TQFT Knot Explorer computes polynomial invariants of knots built from simple tree diagrams — pretzel diagrams and multi‑vertex propagator trees — then looks up which knot the result corresponds to.
Open the Explorer → Open the Builder →How it works
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1
Pick a diagram
Choose a pretzel diagram or a 2‑vertex tree. Each leg and bridge of the diagram is a twist region you control.
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2
Enter your crossings
Type a whole number into each spot on the diagram — the number of crossings (and their sign) in that twist region. Pick the color r for the invariant.
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3
Compute
The invariant is computed on the spot and reported as a Laurent polynomial, along with its determinant and, when possible, the name of the knot it matches.
What you get
- The invariant — a Laurent polynomial in q.
- The determinant — the sum of the absolute values of the polynomial's coefficients.
- Identification — the matching knot name (and whether it is the mirror image), when the invariant is in the table.