds quite visionary but is in no way utopic. We operate a first
prototypical node of a tool that realizes the challenging concept of a Distributed
Semantic Social Network (DSSN) [19].
6
See, e.g., the entry https://zbmath.org/authors/?q=ai:grabe.hans-gert of the
first author of this paper.
7
See http://codex.wordpress.org/Shortcode.
We set up a second RDF data store at http://symbolicdata.org/casn/
with information about
– upcoming conferences (about 20 entries of type sd:Event),
– publications within the “CA Rundbrief” of the German Fachgruppe,
– dissertations in CA reported to the board of the German Fachgruppe,
– CA projects (initial: projects from the German SPP 1489 priority program)
– and CA working groups (initial: as listed by the German Fachgruppe).
As the project matures this will be interrelated with the DSSN node at http://
symbolicdata.org/xodx/ running a software under development by the AKSW
group in such a way that you can join the CASN and supply your contributions
as you can do (also not yet semantically) in any other social network. We refer
to our wiki [17] for more information.
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[2014-02-19]
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[2014-05-24]
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17. The SymbolicData project wiki. http://symbolicdata.org/wiki
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