Aman-Amith-Shastry-scientific_computation_mcp

laplacian

Read-onlyIdempotent

    Computes the Laplacian of a scalar or vector field symbolically.

    Args:
        f_str (str): Scalar function as "x**2 + y*z" or vector "[Fx, Fy, Fz]".
        is_vector (bool): Set True to compute vector Laplacian.

    Returns:
        str: Symbolic result of the Laplacian—scalar or list of 3 components.

Input Schema

TableJSON Schema

Name	Required	Description	Default
`f_str`	Yes	Scalar function such as "x*2 + yz", or a bracketed vector field such as "[Fx, Fy, Fz]".
`is_vector`	No	Set True when f_str is a vector field, so the Laplacian is taken componentwise.

Output Schema

TableJSON Schema

Name	Required	Description	Default
`result`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

Changed2 schema fields changedSep 10, 2026

addedInput schema / properties / f_str / description

Added value: +"Scalar function such as \"x**2 + y*z\", or a bracketed vector field such as \"[Fx, Fy, Fz]\"."

addedInput schema / properties / is_vector / description

Added value: +"Set True when f_str is a vector field, so the Laplacian is taken componentwise."

First observedJan 31, 2026

TDQS

A4.5/5.0

Behavior4/5

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

Annotations already cover read-only and idempotent hints. The description adds value by disclosing the return format (string, scalar or list of 3 components) and noting the symbolic nature of the result. It does not contradict annotations, and the added behavioral context is helpful.

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 a compact docstring with a clear structure: purpose, Args, Returns. Every sentence adds information—no filler. The key purpose is stated first, and the parameter/return details are neatly organized.

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 symbolic math tool, the description is complete: it explains inputs, the scalar/vector distinction, and the output format. With annotations covering safety and an output schema present (though not shown), nothing essential is missing for an agent to call it correctly.

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

Parameters4/5

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

Schema coverage is 100% with both parameters described. The description reinforces the parameter meanings with concrete examples (e.g., 'x**2 + y*z' and '[Fx, Fy, Fz]') and clarifies the effect of is_vector on the computation. While it largely repeats schema info, the examples add practical clarity beyond the schema.

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 computes the Laplacian of a scalar or vector field symbolically, with explicit examples of input formats. It distinguishes itself from sibling vector calculus tools (gradient, curl, divergence) by its specific operation, making the purpose unambiguous.

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

Usage Guidelines4/5

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

The description gives clear context for when to use it (computing Laplacians) and explains the scalar vs. vector distinction via the is_vector flag. It does not explicitly name alternatives or exclusions, but the purpose is so specific that usage is implied. A 4 reflects clear context without explicit exclusionary guidance.

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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