🔦 Tutorials

• Formulating and solving systems
  • 🌐 Finding all the solutions
  • 🎯 Solving a system with ZeroDimSolver
  • 📍 A real point on every component (the Trott curve)
  • 🎯 Critical points by rank deficiency (a null vector, not a determinant)
  • 🧮 Eigenvalues by homotopy continuation
  • 🔁 Parameter homotopy: solve once, re-solve many times
  • 🧱 Build a system in pieces with clone and concatenate
  • 🎲 Randomize an overdetermined system
  • 🪢 Author your own start system: a product of linears
  • 🧮 Canonical ordering, and opting out
  • 🗃️ A dataframe of solutions: filtering and plotting with pandas
• Manipulating solutions
  • ✂️ Intro to slices
  • 🛷 Move a slice, hold the system fixed
• Solver settings & multiprecision
  • ⚙️ Carrying settings across related solves
  • 🪢 Crossed paths: when two paths become one
  • 🎚️ When double precision is not enough
  • 🔬 Precision models: double, multiple, adaptive
• Parallelism in Python
  • 🚀 Solving at scale: many cores, many machines
  • ⚗️ A bistable reaction network, mapped in parallel
• Observing, metadata, and more
  • 👀 Watching the paths: observers and path data
  • 🎨 The continuation cartoon, from real data — and seeing precision change
  • 🖼️ The classic continuation cartoon, from real data
• Performance and benchmarking
  • ⏱️ Timing Bertini 1 vs Bertini 2
• The record-keeping system
  • Automatic record keeping
  • Chained homotopies: provenance all the way back
• Doing things manually
  • ♻️ Evaluation of cyclic-\(n\) polynomials
  • 🎮 Using an endgame to compute singular endpoints
  • 🛤 Tracking to nonsingular endpoints