Sage tutorial at Montpellier (2022)

You can find this webpage on:

• https://lipn.univ-paris13.fr/~monteil/montpellier2022

Sage pedagogical material

Introduction to Sage

• Introductory slides
• Introduction worksheet
• First manipulations (tab completion, doc, sources,...) (solutions)

Python/Sage programming resources

• For complete beginners in programming: on the live USB key, you can open a terminal and type laby, select the Python language and help the ant to find its way out. You can also download laby from this page
• Python short tutorial for people who already programmed in another language: Learn Python in 10 minutes
• Some introductions to Python can be found in the Sage thematic tutorials
• Some exercices:
  • 1 First steps with Sage (solution)
  • 2 Learn about for loops (solution)
  • 3 Learn about conditionals (solution)
  • 4 Write functions
  • 5 While loop
  • 6 More advanced exercises (solution)
• A collection of mathematical puzzles to be solved by a combination of mathematics and programming: http://projecteuler.net
  • Solve the first ten projecteuler problems in one line with Sage (commented solutions)

Technical skills

• Representations of real and complex numbers in Sage
• Use MILP solvers to crack hard combinatorial problems

Modeling

• Solving the lights out game : problem, model, a possible solution in french
• Task assignment with graphs (solution)

Some thematic worksheets

• Dynamics
  • The logistic map (partial solution)
  • Floating point and stability
  • Matrix dynamics
  • Explore the Collatz conjecture (solution)
  • Population dynamics (demo)
• Tilings
  • Draw the Penrose tiling by substitution (solution)
  • Tiling a polyomino (you also need to download polyomino.sage)
  • more to come (domino tilings of the Aztec diamond) !
• Probability and Markov chains (basic)
  • Measure simulation
  • Markov chains
  • Random walks
  • Génération aléatoire de marches (énoncé au format pdf)
  • Mélanges de cartes et chaînes de Markov
• Guessing
  • Introduction to ore_agebra package
  • Guessing a nth derivative (solution)
  • Resultants
• Other
  • Draw the roots of polynomials (solution)
  • Max flow and matchings
  • Learn dictionaries with graph theory (solution)
  • Strings and the Burrows-Wheeler transform

Some debriefings to publish

How to

• I overwrote my solve
• How to measure time and estimate the complexity of an algorihm ?
• How to count ?
• How to deal with deeply nested loops

Sage specifics

• Preparsing (numbers, power, R.<x>=, f(x)=, )
• About the notion of "variable" (name(space)s, undeterminates, symbols)
• Symbolic vs algebraic, formulas vs polynomials, solve vs variety/kernel/..., etc
• About coercion

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