Algebraic geometry

• "A Hybrid Procedure for Finding Real Points on a Real Algebraic Set"
• "Algorithms for computing triangular decomposition of polynomial systems"
• "When a system of real quadratic equations has a solution"
  • This only decides whether there's a solution, rather than finding one, but it might have some tools we can use.
• "Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems"
  • This isn't the kind of quadratic system we have, but it the paper might have some tools we can use.

Geometric algebra

• Ganja.js
  • Tons of examples! We may be able to use it as a ready-made display and drag interface. Also has Julia bindings.
• "G_{6,3} Geometric Algebra; Description and Implementation"
  • Shows how the G_{6,3} Clifford algebra extends G_{4,1} to encode all quadric surfaces.