Software projects
"A software is free of bugs until it is used." – Computer
Science Folklore
Currently, I am involved in the following software projects. Due to
the quote above, I highly encourage the users of my software to
report bugs to me.
ncfactor.lib
ncfactor.lib is a library
inside the computer algebra system Singular (
http://www.singular.uni-kl.de/)
and distributed with Singular since version 3-1-3.
Remark: A major change has
been done in version 3-1-6, which increased the performance and the
versatility of the results significantly.
Remark: Since Singular version
4-0-1, there are some new functions in
ncfactor.lib.
-
Factorization in the n-th Weyl algebras (function facWeyl)
-
Factorization in the n-th shift algebras (function facShift)
-
Factorization of homogeneous elements in the n-th
q-Weyl algebras (function homogfacQWeyl[_all])
These functions make some older functions redundant (
facFirstWeyl,
facFirstShift,
homogfacFirstQWeyl[_all]). We keep those for the
sake of downward-compatibility with older versions of the library.
Symbolic Data (
http://symbolicdata.org/)
is a collection of problems coming from the field of computer algebra
and focuses on interlinking relevant data from different Computer
Algebra Communities.
SDEval is a benchmarking toolbox built on top of Symbolic Data. Some of its main goals are
- providing an easy way of translating existing entries in Symbolic Data into executable code of computer algebra systems,
- providing a feasible way of trustfully reproducing computation results from current research papers,
- meeting the particularities of benchmarking in the field of
computer algebra and
- flexibility in order to be applicable across different communities.
I am involved in developing SDEval. The current source developments can be found in my GitHub repository:
https://github.com/ioah86/symbolicdata
There is also a video tutorial/introduction for SDEval. You van view it
via the following link:
https://www.youtube.com/watch?v=CctmrfisZso
Benchmarks created using SDEval
Here are some benchmarks I have performed using SDEval. You can view
the table with the timing results, and you can also download the
complete Taskfolder. There, the input- and output-files are
given. Furthermore, an execution engine is provided in the Taskfolder
in order to reproduce the timings. For details on how to use it, view
the documentation of SDEval.
-
From the paper "Factoring Linear Partial Differential Operators in n
Variables". Journal of Symbolic Computation (2015):
Timings, TaskFolder.
-
From the Paper "Factoring Linear Differential Operators in n
Variables" (ISSAC'14): Timings, TaskFolder.
-
Comparison of factorization of homogeneous polynomials in the first
Weyl algebra between Maple, Reduce and Singular (from the paper
"Factorization of Z-homogeneous polynomials in the First (q)-Weyl
Algebra", arXiv preprint): Timings, TaskFolder *.
-
Comparison between wrapper function CP1F in Maple and ncfactor.lib in Singular (from the paper
"Factorization of Z-homogeneous polynomials in the First (q)-Weyl
Algebra", arXiv preprint): Timings, TaskFolder *.
-
Factorization attempts of keys generated by our Diffie-Hellman-like
key exchange protocol, using the second Weyl algebra. For every
single example, we could not factor the key within four hours
(automatic termination time limit). (from the paper "A Diffie-Hellman-like
Key Exchange Protocol Based on Multivariate Ore
Polynomials",
arXiv preprint): Timings, TaskFolder
-
Gröbner basis attack for the zero knowledge protocol, using the
second Weyl algebra. A set
time limit of two hours was given; the chosen examples were small
with respect to the degree of the polynomials. (from the paper "A Diffie-Hellman-like
Key Exchange Protocol Based on Multivariate Ore
Polynomials",
arXiv preprint): Timings, TaskFolder
