What this shows. A polygonal knot diagram in the plane with n vertices and m crossings defines a matrix A that sends vertex heights z to crossing heights c = Az (over-strand height minus under-strand height at each crossing). The panels below display A together with its kernel, corange (row space) and cokernel, which update live as you move vertices, change heights, or flip crossings. Green crossings agree with the drawn over/under; red ones don't.
Disclaimer: this tool was created by using Claude.
Starts as a stick trefoil (6 segments). Use the segment buttons, the presets, or the vertical-edge selector (splits one vertex into two stacked vertices joined by a vertical stick, which adds a 3D segment but no crossing). Drag vertices, click a crossing to flip over/under, and set vertex heights z. Everything is recomputed live.