RESEARCH THEMES

• Linear Differential Systems with Singularities
  
  
• Singularly-Perturbed Linear Differential Systems
  
  
• Completely Integrable Pfaffian Systems with Normal Crossings
  
  Download: Resumé of thesis  (September 2015, University of Limoges, Advisor: Moulay Barkatou)
  
  
• Special Functions (recently)
  
  

PUBLISHED PAPERS

1. M.A. Barkatou, S.S. Maddah (2015). Removing Apparent Singularities of Systems of Linear Differential Equations with  Rational Function Coefficients. In Proceedings of the 40th International Symposium on Symbolic and Algebraic Computation, ACM Press, p. 53-60.
   Download: Published version, slides.
   
   
2. S.S. Maddah, M. Barkatou, and H. Abbas  (2014). On the Reduction of Singularly-Perturbed Linear Differential Systems. In Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, ACM Press, p. 320-327.
   Download: Published version, preprint.
   
   
3. S.S. Maddah, M. Barkatou, and H. Abbas  (2014). Formal Solutions of a Class of Pfaffian Systems in Two Variables. In Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, ACM Press, p. 312-319.
   Download: Published version, preprint.

SUBMITTED PAPERS

      4.  M.A. Barkatou, Maximilian Jaroschek , S.S. Maddah (2015).  Formal Solutions of a Class of Pfaffian Systems in Several
           Variables.
           Download: Preprint, slides.
         

PAPERS UNDER REDACTION

      5.  M.A. Barkatou, S.S. Maddah (2015-2016). Formal Solutions of Singularly-Perturbed Linear Differential Systems.





SOFTWARE


The following packages are in preliminary version.  Their are under continuous update and new functionalities are to be added. I would be thankful for any comment/suggestion/bug report. Last updated 4 Nov 2015.

1. Lindalg: Mathemagix package for Symbolic Resolution of Linear Systems of Differential Equations with Singularities. Developed within Google Summer of Code 2014.
   
   Download and install Mathemagix (Lindalg is accompanied with examples of computations - OPEN SOURCE)
   Download Tutorial
   Download Manual
   
   
   
2. miniISOLDE: Maple package for Symbolic Resolution of Linear Systems of Differential Equations with Singularities. This package is a reduced version of ISOLDE and the analog of Lindalg in Maple.
   
   Download Package
   Download Tutorial
   Download Maple sheet of examples
   Click here  for some examples of computations
   
   
   
3. ParamInt: Maple package for symbolic resolution of singularly-perturbed linear systems of differential equations, prototype implementation. Based on papers [2] and [4].
   
   Download Package (A limited version is avaiable for download, i.e. a version excluding Exponential part computation. Examples are given however in a pdf file below. If interested, please send me an email and I will send you the full prototype package of ParamInt.)
   Download Maple sheet of examples
   Download sheets of Exponential Parts Computation: pdf files
   Some examples of computations
   
   
   
4. PfaffInt: Maple package for symbolic resolution of completely integrable Pfaffian systems with normal crossings, prototype implementation. Based on papers [3] and [5].
   
   Download Package
   Download Maple sheet of examples
   Click here and here for some examples of computations
   
   
5. AppSing: Maple package for removing apparent singularities of systems of linear differential equations with rational function coefficients. M.A. Barkatou, S.S. Maddah (2015). Based on paper [1].
   
   Download Package
   Download manual.
   Download Maple sheet of examples.
   Click here for some examples of computations.
   
   
   
6. ParamAlg: Maple package for differential-like reduction of matrices perturbed by a parameter.
   

          Download Package
          Download Maple sheet of examples
          Click here for some examples of computations.



To install any of the Maple packages (e.g. AppSing), one can proceed as follows:

• Open Maple and type   libname;
• Then, type  libname := " the global path of the directory AppSing", the result of the previous step;
• Type march('list', "the global path of the directory AppSing"); to view a list of the functionalities of the package.
• You can try the Maple sheet of examples to verfiy that the package is well-installed.