Symath-MCP

by 3aKHP

Overview Schema Related Servers Score Discussions

Python

Hybrid

Server Quality Checklist

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Latest release: v0.1.0
Disambiguation5/5
Each tool addresses a distinct area of mathematics (calculus, conversion, evaluation, manipulation, matrices, number theory, solving, statistics). There is no overlap in functionality; descriptions clearly differentiate them.
Naming Consistency5/5
All tool names follow the pattern 'math_<operation>' in snake_case, e.g., math_calculus, math_convert. This is consistent and predictable across all eight tools.
Tool Count5/5
8 tools cover a broad range of mathematical operations without being excessive. Each tool has a clear purpose, and the count feels appropriate for a comprehensive math server.
Completeness5/5
The server covers calculus, algebra, linear algebra, number theory, statistics, unit conversion, expression manipulation, and equation solving. This is a very comprehensive set for a math server, with no obvious gaps.
Average 3.9/5 across 8 of 8 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 is passing
This repository is licensed under MIT License.
This repository includes a README.md file.
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}
```
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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?
No annotations are provided, and the description does not disclose behavioral traits such as state mutation, authentication needs, or error handling. As a read-only calculus tool, it likely has no side effects, but this is not explicitly stated.
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 concise, with a one-line summary followed by a bulleted parameter list. Information is front-loaded. It could be more structured (e.g., separating operation list from parameter list) but remains efficient.
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 7 parameters, 1 required, and an output schema, the description covers parameter semantics but lacks explanation of the return value or examples of usage. It is adequate for a straightforward calculus tool but lacks completeness in guiding the agent on output interpretation.
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 description coverage is 0%, but the description adds meaningful explanations for each parameter with examples (e.g., 'x^2*sin(x)' for expression, 'integrate' for operation). It clarifies the role of each parameter beyond the schema's type constraints.
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?
Description clearly states the tool performs calculus operations (integration, differentiation, limits, series expansion, summation, product) with a specific verb and resource. It distinguishes from sibling tools like math_eval or math_solve which handle different mathematical tasks.
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?
Usage is implied through the listed operations, but there is no explicit guidance on when to use this tool versus alternatives (e.g., math_solve for equations, math_eval for expressions). No when-not scenarios or exceptions are mentioned.
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. It does not mention return value structure, error conditions (e.g., singular matrices for inverse, complex eigenvalues), performance implications, or any side effects. The agent lacks critical behavioral context beyond the list of operations.
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 efficiently structured: a brief purpose statement followed by a bulleted list of operations. It front-loads the core idea. However, the list is quite long (17 operations), which slightly reduces conciseness, but the structure remains clear.
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 complexity (many operations, no annotations, no parameter descriptions in schema), the description adequately covers parameters and operation purposes. However, it lacks details on output format, error handling, and specific behavioral nuances (e.g., matrix size limits). The presence of an output schema (unseen) slightly mitigates this gap, but the description alone is not fully complete.
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?
With 0% schema description coverage, the description compensates well: it explains the matrix input format with two examples, enumerates all operations with short descriptions, and clarifies the vector parameter's role for solve_linear. This adds significant value beyond the schema's raw properties.
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 '矩阵与线性代数运算' (matrix and linear algebra operations) and lists 17 specific operations, making the tool's purpose highly specific. It easily distinguishes from sibling tools like math_calculus or math_solve, which cover different domains.
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 lists operations and explains the 'vector' parameter's usage for solve_linear, providing some guidance. However, it does not explicitly state when to use this tool over alternatives or mention prerequisites (e.g., matrix invertibility for inverse). The implicit domain separation from siblings is clear, but no explicit exclusion or best-practice advice is given.
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 present, so the description should disclose behavioral traits. It only describes input formats and basic functionality, but lacks any mention of error handling, performance characteristics, or limitations. For a tool with many operations, more transparency is needed.
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 relatively long but well-structured: first a line summarizing purpose, then value format rules, then a clear bullet list of operations. It is front-loaded with the purpose. While it could be more concise, the density of information justifies its length.
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 complexity (20 operations, 2 parameters, output schema available), the description covers the input semantics comprehensively. It does not explain return values, but output schema exists. Minor gap: the default value of 'operation' (factor) is not mentioned. Overall, it is nearly complete.
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?
Schema coverage is 0%, so the description must compensate, which it does thoroughly. It explains the 'value' parameter format for each operation (e.g., '1234567890' for factor, '1234,5678' for GCD) and lists all operation options with brief descriptions. This adds essential meaning 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 it performs number theory operations ('数论运算') and lists 20 specific operations (factor, gcd, etc.). It distinguishes itself from sibling tools like math_calculus or math_eval by focusing exclusively on number theory calculations.
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 on when to use this tool versus siblings. There is no mention of alternatives or contexts where other math tools would be preferred. The description only lists operations without usage heuristics.
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?
The description adds behavioral details for some operations (e.g., collect uses variable parameter or auto-selects), but lacks comprehensive behavior disclosure such as error handling, restrictions, or side effects. Since no annotations are provided, the description partially compensates but is not fully transparent.
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 concise and well-structured: a clear statement of purpose followed by a bullet list of operations with short descriptions. No unnecessary text, and the most important information (purpose) is front-loaded.
