Contents Menu Expand Light mode Dark mode Auto light/dark, in light mode Auto light/dark, in dark mode Skip to content
Bertini 4.0.0 documentation
Logo
Bertini 4.0.0 documentation
  • 👋 Welcome to Bertini 2
  • 🔦 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
      • 🧮 Eigenvalues by homotopy continuation
      • 🔁 Parameter homotopy
      • 🧱 Build a system in pieces with clone and concatenate
      • 🎲 Randomize an overdetermined system
      • 🪢 Author your own start system: a product of linears
      • 🧮 Canonical monomial 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
      • 📈 Plotting solutions and paths
    • Solver settings & multiprecision
      • Auxiliary coordinates
      • ⚙️ Carrying settings across related solves
      • 🪢 Crossed paths: when two paths (accidentally) become one
      • 🎚️ When double precision is not enough
      • 🔬 Precision models: double, multiple, adaptive
      • ⏱️ Stopping a solve, and using a wall-clock budget
    • Parallelism in Python
      • 🚀 Solving at scale: many cores, many machines
      • ⚗️ Parameter homotopy in parallel
    • Observing, metadata, and more
      • 👀 Watching paths: observers and path data
      • 🎨 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
      • 〰️ Tracking an analytic homotopy
  • 🌟 Everyday API
  • ✨ Showpieces
    • 🧬 The Monodromy Loom
    • ✈️ The Flight Recorder
  • ⚙️ Configuration reference
  • Multiprecision numbers and NumPy
  • 🔎 Full API reference
    • bertini.algorithms
      • bertini.algorithms.zerodim
    • bertini.config
    • bertini.endgame
    • bertini.logging
    • bertini.multiprec
    • bertini.nag_algorithm
    • bertini.operators
    • bertini.parallel
    • bertini.parse
    • bertini.random
    • bertini.records
    • bertini.symbolics
    • bertini.sympy_bridge
    • bertini.system
      • bertini.system.start_system
    • bertini.tracking
      • bertini.tracking.observers
        • bertini.tracking.observers.amp
        • bertini.tracking.observers.double
        • bertini.tracking.observers.multiple
  • 📚 Bibliography
Back to top
View this page

Doing things manually¶

  • ♻️ Evaluation of cyclic-\(n\) polynomials
  • 🎮 Using an endgame to compute singular endpoints
  • 🛤 Tracking to nonsingular endpoints
  • 〰️ Tracking an analytic homotopy
Next
♻️ Evaluation of cyclic-\(n\) polynomials
Previous
Chained homotopies: provenance all the way back
Copyright © 2015-2026, Bertini Team
Made with Sphinx and @pradyunsg's Furo
Built from d882924 on 2026-10-06 20:10 UTC.