Desmos MCP Server

by TheGrSun

Overview Schema Related Servers Score Discussions

Python

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Server Quality Checklist

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Latest release: v1.0.0
Disambiguation4/5
Most tools have distinct purposes: analyze_formula, plot_math_function, plot_multiple_functions, and validate_formula each target different mathematical tasks. However, analyze_formula and validate_formula could be slightly confused as both involve formula inspection, but their descriptions clarify analysis vs. syntax validation. The hello tool is clearly distinct but trivial.
Naming Consistency4/5
Tools follow a consistent verb_noun pattern (e.g., analyze_formula, plot_math_function) with clear, descriptive names. The only minor deviation is hello, which is a simple noun without a verb, but this does not significantly disrupt the overall consistency.
Tool Count4/5
With 5 tools, the count is reasonable for a mathematical plotting and analysis server. It covers core functionalities like plotting and formula handling without being overwhelming. However, it feels slightly thin for a full mathematical toolkit, as it lacks tools for operations like solving equations or data manipulation.
Completeness3/5
The server covers basic plotting and formula analysis well, but there are notable gaps. For a Desmos-like domain, missing operations include solving equations, manipulating graphs (e.g., zoom, pan), exporting plots, or handling parametric functions. The hello tool adds no functional value, and the set feels incomplete for advanced mathematical workflows.
Average 3.1/5 across 5 of 5 tools scored.
See the Tool Scores section below for per-tool breakdowns.
- No community issues in the last 6 months
- 0 commits in the last 12 weeks
- No stable releases found
- No critical vulnerability alerts
- No high-severity vulnerability alerts
- No code scanning findings
- CI status not available
This repository is licensed under Apache 2.0.
This repository includes a README.md file.
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How is the quality score calculated?

The overall quality score combines two components: Tool Definition Quality (70%) and Server Coherence (30%).

Tool Definition Quality measures how well each tool describes itself to AI agents. Every tool is scored 1–5 across six dimensions: Purpose Clarity (25%), Usage Guidelines (20%), Behavioral Transparency (20%), Parameter Semantics (15%), Conciseness & Structure (10%), and Contextual Completeness (10%). The server-level definition quality score is calculated as 60% mean TDQS + 40% minimum TDQS, so a single poorly described tool pulls the score down.

Server Coherence evaluates how well the tools work together as a set, scoring four dimensions equally: Disambiguation (can agents tell tools apart?), Naming Consistency, Tool Count Appropriateness, and Completeness (are there gaps in the tool surface?).

Tiers are derived from the overall score: A (≥3.5), B (≥3.0), C (≥2.0), D (≥1.0), F (<1.0). B and above is considered passing.

