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sdiehl
by sdiehl

intro_many

Define and store multiple symbolic variables with specific assumptions efficiently. Ideal for managing complex mathematical variables in symbolic algebra tasks.

Instructions

Introduces multiple sympy variables with specified assumptions and stores them.

Takes a list of VariableDefinition objects for the 'variables' parameter.
Each object in the list specifies:
- var_name: The name of the variable (string).
- pos_assumptions: A list of positive assumption strings (e.g., ["real", "positive"]).
- neg_assumptions: A list of negative assumption strings (e.g., ["complex"]).

The JSON payload for the 'variables' argument should be a direct list of these objects, for example:
```json
[
    {
        "var_name": "x",
        "pos_assumptions": ["real", "positive"],
        "neg_assumptions": ["complex"]
    },
    {
        "var_name": "y",
        "pos_assumptions": [],
        "neg_assumptions": ["commutative"]
    }
]
```

The assumptions must be consistent, so a real number is not allowed to be non-commutative.

Prefer this over intro() for multiple variables because it's more efficient.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
variablesYes
Behavior4/5

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

With no annotations provided, the description carries the full burden of behavioral disclosure. It effectively describes key behaviors: the tool creates and stores variables, requires consistent assumptions, and provides a detailed JSON payload example. However, it doesn't mention error handling, side effects, or what 'stores them' means in practice (e.g., where variables are stored, persistence). The description adds substantial value but leaves some behavioral aspects implicit.

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 well-structured and appropriately sized. It starts with a clear purpose statement, then details the parameter structure with a helpful example, adds a constraint note, and ends with usage guidance. Every sentence adds value, and there's no redundancy or fluff. The formatting with code blocks enhances readability without wasting space.

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

Completeness4/5

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

Given the tool's moderate complexity (1 parameter but with nested objects), no annotations, and no output schema, the description does an excellent job covering most aspects. It explains the tool's purpose, parameter semantics, usage guidelines, and behavioral context. However, it doesn't describe the return value or what happens after variables are stored (e.g., are they available globally?), leaving a minor gap in completeness.

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

Parameters5/5

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

The input schema has 0% description coverage, so the description must fully compensate. It does this excellently: it explains the 'variables' parameter as a list of VariableDefinition objects, details each object's structure (var_name, pos_assumptions, neg_assumptions), provides a comprehensive JSON example, and adds semantic constraints ('assumptions must be consistent'). This goes far beyond what the bare schema provides.

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 clearly states the tool's purpose: 'Introduces multiple sympy variables with specified assumptions and stores them.' It uses specific verbs ('introduces', 'stores'), identifies the resource ('sympy variables'), and distinguishes from its sibling 'intro' by emphasizing efficiency for multiple variables. This is a complete and precise purpose statement.

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?

The description provides explicit usage guidance: 'Prefer this over intro() for multiple variables because it's more efficient.' It directly compares to the sibling tool 'intro' and gives a clear condition for when to use this tool (multiple variables) versus the alternative. This is optimal guidance for tool selection.

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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