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Symbolic Algebra MCP Server

Symbolic Algebra MCP Server

create_custom_metric

Build a custom metric tensor from specified components and symbols for symbolic tensor and general relativity calculations.

Instructions

Creates a custom metric tensor from provided components and symbols.

Input Schema

NameRequiredDescriptionDefault
configNoll
symbolsYes
componentsYes

Output Schema

NameRequiredDescriptionDefault
resultYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observedv0.1.0

TDQS

C2.7/5.0
Behavior2/5

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

No annotations are provided, so the description must carry the full behavioral burden. It states that the tool creates a tensor, but does not describe permissions, state changes, coordinate-system requirements, or other behavioral traits relevant to a creation operation.

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

Conciseness4/5

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

The description is a single front-loaded sentence with no wasted wording. It is efficient, though its brevity contributes to the missing detail captured in other dimensions.

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

Completeness2/5

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

For a custom-metric creation tool with no annotations and 0% schema description coverage, the description omits essential context about parameter meaning and usage relative to predefined metrics. The existence of an output schema covers return values, but it does not compensate for the missing input and behavioral context.

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

Parameters2/5

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

Schema description coverage is 0% for all three parameters, and the description only restates that components and symbols are provided. It does not explain the nested array format of components, what symbols represent, or what the config enum values 'll' and 'uu' mean.

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

Purpose4/5

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

The description states a specific verb and resource: creates a custom metric tensor from provided components and symbols. It is clear what the tool does, but it does not distinguish itself from sibling tools such as create_predefined_metric or search_predefined_metrics.

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

Usage Guidelines2/5

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

There is no explicit guidance on when to use this tool versus create_predefined_metric or search_predefined_metrics. The word 'custom' implies an alternative to predefined metrics, but the description gives no conditions, exclusions, or prerequisites.

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