THESIS TOPICS

• Linear Differential Systems with Singularities
  
  
• Singularly-Perturbed Linear Differential Systems
  
  
• Completely Integrable Pfaffian Systems with Normal Crossings

PUBLISHED PAPERS

1. M.A. Barkatou, S.S. Maddah (2015). Removing Apparent Singularities of Systems of Linear Differential Equations with  Rational Function Coefficients. To appear in Proceedings of the 40th International Symposium on Symbolic and Algebraic Computation, ACM Press.
   
   
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, S.S. Maddah (2015). Formal Solutions of Singularly-Perturbed Linear Differential Systems.
           Download: Preprint.

PAPERS UNDER REDACTION

      5.  M.A. Barkatou, Maximilian Jaroschek , S.S. Maddah (2015).  Formal Solutions of a Class of Pfaffian Systems in Several
           Variables. Slides.

SOFTWARE

This section is under construction and some images are broken.

The following packages and their manuals are under continuous update and new functionalities are to be added soon. I would be thankful for any comment/suggestion/bug report.

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 or on the numbers for some examples of computations: 1 2 3 4 5
   
   
   
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
   Download Maple sheet of examples
   Download sheets of Exponential Parts Computation: Maple sheets , pdf files
   Click here or on the numbers for some examples of computations: 1 2 3 4 5
   
   
   
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 or on the numbers for some examples of computations: 1 2 3 4
   
   
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 and 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.