SciMath MCP

by matheusbgodoi

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Latest release: v0.1.1
Disambiguation5/5
Each tool has a clear, non-overlapping purpose: calculate evaluates expressions, solve handles equations, calculus does symbolic differentiation/integration, linear_algebra handles matrix operations, etc. Even superficially similar tools like calculate and calculus are distinct in scope.
Naming Consistency4/5
All names use lowercase with underscores for multi-word tools, but the pattern is mixed: some are verbs (calculate, solve), some are noun phrases (linear_algebra, physical_constant). This is mostly consistent but deviates from a uniform verb_noun style.
Tool Count5/5
With 8 tools, the set is well-scoped for scientific mathematical computation. Each tool covers a major area (arithmetic, units, equations, calculus, linear algebra, statistics, uncertainty, constants) without redundancy or bloat.
Completeness4/5
The tool surface covers the core scientific computing workflow: expression evaluation, unit conversion, equation solving, symbolic calculus, matrix operations, statistical analysis, uncertainty propagation, and constants lookup. Minor gaps like numeric root-finding or optimization exist, but the set is comprehensive for typical math/science use.
Average 4/5 across 8 of 8 tools scored. Lowest: 3.4/5.
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
- Last stable release on August 11, 2026
- 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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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

Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
The annotations already declare the tool read-only, idempotent, and non-destructive. The description adds the behavioral assumption of independent uncertainties and the note that output_unit is needed for dimensionful results. It does not contradict any annotations, but it also doesn't disclose potential limitations or edge cases.
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 two sentences and front-loads the core function. It avoids redundancy and every clause contributes to understanding.
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 the presence of an output schema, the description is not fully complete. It lacks details on how to structure the expression, how measurements map to variable names, and the role of coverage_factor and precision. These are essential for an agent to invoke the tool correctly.
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?
With 0% schema description coverage, the description must compensate. It explains that each measurement consists of value, uncertainty, and optional unit, and it gives guidance on output_unit. However, it leaves parameters like expression, precision, angle_unit, and coverage_factor without semantic explanation.
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's function: propagating independent standard uncertainties through an expression. It specifies the key resource (uncertainty propagation) and distinguishes it from sibling tools like calculate or statistics.
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 provide any guidance on when to use this tool versus alternatives. It neither names sibling tools nor explains the circumstances that call for uncertainty propagation over other calculations. The only instruction ('use output_unit when the result is dimensionful') is parameter-specific, not about tool selection.
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?
Annotations already declare readOnlyHint=true, destructiveHint=false, and idempotentHint=true, so the safety profile is covered. The description adds a note about data_y behavior, but does not disclose side effects, edge cases, or other operational details. It does not contradict annotations, and with annotations present, a 3 is appropriate.
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 two sentences, front-loaded with the main purpose, and every word contributes. It lists operations in a compact list and adds a single actionable note about data_y, with no fluff or repetition.
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 that an output schema exists and annotations cover safety, the description provides sufficient context for the core operations and the key data_y nuance. It is slightly thin on optional parameters (precision, confidence), but their defaults in the schema mitigate the gap, making it generally complete for a read-only statistical tool.
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 description must compensate. It clarifies that data_y is used for paired correlation/regression or the second t-test sample, adding meaning beyond the bare schema. However, it does not explain precision or confidence parameters, which remain undocumented in both schema and description, so compensation is incomplete.
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 explicitly lists the specific statistical operations (descriptive statistics, Pearson correlation, linear regression, confidence interval, Welch t-test) with a clear verb 'Compute'. It distinguishes itself from sibling tools by naming statistical tests, but does not explicitly contrast with non-statistical tools like calculate or linear_algebra, so it lacks full sibling differentiation.
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 second sentence provides concrete guidance on when to supply data_y ('for paired correlation/regression or the second t-test sample'), which helps usage. It implies the tool is for statistics but does not explicitly state when not to use it or name alternatives, but the context is clear enough for a 4.
