Arithym

Tools (50)

• help

  Arithym — precision math engine for AI agents. Eliminates math hallucination.

• domain_check

  ★ CALL THIS FIRST — your computation steering wheel. Exact routing, zero guesswork.

• discover

  Search all 202 exact-math methods by keyword. Returns matching methods with ready-to-use call syntax.

• list_refs

  List all 22 reference modules with domain-specific rules, formulas, and pitfalls.

• read_ref

  Load a reference module's rules, tables, and guidance on demand. Example: read_ref('calculus')

• guide_call

  Universal dispatcher — call any of 202 exact-math methods across 22 domain modules.

• guide_list

  List available modules and their methods. No args = all 22 modules. With name = methods in that module.

• factorize

  Exact prime factorization of any integer. Handles arbitrarily large numbers.

• compute

  Exact integer arithmetic: add, subtract, multiply, divide, gcd, lcm, power. No floating point.

• exact_sqrt

  Exact symbolic square root via the computation layer. No decimal approximation.

• rational_sqrt

  Exact symbolic square root of any rational number (integers, fractions, decimals).

• exact_trig

  Exact trig for special angles, IEEE 754 for others (clearly flagged).

• compare

  Compare two integers: exact GCD, LCM, shared factors, and similarity.

• verify

  Cross-verify an integer's properties: factorization roundtrip, divisor count, consistency checks.

• project

  Classify a value's mathematical domain and structural properties.

• route

  Show domain path between two values.

• landmarks

  List reference values in a domain: integer, rational, radical, trig, complex, or all.

• recommend

  Describe a problem in natural language, get the optimal tool call. Use when unsure which of the 202 methods to use.

• field_create

  Create or reset the computation workspace. Only needed when building a persistent model with multiple related values.

• field_add

  Store a single raw value (urchin) in the workspace. Use for constants, rates, and single inputs.

• field_read

  Read workspace state or compare two stored urchins (GCD, LCM, ratio, divisibility).

• field_gcd

  Exact GCD of 3+ values in one call. Takes raw numbers — no workspace needed.

• field_lcm

  Exact LCM of 3+ values in one call. Takes raw numbers — no workspace needed.

• field_lattice

  Full divisibility lattice from a set of values. All pairwise GCDs and LCMs.

• field_ratios

  All pairwise exact ratios for a set of values. For comparing proportions across a dataset.

• field_derive

  Compute from workspace urchins with tracked dependencies and auto-cascade.

• field_update

  Update an urchin's value — all dependents auto-recompute through the full dependency graph.

• field_sensitivity_all

  Compute sensitivity gradients for ALL tunable inputs against all outputs.

• field_optimize

  Iterative gradient-based optimization on the urchin field.

• field_links

  View dependency graph between workspace urchins. Shows what derives from what.

• field_query

  Search workspace by structural properties: dimension, similarity, domain, tag, or all.

• field_cluster

  Auto-group workspace urchins by similarity. Only useful with 5+ stored urchins.

• field_snapshot

  Save, restore, list, or delete named workspace states. For branching scenarios and what-if analysis.

• field_export

  Export workspace + snapshots to JSON. For persisting a model across sessions.

• field_import

  Import workspace state from a previous JSON export. For resuming work on a saved model.

• field_diff

  Compare two workspace snapshots. Shows added, removed, and modified urchins.

• field_note

  Annotate workspace urchins, pairs, or the field itself.

• field_notes

  Read annotations from the workspace log. Optional filter by target.

• field_clear_notes

  Clear annotations. No args = all. With target = matching only.

• scratch_math

  ★ SCRATCH PAD — Multi-step exact calculations in one call.

• scratch_math_units

  scratch_math with dimensional analysis — tracks units through every step.

• slide

  Exact addition and subtraction for raw values. Use for leaf inputs, not for combining urchins.

• fraction_math

  Exact fraction arithmetic — add, subtract, multiply, divide.

• graph_define

  Define a complete computational graph in one call.

• graph_observe

  Read full computational graph state — all inputs, intermediates, and outputs with values and lineage.

• graph_forward

  Forward pass: update inputs, cascade through graph, return all outputs.

• graph_sensitivity

  Compute exact gradients: how much each output changes per unit change in an input.

• graph_solve

  Inverse solve: find the input value that produces a target output via bisection search.

• graph_what_if

  Run multiple scenarios against the graph and compare outcomes.

• graph_learn

  Iterative gradient-based adjustment toward target outputs using exact-fraction gradients.