TensorConstructions

A Maple package for handling tensor constructions on linear differential systems

(in development)

Author: J.-A. Weil (Université de Limoges ; CNRS ; XLIM UMR 6172 ; DMI)
(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 IntegrableConnections, 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. Weil.
It may also be used in the context of integrability of Hamiltonian systems, using tools developed with Ainhoa Aparicio-Monforte.

II - Download and installation

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:

Copy the above files in a directory called "TensorConstructions"
Add this directory to your libname, for example by performing the two following steps:
- Open Maple and type
  
  libname;
- Then, type
  
  libname := " the global path of the directory TensorConstructions", libname;
Type

with(TensorConstructions);

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.

If you do not manage to install the package, then contact us.

III - Examples of calculations

We illustrate here our three main procedures on some examples:

Symmetric Powers

Input:

Output:

Example files:
Eigenring

Input:

Output:

Example file:

More examples (more examples will be added)

IV - Bug reports

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 differential equations.
Grundlehren der Mathematischen Wissenschaften, 328. Springer-Verlag, Berlin, 2003.
Aparicio-Monforte, Ainhoa ; Compoint, Elie; Weil, Jacques-Arthur.
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.
ISSAC 2012.