PRIMAL
Tropical curve
bounded edgeray
Drag to pan · wheel to zoom · select a feature
OBSERVATION CHAMBER / ACTIVE
Tropical Curve Balancer
Edit integer heights in a max-plus polynomial, build its tropical curve, and inspect exact vertices, weighted balancing, and the dual Newton subdivision.
tropical
Operational
Coefficient heights
Ready for an exact build.
BALANCEDPENDING
- Vertices
- —
- Bounded / rays
- — / —
- Dual cells
- —
- Selected feature
- not calculated
- Selected Σw·u
- not calculated
DUAL
Newton subdivision
dual cellcoefficient
Select a lattice point to edit its height
SELECTED FEATUREnot calculatedBuild the curve, then select a feature.
No certified feature is available.
EXACT FEATURE INDEX
Vertices, bounded edges, and rays
Build the curve to populate every exact feature.
Advanced exact data, duality, and lifecycle
Exact vertices
not calculated
Upper facets and dual cells
not calculated
Invariant checks
- Status
- not calculated
Committed snapshot
- Input revision
- 0
- Job
- 0
- Snapshot hash
- —
- Runtime
- —
- Convention
- max-plus
- Provenance
- local exact core; no external runtime
OUTPUT
REPORT
Model boundary: degree ≤ 5, support ≤ 21, integer heights, exact BigInt rational decisions, and a finite drawing viewport. This is an observation instrument, not a formal proof or engineering design tool.
OBSERVATION GUIDE
Touchpoints for Observation
Edit a max-plus polynomial and watch its weighted tropical curve appear beside the dual regular upper Newton subdivision.
- Start with Tropical line, adjust an integer height, then BUILD CURVE. Select any vertex, bounded edge, or ray from the canvas or the complete Feature index.
- The two-dimensional model accepts integer heights with degree at most 5, support at most 21, and coefficients up to 100 digits.
- Topology, weights, primitive directions, duality, and balancing use exact BigInt rationals; Number coordinates are only for the finite drawing viewport.
- Rays are mathematically unbounded and are clipped only for display; an export or layout failure does not change a certified BALANCED result.
A finite complexity cap can stop an ambiguous or oversized input with an explicit reason. This is not a formal proof system, a general CAS, a cryptographic tool, or an engineering design system.
Runs inside the browser with no upload and no registration.
SYSTEM NOTE
For F(x,y)=max_(i,j)(h_ij+i·x+j·y), the tropical curve is the locus where at least two terms share the maximum. Lifting exponent points to (i,j,h_ij) gives a regular upper Newton subdivision dual to the curve: vertices correspond to upper 2-cells, curve edges to dual edges, and rays to boundary edges. A dual exponent difference (Δi,Δj) has weight gcd(|Δi|,|Δj|); dividing by that weight and orienting outward gives the primitive direction u. Every certified vertex satisfies Σ weight·u=(0,0) exactly. Adding a constant to all heights leaves the curve unchanged, while h′_ij=h_ij+a·i+b·j+c translates it by (−a,−b).
OBSERVATION POLICY
This lab runs in your browser. Coefficient heights, exact calculations, reports, and images are not uploaded by this lab.
Route
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