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Calculators, numerics, date logic, statistics, and finance tools
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Writing, cleanup, formatting, extraction, and text analysis tools
Developer utilities, networking, web debugging, and automation helpers
Format, file, archive, unit, and encoding conversion tools
Finance
Turn Polymarket odds into a probability term structure: implied probabilities by expiry, with overround removed.
Simulate the yearly revaluation (perequazione) of an Italian pension: per-band breakdown, scaglioni vs blocchi, and 2026 vs the 2027 draft.
Side-by-side monthly rent-vs-buy simulation: mortgage amortization, property tax, insurance, HOA and maintenance against rent plus renter insurance; the renter invests the down payment and monthly savings at an opportunity-cost rate. Outputs break-even year on net sale proceeds, per-year differential NPV, SALT-cap-aware after-tax cash flows, a differential IRR, and a ±20% tornado sensitivity chart.
Math & Numbers
Smallest primitive root mod n with certificate g^(φ/q) ≠ 1, root count φ(φ(n)), up to 50 listed roots, and candidate verification. n ≤ 10¹².
(n−1)! ≡ −1 (mod n) ⟺ n is prime. Exact factorial residue for n ≤ 10⁷, Miller–Rabin cross-check, composite factorial law, optional running-products trace.
Exact π(n) via a single-pass Sieve of Eratosthenes (n ≤ 10⁷) with n/ln n comparison, density, average gap, and the largest prime ≤ n.
Dijkstra with a full per-iteration trace: settled nodes, relaxations, distance table, and the final path; undirected or directed, negative weights rejected, unreachable targets reported.
Table lookup of the unilateral Z-transform for 11 standard pairs, with parameter substitution, region of convergence, derivation note, and optional numeric X(z₀) evaluation.
Compute remaining radionuclide activity A(t) = A₀·2^(−t/T½) with λ = ln2/T½ in Bq/Ci/dpm units, for Tc-99m, F-18 and other isotopes.
Convert illuminance between lux (lx = lm/m², SI base), kilolux (1 = 1000 lx), footcandle (1 = 10.7639104 lx), phot (1 = 10000 lx), and nox (1 = 0.001 lx). Converts via lux to the target unit and lists the equivalent value in all five units for reference. Reference values: full moon ≈ 0.25, office lighting ≈ 300–500, overcast day ≈ 1000, direct sunlight ≈ 100000 lux.
Calculate Poisson's ratio ν = −ε_transverse / ε_longitudinal and solve any of the three unknowns: ratio, lateral strain, or longitudinal strain. Tensile ε_long > 0 produces lateral contraction ε_lat < 0. Typical values: steel ≈ 0.30, aluminum ≈ 0.33, rubber ≈ 0.49, cork ≈ 0. Theoretical isotropic range 0 ≤ ν ≤ 0.5.
Solve Young's modulus (modulus of elasticity) in the linear-elastic region using E = σ/ε (Hooke's law). Three directions: modulus E = σ/ε, stress σ = E·ε, strain ε = σ/E. Pick the unknown, supply the other two positive values. Result in MPa with a GPa reading (e.g. steel ≈ 200 000 MPa).