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?
Annotations already declare readOnly, idempotent, non-destructive, and closed-world behavior. The description adds useful behavioral context beyond annotations: it returns value, unit, standard uncertainty, source metadata, and optional unit conversion. It also notes alias support and gives examples. This enriches the agent's understanding without contradiction.
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 two sentences, front-loaded with the core purpose, and includes concrete examples. Every sentence contributes value, with no redundant or vague filler.
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?
Since an output schema exists, the return values are structurally documented. The description covers the tool's domain, source, alias behavior, and optional unit conversion, which is adequate for a simple lookup. However, the omission of precision semantics is a minor gap given the three-parameter schema.
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. It only hints at 'optional compatible unit conversion' (mapping to output_unit) and implicitly covers 'query' via the lookup phrase. The 'precision' parameter is entirely undocumented, and no parameter names or formats are given. This leaves the agent with gaps for two of three parameters.
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 a specific verb ('Look up') and resource ('SciPy's bundled CODATA table') with a scope ('by common alias or name'). It distinguishes itself from siblings like calculate and convert_units by focusing on physical constant retrieval, and the examples (c, G, hbar) reinforce its domain.
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 the primary use case (looking up physical constants) but does not explicitly contrast with sibling tools like convert_units or calculate. It doesn't state when to prefer this over alternatives or mention any exclusions (e.g., 'not for general unit conversion'). The context is clear but lacks explicit guidance.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior5/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Beyond the readOnly/idempotent/non-destructive annotations, the description adds rich behavioral context: exact arithmetic, the 25x25 matrix size limit, preservation of exact fractional string entries, and numerical-stability warnings for condition numbers. No contradiction with annotations.
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?
Four short, information-dense sentences, front-loaded with the core purpose and followed by practical details. Every sentence earns its place and there is no filler or tautology.
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?
The description covers key constraints and behavioral caveats for a complex matrix tool, while the output schema handles return details. It omits precision semantics and explicit alternative-tool guidance, but the operation enum and annotations fill many gaps.
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?
The description clarifies matrix (size limit, exact string entries) and other_matrix (multiplication or solve RHS), but the precision parameter is not explained. Since schema description coverage is 0%, the description only partially compensates for the lack of parameter documentation.
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 performs exact matrix/linear-algebra operations on matrices up to 25x25, and mentions matrix inputs, other_matrix, and condition-number warnings. It does not explicitly contrast with sibling tools like solve or calculate, so it misses the full sibling-differentiation criterion.
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 context is implied: the tool is for exact matrix operations. It gives parameter-level guidance (other_matrix for multiplication or solve RHS, string entries preserve exact values), but it does not state when to choose this tool over alternatives or mention exclusions.
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?
Annotations already declare read-only, idempotent, and non-destructive behavior, lowering the bar. The description adds useful context about return forms (exact/high-precision when unitless) and cautions about conversion factors, which goes beyond the annotations. No contradictions found.
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 three concise sentences, front-loaded with the core purpose. Every sentence adds value—purpose, dimensional guidance, and return behavior—with no wasted words.
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 output schema and annotations, the description covers the key behavioral aspects: evaluation, dimensional handling, and return forms. It misses details on precision and angle_unit, but those are secondary and reasonably inferable from schema defaults. Overall, it provides enough context for correct invocation in most scenarios.
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 description must compensate. It adds meaning for expression (explicit *), variables (unit-bearing strings), and output_unit (always set). However, it omits semantics for precision and angle_unit, leaving those to schema defaults and names, which is only partial compensation.
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 one arithmetic/scientific expression safely, which distinguishes it from sibling tools like solve (equations) and convert_units (unit conversion). The focus on expression evaluation is specific and 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 provides clear context for dimensional work, instructing to pass unit-bearing variables, set output_unit, and avoid manual conversion factors. However, it does not explicitly name alternatives or explain when not to use this tool, so it falls short of a full 5.
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?
