312.200 (19W) Symbolic Computation Lab

Wintersemester 2019/20

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Erster Termin der LV
15.10.2019 16:00 - 18:00 , N.2.01
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LV-Titel englisch
Symbolic Computation Lab
Praktikum (prüfungsimmanente LV )
6 (25 max.)
mögliche Sprache/n der Leistungserbringung
Deutsch , Englisch
zum Moodle-Kurs


Intendierte Lernergebnisse

After successful completion of this course, students know the mathematical foundations in selected topics in symbolic computation (concretely in this version of the course: algebraic combinatorics, lattice theory). Furthermore, they have also collected practical experience in the implementation and applications of algorithms (concretely: guessing of sequences, the LLL-algorithm) from these selected topics.


Discussion of the theoretical foundations based on short lectures with some exercises and supplementary materials, followed by practical work on small projects.


  • algebraic classification of sequences (especially: hypergeometric, C-finite, and holonomic sequences)
  • relations between symbolic sums, recurrence equations, generating functions, and asymptotic estimates
  • basic lattice theory  in context of the geometry of numbers
  • the Lenstra-Lenstra-Lovász (LLL) basis reduction algorithm and its applications

Erwartete Vorkenntnisse

  • Experience with SageMath (course: Computermathematics)
  • Elementary combinatorics (course: Combinatorial Structures)
  • Elementary group theory (course: Linear Algebra / Algebraic Structures)


  • Modern Computer Algebra (Joachim von zur Gathen, Jürgen Gerhard; 3rd Edition)
  • The Concrete Tetrahedron (Manuel Kauers, Peter Paule)



The course covers two (related) topics: algebraic combinatorics and lattice theory + applications. For each of these topics, there will be a set of project assignments from which students can choose from; at least one project has to be chosen for every topic. Students are expected to hand in a written report giving a detailed description on their work on the project assignments. In the final session, the students will give a short presentation on the assignments they chose.


  • Completeness and documentation of the project assignments in the report
  • Quality of the corresponding final presentation


Within the course it is possible to obtain report points (up to 20) and presentation points (up to 5). Provided that at least 12 report points were obtained (otherwise the course is failed), the final grade is obtained from the following table:

< 12,55 (Nicht genügend)
< 15,754 (Genügend)
< 193 (Befriedigend)
< 222 (Gut)
≥ 221 (Sehr gut)

Report points

  • There are 20 report points in total.
  • The report is split in two parts: one part on algebraic combinatorics (guessing) and one part on lattice theory (LLL-algorithm). Each part is worth 10 points and consists of detailed descriptions of the solution approach for all selected projects.
  • It is possible to reach 10 points per chosen project, but it is also possible to choose multiple projects per part.  (You cannot earn more than 10 points per part, though.)
  • Working in groups to solve the projects is allowed, the project reports have to be written individually. In case of joint work on the projects, the people that are part of your group have to be declared in the project report.
  • The report has to be written in LaTeX under consideration of our guidelines (see Moodle). In case of severe violations of the guidelines, report points will be deducted.
  • Deadline for handing in the report: 29.2.2020

Presentation points

  • In the final session of the course (preliminary: 14.1.2020) students will present their work on the project assignments and discuss their approaches.
  • Presentations can be done in groups. If so, please declare (as a part of the presentation) who worked on what.
  • Every student can earn up to 5 presentation points, which are awarded for the quality of the presentation.


Note/Grade Benotungsschema

Position im Curriculum

  • Doktoratsprogramm Modeling-Analysis-Optimization of discrete, continuous and stochastic systems (SKZ: ---, Version: 16W.1)
    • Fach: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems (Pflichtfach)
      • Modeling-Analysis - Optimization of discrete, continuous and stochastic systems ( 0.0h XX / 0.0 ECTS)
        • 312.200 Symbolic Computation Lab (1.0h PR / 3.0 ECTS)
  • Masterstudium Mathematics (SKZ: 401, Version: 18W.1)
    • Fach: Discrete Mathematics (Wahlfach)
      • 6.9 Symbolic Computation Lab ( 1.0h PR / 3.0 ECTS)
        • 312.200 Symbolic Computation Lab (1.0h PR / 3.0 ECTS)
  • Masterstudium Mathematics (SKZ: 401, Version: 18W.1)
    • Fach: Applied Mathematics (Wahlfach)
      • Lehrveranstaltungen aus den Vertiefungsfächern ( 0.0h XX / 12.0 ECTS)
        • 312.200 Symbolic Computation Lab (1.0h PR / 3.0 ECTS)
  • Masterstudium Technische Mathematik (SKZ: 401, Version: 13W.1)
    • Fach: Seminar und Praktikum (Pflichtfach)
      • Praktikum Angewandte Mathematik ( 2.0h PR / 4.0 ECTS)
        • 312.200 Symbolic Computation Lab (1.0h PR / 3.0 ECTS)
  • Doktoratsstudium Doktoratsstudium der Technischen Wissenschaften (SKZ: 786, Version: 12W.4)
    • Fach: Studienleistungen gem. § 3 Abs. 2a des Curriculums (Pflichtfach)
      • Studienleistungen gem. § 3 Abs. 2a des Curriculums ( 16.0h XX / 32.0 ECTS)
        • 312.200 Symbolic Computation Lab (1.0h PR / 3.0 ECTS)

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