symath

by lingeerr

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Latest release: v0.2.0
Disambiguation5/5
Each tool targets a distinct area of mathematics: basic arithmetic, expression evaluation, calculus, LaTeX conversion, number theory, and statistics. No overlapping purposes.
Naming Consistency4/5
Names are mostly single-word or snake_case nouns describing the domain. 'latex_to_expression' and 'number_theory' are descriptive and follow a consistent pattern, though mixing single-word and multi-word names is a minor inconsistency.
Tool Count5/5
Six tools is well-scoped for a symbolic math server, covering core mathematical operations without being overly numerous or sparse.
Completeness4/5
Covers arithmetic, expression evaluation, calculus, LaTeX conversion, integer theory, and statistics. Minor gaps like solving equations or linear algebra are absent but not critical for basic math support.
Average 3/5 across 6 of 6 tools scored.
See the Tool Scores section below for per-tool breakdowns.
- No community issues in the last 6 months
- 3 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 MIT License.
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 must disclose behavioral traits. It mentions 'high precision' but does not explain error handling, edge cases (e.g., division by zero), or whether operations are destructive. Significant gaps exist.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence, which is concise but overly sparse. It lacks structure and front-loads only a list of operations. While not verbose, it sacrifices informativeness for brevity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the lack of annotations, low schema coverage, and no output schema, the description is severely incomplete. A tool with 4 parameters and multiple operations requires details on return format, error handling, precision behavior, and operation-specific nuances. The description fails to cover these essential aspects.
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 only 25% (only 'values' has a description). The description adds minimal meaning beyond the schema: it lists operations but does not explain the 'format', 'precision', or 'operation' enum values. The agent would need to infer semantics from names alone.
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 lists specific arithmetic operations (add, subtract, etc.), making the purpose clear. However, it does not differentiate from sibling tools like 'calculate' or 'calculus', which may overlap. A more explicit distinction would improve clarity.
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 lacks context on prerequisites, suitability, or exclusions. The phrase 'with explicit operands' is too vague to guide tool selection.
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 full burden. It mentions Simpson's rule for integration but omits details on error handling, precision limitations, return format, or behavior for invalid inputs.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence, which is concise. However, it is too sparse; while it earns its place by stating the three operations, it lacks necessary detail for effective use.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness1/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (9 parameters, no output schema, no annotations), the description is inadequate. It does not explain return values, parameter usage, or constraints, leaving the AI agent underinformed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters1/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is low (33%), and the description adds no parameter information. It does not explain the required 'operation' and 'expression' parameters or optional ones like 'lower', 'upper', 'intervals', etc.
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 three specific calculus operations: symbolic differentiation, symbolic simplification, and numeric definite integration via Simpson's rule. This clearly identifies the tool's purpose and distinguishes it from sibling tools like arithmetic and calculate.
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 does not specify when to use this tool over alternatives such as calculate for numeric evaluation or latex_to_expression for conversion. No guidance is provided on prerequisites or when not to use the tool.
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 the description must disclose behavior. It mentions 'supported LaTeX' implying limitations but does not elaborate on error handling, supported subset, or side effects. A simple conversion tool likely has no destructive actions, but this is not stated.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single concise sentence, but it lacks additional structure or detail that would aid understanding. It is not front-loaded with critical information beyond the basic purpose.
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?
Given the tool's simplicity and lack of output schema, the description is too brief. It does not explain what 'supported LaTeX' means, the exact output format, error behavior, or provide an example, leaving gaps in understanding.
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 schema has 0% description coverage for the 'latex' parameter. The description only mirrors the parameter name without adding format, examples, or constraints beyond the schema's minLength and type.
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 action (convert) and the input/output (LaTeX math syntax to mathjs expression). It distinguishes from computational sibling tools like arithmetic or calculate, but could be more specific about the output format.
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?
No explicit guidance on when to use this tool versus alternatives. The purpose is implicit from the name, but the description does not provide context such as 'use when you need to parse a LaTeX string into an expression for evaluation'.
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 provided; description only mentions BigInt for precision, but lacks disclosure of performance, limits, side effects, or other behavioral traits.
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?
Extremely concise at 7 words, no wasted text, but could include more useful information without becoming verbose.
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?
Given no output schema, an enum of 7 operations, and no annotations, the description is too minimal to fully inform an agent about tool behavior and return values.
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 describes two parameters with 50% coverage (only 'values' has a note on string usage). Description adds no extra meaning to 'operation' or parameter details.
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?
Clearly states verb 'run' and resource 'exact integer operations using BigInt', distinguishing it from siblings like arithmetic or calculus which deal with floating-point or calculus.
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?
Implies use for exact integer math with BigInt, but provides no explicit guidance on when to use versus alternatives like arithmetic or calculate.
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 provided, the description carries the full burden of behavioral disclosure. It fails to mention that the tool is read-only (non-destructive), whether there are rate limits, or how inputs like string values are handled. The description only lists operations, lacking essential behavioral context.
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, efficient sentence listing all operations in a readable format. It front-loads the key information without extraneous words. However, it could be slightly restructured to separate operations from usage notes, but overall it is appropriately concise.
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?
Given the tool has 6 parameters (2 required) and no output schema, the description is incomplete. It omits critical details: parameter dependencies (percentile requires the 'percentile' param), output format, and error handling (e.g., empty array). The 33% schema coverage exacerbates the gaps, leaving the agent without sufficient context for correct invocation.
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 only 33% (only sample and percentile have descriptions). The tool description does not add meaning to other parameters (format, precision, values). For example, it doesn't explain that 'values' can include string numbers or that 'precision' controls significant digits. The low coverage and lack of explanation hinder correct invocation.
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 common statistical measures (count, sum, mean, etc.), which distinguishes it from sibling tools like arithmetic (basic operations) and calculus (differentiation/integration). The verb 'compute' and enumeration of specific resources make 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 Guidelines3/5
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description lists operations but provides no guidance on when to use this tool versus alternatives (e.g., arithmetic for simple sums). It does not specify prerequisites, typical use cases, or when to avoid using the tool. Usage is implied but not explicitly stated.
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 carries the full burden. It mentions configurable precision and expression format support, implying a read-only operation, but does not explicitly state lack of side effects, safety, or any other behavioral traits beyond what is implied by 'evaluate'.
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 conveys the core functionality without extraneous words. Every word serves a purpose.
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?
Despite no output schema, the description does not clarify return value format or behavior (e.g., whether it returns a number or string). With 4 parameters and sibling tools, additional context on usage distinctions would be beneficial.
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 coverage is 100% with each parameter described. The description adds general context about configurability and syntax support but does not enhance individual parameter semantics beyond the schema definitions. Baseline 3 is appropriate.
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 evaluates mathjs or LaTeX expressions with configurable high precision. It uses a specific verb 'Evaluate' and identifies the resource, making it distinct from sibling tools like arithmetic or latex_to_expression.
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 explicit guidance on when to use this tool versus alternatives. It does not mention prerequisites, exclusions, or specific scenarios where this tool is preferred over siblings like arithmetic or calculus.
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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