Elysia Tools
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Calculators, numerics, date logic, statistics, and finance tools
Image, audio, and video processing, conversion, and optimization tools
Color, layout, graphics, visual styling, and design helper tools
Writing, cleanup, formatting, extraction, and text analysis tools
Developer utilities, networking, web debugging, and automation helpers
Format, file, archive, unit, and encoding conversion tools
Math & Numbers
Plot a normal-distribution bell curve as SVG with z-score markers, interval or tail-probability shading, and 68/95/99.7 standard-deviation bands.
Finance
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.
Date & Time
Parse ISO 8601 durations, validate ISO 8601-2 extensions, run calendar-true arithmetic, sort by real length at an anchor, and diff datetimes.
Enumerate primes up to 10⁷ (or within [m, n]) with the classic sieve; shows base primes, crossing-out operations, exact counts, and up to 200 primes.
Textbook Hungarian algorithm for 2–8 × 2–8 assignment problems: row/column reductions, augmenting-path zero matching, König line covers, and substitution-verified optimal assignments.
Activity-on-node CPM: ES/EF/LS/LF, total float, project duration, and every critical path; cycles and unknown predecessors are rejected.
Two-person zero-sum games: saddle-point test first, then mixed strategies from a single-phase simplex LP with dual shadow prices, verified by security-level checks.
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.
Minimal SOP via Quine–McCluskey with essential prime implicants, exact minimum cover, Gray-coded Karnaugh map, and full-assignment verification.
Numeric convergence tests for Σ aₙ: nth-term, ratio, root, p-series comparison, and integral test; alternating series classified by Leibniz with a sum estimate.
Union, intersection, difference, symmetric difference, and Cartesian product of two comma-separated sets, with cardinalities and capped pair display.
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.