A Maple package
for handling tensor constructions on linear differential
Weil (Université de Limoges ; CNRS ; XLIM UMR 6172 ;
(with participation of T. Cluzeau for this page)
I - Content
This web page is dedicated to a Maple package called TensorConstructions which
contains utilities to perform tensor constructions on linear
differential systems (tensor products, direct sums, symmetric
powers, exterior powers and duals) as described in Chapter 2 of the
book of van der Put and Singer.
It is to be used in conjunction with the package implementations
algorithms for rational and exponential solutions of linear
(D-finite partial) differential systems (based on Barkatou's
algorithm) developped in the Issac'12 paper Computing Closed Form Solutions of
Integrable Connections by M. Barkatou,
T. Cluzeau, C. El
Bacha and J.-A.
It may also be used in the context of integrability of Hamiltonian
systems, using tools developed with Ainhoa Aparicio-Monforte.
II - Download
Our package is available for download: TensorConstructions.m
You may also download the (yet very basic) help page.
To install it, you should proceed as follows:
If you do not manage to install the package, then contact us.
- Copy the above files in a directory called
- Add this directory to your libname,
for example by performing the two following steps:
- Open Maple and type
- Then, type
libname := " the global path of the directory
You will get the list of the functions contained in the package.
If you obtain an error message, then you may have done something
wrong in Step 2.
Examples of calculations
We illustrate here our three main procedures on some examples:
More examples (more examples will be added)
- Symmetric Powers
IV - Bug
You can now run your own examples.
If you have any problem with the package, find a bug or want to ask
questions, then contact us.
In case of an error, please
attach to your e-mail a Maple worksheet which documents the error on
a particular example.
V - References
- van der Put, Marius ; Singer, Michael F.
Galois theory of linear
Grundlehren der Mathematischen Wissenschaften, 328.
Springer-Verlag, Berlin, 2003.
- Aparicio-Monforte, Ainhoa ; Compoint, Elie; Weil,
A characterization of reduced
forms of linear differential systems,
Arxiv, to appear in
Journal of Pure and Applied Algebra.
- M. A. Barkatou, T. Cluzeau, C. El Bacha, and J.-A. Weil
Computing Closed Form
Solutions of Integrable Connections.