Aman-Amith-Shastry-scientific_computation_mcp

divergence

Read-onlyIdempotent

    Computes the symbolic divergence of a vector field, optionally evaluated at a point.

    Args:
        f_str (str): A string representing the vector field in list format (e.g., "[x+y, x, 2*z]").
        point (list[float], optional): A list of coordinates [x, y, z] to evaluate the divergence numerically.

    Returns:
        dict: A dictionary with the symbolic divergence as a string, and optionally the evaluated scalar.

Input Schema

TableJSON Schema

Name	Required	Description	Default
`f_str`	Yes	Vector field in bracketed list form with components in x, y, z, e.g. "[x+y, x, 2*z]".
`point`	No	Optional [x, y, z] coordinates at which to evaluate the result numerically.

Output Schema

TableJSON Schema

Name	Required	Description	Default
No arguments

Schema Changelog

Changes observed during successful MCP inspections.

Changed6 schema fields changedSep 10, 2026

addedInput schema / properties / f_str / description

Added value: +"Vector field in bracketed list form with components in x, y, z, e.g. \"[x+y, x, 2*z]\"."

addedInput schema / properties / point / anyOf

Added value: +[
+  {
+    "items": {
+      "type": "number"
+    },
+    "type": "array"
+  },
+  {
+    "type": "null"
+  }
+]

addedInput schema / properties / point / description

Added value: +"Optional [x, y, z] coordinates at which to evaluate the result numerically."

removedInput schema / properties / point / items
```
Removed value: -{
-  "type": "number"
-}
```
removedInput schema / properties / point / type
```
Removed value: -"array"
```

changedOutput schema / (root)

Previous value: -nullNew value: +{
+  "additionalProperties": true,
+  "title": "divergenceDictOutput",
+  "type": "object"
+}

First observedJan 31, 2026

TDQS

A3.8/5.0

Behavior3/5

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

Annotations already declare read-only, idempotent, non-destructive behavior. The description adds that the result is symbolic and optionally numerically evaluated at a point, but does not discuss errors, expression constraints, or exact return shape beyond 'dict'.

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?

Concise, front-loaded with the core operation; the example and point-evaluation detail are relevant without bloat.

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?

Together with annotations and schema, the description covers what the tool computes, the string format, and the optional numerical evaluation. It does not specify key names in the returned dict or error/edge cases, but the output schema likely supplies that.

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?

Schema already covers f_str and point with 100% parameter coverage. The description adds an example string and the optional evaluation semantics, which is helpful but not a major semantic layer 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 states a specific operation ('computes the symbolic divergence of a vector field') with a clear subject, input domain, and an optional numeric-evaluation behavior. No ambiguity about what the tool does.

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

Usage Guidelines3/5

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

It clearly defines the computation but gives no guidance on when to choose it over closely related sibling tools like curl or gradient, nor conditions for using the optional point parameter. Context is implied by the operation itself, not by explicit selection 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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