arithym

Exact precision math engine — 209 methods across 22 domains, all arithmetic as exact fractions with zero floating-point error. Use the 'tool' parameter to select a subsystem:

compute — Exact arithmetic, factorization, sqrt, trig, unit conversion. Examples: tool="compute" action="factorize" n="360" | action="sqrt" n="7920"

calculate — Multi-step chains with $prev/$label references. Example: tool="calculate" operations=[{values:["a","b"], read:"multiply", label:"result"}]

reference — Knowledge gateway backed by Epithreads (289 curated entries, 989 searchable aliases, 407 exact values). 118 chemistry (elements + compounds), 82 unit definitions & conversions, 79 physics constants, 10 math constants. Sources: CODATA 2022, IUPAC 2021, SI definitions. Browse: action='query_entries' domain='unit.conversion' | 'chemistry.elements' | 'physics.constants' | 'math.constants'. Lookup by name/symbol: action='lookup' query='Fe' or query='speed of light'. Also: 209 computation methods via action='guide', discover by keyword via action='discover'. call 209 computation methods (matrix, statistics, chemistry, physics, geometry...), discover by keyword. Examples: tool="reference" action="lookup" query="Fe" | action="guide" module="matrix" method="eigenvalues" args="[[4,1],[2,3]]"

model — Computational graph engine (up to 2,000 nodes). Define models, forward-pass, what-if scenarios, solve for target outputs. Graph ops: add, subtract, multiply, divide, power, gcd, lcm, product, sin, cos, tan, log, exp, abs. For large models (50+ nodes), build incrementally with workspace add/derive across multiple calls. Example: tool="model" action="define" spec={...}

workspace — Persistent named values with dependency tracking and cascade updates. State accumulates across calls — build large models incrementally (up to 2,000 nodes). The resulting graph supports the full model toolchain. Example: tool="workspace" action="add" name="mass" value="120"

analyze — Structural comparison (GCD, LCM, prime similarity), cross-domain verification, prime-space projection. Example: tool="analyze" action="compare" a="360" b="540"

optimize — Exact calculus via reverse-mode autodiff. Derivatives, gradients, Jacobians, integrals, critical points, curve analysis. Requires a model. Example: tool="optimize" action="gradient" output_name="total_cost"