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Python
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Algebraic Equiv

algebraic_equiv
Read-onlyIdempotent

Check whether two algebraic expressions are mathematically equivalent, providing an exact symbolic identity comparison. Not for float rounding or overflow.

Instructions

Are two expressions algebraically identical? 'is (ab)/c the same as a(b/c)?' answered exactly. Use symbolic(op="simplify"), not this, to see one expression's own simplified/factored/expanded forms rather than compare two; use verify_translation to compare running PROGRAMS, not expressions. Caveat: symbolic identity says nothing about float rounding, integer truncation or modular overflow.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
aYesFirst symbolic expression to compare for algebraic identity
bYesSecond symbolic expression to compare for algebraic identity

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

Schema Changelog

Changes observed during successful MCP inspections.

  1. Changed2 schema fields changedv0.12.0
    • addedInput schema / properties / a / description
      Added value: +"First symbolic expression to compare for algebraic identity"
    • addedInput schema / properties / b / description
      Added value: +"Second symbolic expression to compare for algebraic identity"
  2. Changed1 schema field changedv0.11.0
    • changedOutput schema / (root)
      Previous value: -nullNew value: +{
+  "additionalProperties": true,
+  "title": "algebraic_equivDictOutput",
+  "type": "object"
+}
  3. Changed5 schema fields changedv0.2.0
    • removedInput schema / additionalProperties
      Removed value: -false
    • addedInput schema / properties / a / title
      Added value: +"A"
    • addedInput schema / properties / b / title
      Added value: +"B"
    • addedInput schema / title
      Added value: +"algebraic_equivArguments"
    • changedOutput schema / (root)
      Previous value: -{
-  "additionalProperties": true,
-  "type": "object"
-}New value: +null
  4. First observedv0.1.0

TDQS

A4.5/5.0
Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already provide readOnlyHint, idempotentHint, and destructiveHint, so the description's burden is reduced. It adds a meaningful behavioral caveat: the tool answers based on exact symbolic identity and says nothing about numeric execution semantics such as floating-point rounding, integer truncation, or modular overflow.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is compact and front-loaded with the core purpose. Every sentence earns its place: the first gives the exact question and example, the second routes to siblings, and the third provides an important correctness caveat. There is no filler or restatement of the title.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a two-parameter, read-only comparison tool with full schema coverage and an output schema, the description is complete enough. It gives the intended use, differentiates against the most likely sibling tools, and flags the main limitation the agent needs to know before relying on the result.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The input schema has 100% description coverage for both parameters, so the baseline is 3. The description adds context about comparing two expressions and gives a usage example, but it doesn't define a specific expression grammar or syntax beyond what the schema already indicates.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description opens with a precise purpose—testing whether two expressions are algebraically identical—and grounds it with a concrete example. It also names sibling tools for closely related but different tasks, allowing an agent to disambiguate without opening each schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines5/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

It gives explicit routing: use symbolic(op="simplify") when dealing with a single expression's simplified/factored/expanded forms rather than a comparison, and use verify_translation when comparing running programs. The caveat about float rounding, integer truncation, and modular overflow also tells the agent when not to rely on the result.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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