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 complexity, parameter count, and presence of output schema, the description covers the main operations adequately. It does not explain return values or edge cases, but the output schema likely handles that. Some missing context like error behavior or expression format expectations.
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?
Input schema coverage is 0%, but the description clearly explains each parameter: expression is the math expression, operation lists all options with brief descriptions, and variable is for collect with auto-selection note. This adds significant meaning beyond the schema, though explanations could be more detailed.
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 '表达式变换与化简' (expression transformation and simplification), clearly indicating the tool's purpose. It lists many specific operations, making the scope well-defined. However, it does not explicitly distinguish from sibling tools like math_solve or math_eval, but the operations are distinct enough.
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 through the listed operations (e.g., simplify, expand, factor), but does not provide explicit guidance on when to use this tool versus alternatives like math_solve or math_calculus. No when-not-to-use or alternative tool mentions are given.
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 exist, so description must disclose behavior. It focuses on input formats but omits output behavior, limitations, or error handling—critical for an AI agent.
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?
Front-loaded purpose and well-structured with bullet points, but slightly verbose; could be more concise without losing clarity.
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?
Covers input comprehensively; output is handled by the existing output schema per rules. Lacks mention of constraints or edge cases.
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?
With 0% schema description coverage, the description fully compensates by explaining each parameter with examples and defaults, adding significant meaning.
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 it solves equations and systems, with a specific verb 'solve' and resource. Sibling tools like math_calculus and math_eval are distinct, so purpose is well-defined.
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?
Provides examples of different equation types and how to set parameters, but no explicit comparison to siblings or when-not-to-use.
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, the description bears the full burden of transparency. It describes operations and distribution queries but does not mention potential errors, side effects, or statelessness. For a computation tool, the coverage is adequate but not exhaustive.
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 moderately lengthy but well-structured with bullet-like formatting for operations and distributions. It front-loads the purpose and efficiently conveys necessary details without redundancy.
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 complexity (multiple operations, distribution queries), the description is comprehensive. It covers data formats, operation types, and distribution parameters. The presence of an output schema reduces the need to document return values, but missing error or constraint information slightly lowers 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 fully compensates by explaining the 'data' format (including examples for both single and paired data) and the 'operation' parameter with all available options and default. This adds substantial meaning 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 '统计与概率计算' (statistics and probability calculation), distinguishing it from sibling tools like math_calculus and math_eval. It lists operations and distributions, making the tool's scope explicit.
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 explains data formats and operation options but does not provide explicit guidance on when to use this tool versus alternatives. There are no when-to-use or when-not-to-use statements, though the detail implies usage for statistical and probability tasks.
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?
No annotations are provided, so the description must carry the full burden. It discloses the core behavior (conversion and constant lookup) and lists supported unit categories, but does not discuss error handling, validation, or edge cases (e.g., invalid units).
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 well-structured: it starts with the purpose, then lists parameters, provides examples, and ends with supported categories. It is slightly verbose but clear and efficient.
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?
Given the tool's moderate complexity with 4 optional parameters and an output schema, the description adequately covers all aspects: purpose, parameter semantics, examples, and supported unit categories. No critical information is missing.
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 fully compensates by explaining each parameter (value, unit_from, unit_to, constant) with examples. It clarifies that value is a numeric string and that constant is for querying constants.
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 performs unit conversion and physical constant queries. Examples and supported categories further clarify the purpose, and it is distinct from sibling tools like math_calculus or math_solve.
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 provides examples showing typical use cases but does not explicitly state when to avoid this tool or compare it to siblings. However, the sibling tools are in different domains (calculus, algebra, etc.), so the context is sufficient.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations present, so description carries full burden. It outlines supported features (precision, complex numbers, symbolic computation) and gives examples, but does not mention error handling, rate limits, or edge cases. Overall good transparency for a computation tool.
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?
Description is front-loaded with purpose, but includes a block of examples that could be shortened. Still, each example adds value. Minor redundancy in listing capabilities both in prose and examples.
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?
Given complexity (supports arbitrary precision, complex numbers, symbolic ops, many functions) and no annotations, description covers features, parameter details, and usage examples fully. Output schema exists but not needed for 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?
Schema has 0% description coverage, but description explains each parameter: expression format with examples, precision default of 50, substitutions format as 'x=5,y=10'. Adds significant meaning 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?
Description clearly states it evaluates mathematical expressions with specific capabilities (arbitrary precision, complex numbers, symbolic operations). It distinguishes from sibling tools like math_calculus, math_solve, etc., by focusing on direct evaluation.
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?
Description implies use for computing mathematical expressions, but does not explicitly state when to use over alternatives like math_calculus or math_solve. No exclusions or when-not guidance provided.
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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