Tool Scores

Behavior2/5
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 but only states the basic action without details on output format, error handling, or performance traits. It doesn't mention whether the plot is interactive, saved, or displayed, nor does it cover rate limits or authentication needs, which are critical for a plotting tool.
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 extremely concise with a single sentence that directly states the tool's function without any fluff or redundancy. It is front-loaded and wastes no words, making it efficient for quick comprehension, though this brevity contributes to gaps in other dimensions.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (3 parameters, no annotations, but with an output schema), the description is incomplete. It lacks details on parameter usage, behavioral traits, and differentiation from siblings, though the presence of an output schema mitigates the need to explain return values. This results in a minimally adequate but insufficiently informative description.
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?
The input schema has 0% description coverage, so the description must compensate but adds no parameter semantics beyond implying 'formulas' are plotted. It doesn't explain what 'formulas' entail (e.g., mathematical expressions), the format of 'x_range' and 'y_range' (e.g., arrays of two numbers), or default behaviors, leaving significant gaps in understanding.
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 clearly states the tool's purpose with a specific verb ('plots') and resource ('multiple functions on the same graph'), making it immediately understandable. However, it doesn't explicitly distinguish itself from sibling tools like 'plot_math_function', which might handle single functions, leaving some ambiguity about when to choose one over the other.
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?
The description provides no guidance on when to use this tool versus alternatives, such as 'plot_math_function' for single functions or 'analyze_formula' for non-graphical analysis. It lacks explicit instructions on prerequisites, context, or exclusions, leaving the agent to infer usage based on the tool name alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden of behavioral disclosure. It states what the tool does but doesn't describe how it behaves: no information on computational complexity, error handling for invalid formulas, output format details (though an output schema exists), or whether this is a read-only operation. For a tool with no annotations, this leaves significant behavioral gaps.
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 single, efficient sentence that front-loads the core purpose. Every word earns its place: 'analyzes' (verb), 'mathematical properties' (scope), 'formula' (resource), and specific examples in parentheses. There's zero waste or redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's moderate complexity (2 parameters, one with enum), no annotations, and the presence of an output schema, the description is minimally adequate. The output schema reduces the need to explain return values, but the description lacks details on behavioral traits and parameter usage. It's complete enough for basic understanding but has clear gaps in guidance and transparency.
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 description coverage is 0%, so the schema provides no parameter descriptions. The description mentions 'analysis_type' implicitly through the examples (domain, range, critical points), which correspond to the enum values, but doesn't explain the 'formula' parameter's format or constraints. It adds some meaning beyond the bare schema but doesn't fully compensate for the coverage gap, especially for the required 'formula' parameter.
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 clearly states the verb 'analyzes' and the resource 'mathematical properties of a formula', with specific examples (domain, range, critical points). It distinguishes from siblings like 'plot_math_function' or 'validate_formula' by focusing on analysis rather than visualization or validation. However, it doesn't explicitly differentiate from all siblings (e.g., 'hello' is unrelated).
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?
The description provides no guidance on when to use this tool versus alternatives. It doesn't mention when to choose 'analyze_formula' over 'validate_formula' for formula checking, or when analysis is preferred over plotting with 'plot_math_function'. There are no explicit when/when-not statements or named alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries the full burden. It states the tool returns a greeting but doesn't disclose any behavioral traits like whether it's idempotent, has side effects, or what the output format is. The description is minimal and lacks context beyond the basic action.
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 single, efficient sentence with no wasted words. It's appropriately sized for such a simple tool and front-loads the core purpose clearly.
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 low complexity (1 optional parameter) and the presence of an output schema, the description is complete enough for basic understanding. However, it could benefit from slightly more context about the greeting format or usage scenarios to be fully comprehensive.
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?
The input schema has 1 parameter with 0% description coverage, but the description doesn't mention parameters at all. Since there's only one parameter and the tool is very simple, the baseline is high. However, the description doesn't add meaning beyond the schema, so it doesn't fully compensate for the lack of schema descriptions.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose3/5
Does the description clearly state what the tool does and how it differs from similar tools?
The description states the tool 'returns a greeting', which is a clear purpose but vague about what kind of greeting or how it's generated. It doesn't differentiate from sibling tools (like analyze_formula or plot_math_function), but the purpose is understandable albeit basic.
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?
No guidance is provided on when to use this tool versus alternatives. The description doesn't mention any context, prerequisites, or exclusions, leaving the agent to infer usage based on the simple purpose alone.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden. It discloses the fallback behavior between Desmos API and local rendering, which is useful context. However, it doesn't mention other behavioral traits like performance implications, error handling, authentication needs, rate limits, or output format details, leaving gaps for a tool with 4 parameters.
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 highly concise with two sentences that efficiently convey the core functionality and fallback mechanism. It's front-loaded with the main purpose and wastes no words, making it easy to parse.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given 4 parameters with 0% schema coverage and no annotations, the description is incomplete as it lacks parameter explanations and behavioral details. However, the presence of an output schema reduces the need to describe return values, and the purpose is clear, making it minimally adequate but with significant gaps.
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%, so the description must compensate, but it adds no information about parameters beyond the general context of plotting. It doesn't explain what 'formula', 'x_range', 'y_range', or 'use_api' mean or how they affect the plot, leaving all 4 parameters semantically unclear.
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 clearly states the tool's purpose: 'Generates a 2D plot' with a specific mathematical context. It distinguishes from siblings like 'analyze_formula' and 'validate_formula' by focusing on visualization rather than analysis or validation, though it doesn't explicitly contrast with 'plot_multiple_functions'.
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?
The description implies usage for plotting mathematical functions, with a fallback mechanism mentioned ('Tries Desmos API if available, otherwise falls back to local rendering'). However, it lacks explicit guidance on when to use this tool versus alternatives like 'plot_multiple_functions' or other siblings, and doesn't specify prerequisites or exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries the full burden. It discloses that the tool validates syntax and provides 'intelligent help on failure', which adds behavioral context about error responses. However, it doesn't mention other traits like performance characteristics, rate limits, or authentication needs. The description adds some value but leaves gaps for a tool with mutation-like validation behavior.
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 single, well-constructed sentence that efficiently communicates the core functionality and error-handling behavior. Every word earns its place, with no redundancy or unnecessary elaboration. It's appropriately sized for a simple validation tool.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has an output schema (which should document return values), the description doesn't need to explain outputs. However, with no annotations and incomplete parameter documentation, the description provides adequate but minimal context for a validation tool. It covers the 'what' and error behavior but lacks details on formula requirements or validation rules.
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?
The input schema has 0% description coverage, with only one parameter 'formula' of type string. The description doesn't add any parameter-specific semantics beyond the tool's overall purpose. It doesn't explain what constitutes a valid formula, expected format, or examples. With low schema coverage, the description fails to compensate adequately.
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 clearly states the tool's purpose: 'Validates the syntax of a mathematical formula' with the specific verb 'validates' and resource 'mathematical formula'. It distinguishes from siblings like 'analyze_formula' (which might check semantics) and 'plot_math_function' (which visualizes), but doesn't explicitly name these alternatives. The addition of 'offering intelligent help on failure' adds useful context about error handling.
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?
The description implies usage context through 'validates the syntax' and 'on failure', suggesting it should be used to check formula correctness before further processing. However, it doesn't explicitly state when to use this vs. alternatives like 'analyze_formula' or provide clear exclusions. The guidance is present but not comprehensive.
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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