Annotations already declare read-only, idempotent, and non-destructive behavior. The description adds valuable behavioral context beyond annotations by specifying that dimensional mismatches are errors rather than guessed conversions, which clarifies failure semantics.
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-structured sentence that is front-loaded with the primary action and supported by relevant examples. Every part adds value, with no redundant or filler content.
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, an output schema, and strong annotations, the description covers the essential operation and error behavior. It does not discuss the precision parameter's effect, but this is a minor omission given the compactness and clarity of the overall description.
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 description must compensate. It clarifies 'value' with examples like '32 degF' and implies 'to_unit' is the target unit, but it does not explicitly describe the 'precision' parameter. The examples help map 'value' and 'to_unit', but precision remains undocumented.
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 uses a specific verb ('Convert') and identifies the resource ('a dimensionful value') with concrete examples. It clearly distinguishes itself from sibling tools like calculate or physical_constant by focusing on unit conversion and explicitly stating that dimensional mismatches are errors.
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 clearly establishes when to use this tool: when converting a value from one unit to a compatible target unit. It does not name alternative tools explicitly but provides unambiguous usage context through examples and the error condition.
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?
Annotations already indicate the tool is read-only, idempotent, and non-destructive. The description adds the crucial behavioral detail that all operations are symbolic, which affects user expectations about output type and computational nature. It also clarifies operation-specific parameter requirements, going beyond the annotations.
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, consisting of two sentences that front-load the core functionality. Every sentence adds value, and the parameter guidance is embedded naturally without waste. It achieves high information density without becoming bulky.
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 (9 parameters, 4 operations) and the presence of an output schema, the description covers the most critical usage aspects: which parameters are needed for each operation and what `order` means. It does not mention `direction` or `precision`, but those are less critical and have schema defaults/enums. Overall, it is sufficient for an agent to invoke the tool correctly for typical calculus tasks.
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%, so the description must compensate. It explains `order` (derivative order vs series terms), and implicitly clarifies `lower_bound`/`upper_bound` for definite integrals and `point` for limits/series. It does not explain `direction` (for one-sided limits) or `precision`, but the main non-obvious parameters are handled well given the tool's complexity.
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's purpose: it performs symbolic differentiation, integration, limits, and series expansion. The verb 'Differentiate, integrate, take a limit, or expand a series' is specific and distinguishes it from sibling tools like calculate or solve. The scope is precisely defined and not a tautology.
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 concrete usage instructions: for definite integrals provide bounds, for limits/series provide a point, and `order` has operation-specific meaning. This helps the agent invoke it correctly. It does not explicitly exclude alternatives (e.g., numeric vs symbolic) but the context is clear enough for a specialized calculus tool.
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?
Beyond the annotations (readOnly, idempotent, non-destructive), the description adds valuable behavioral details: the exact/numerical output format, the ability to choose real or complex domain, the equation format ('left = right' or zero-valued), and the capacity limit of eight equations. This contextualizes the tool's behavior without contradicting the annotations.
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 two sentences, front-loaded with the primary purpose, and every phrase adds value. It avoids redundancy and is appropriately concise.
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 (algebraic solving) and the presence of an output schema, the description covers key aspects: input format, output form, domain selection, and capacity. It does not explicitly mention edge cases like no solutions or infinite solutions, but the output schema may handle these, making the description reasonably 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 by explaining the 'equations' format, 'variables' as explicitly named, and 'domain' with real/complex choice. It also implies precision via 'numerical form,' but does not explicitly explain the 'precision' integer parameter, which is a minor gap.
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 'solve[s] up to eight algebraic equations for explicitly named variables,' which is a specific verb+resource action. It also distinguishes from sibling tools like calculate and calculus by focusing on equation solving rather than arithmetic or calculus operations.
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 clear context for when to use the tool: when solving algebraic equations for named variables, with domain selection as required. However, it does not explicitly mention exclusions or alternative tools, so there is no direct when-not-to-use 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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