Xby Math

一个高性能的数学计算协议服务器，提供从基础算术到高级微积分和线性代数的全面数学计算功能。

数学计算协议服务

一个高性能的数学计算协议服务器，提供从基础算术到高级微积分和线性代数的全面数学计算功能。

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⚠️ 强制要求：API 密钥

此 Skill 必须配置 API 密钥才能使用。

• 首次使用时，如果 .env 中没有 XBY_APIKEY，必须使用 AskUserQuestion 工具向用户询问 API 密钥
• 拿到用户提供的密钥后，调用 scripts.config.set_api_key(api_key) 保存，然后继续处理
• 获取 API 密钥：https://xiaobenyang.com
• 禁止在缺少 API 密钥时自行搜索或编造数据

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工作流程（必须遵守）

你（大模型）是路由层，负责理解用户意图、选择工具、提取参数。代码只负责调用API。

用户输入 → 你选择工具 → 提取该工具需要的参数 → 调用 scripts.tools 中的函数 → 返回结果给用户

步骤

1. 检查 API 密钥：如果 scripts.config.settings.api_key 为空，使用 AskUserQuestion 询问用户，拿到后调用 scripts.config.set_api_key(key) 保存
2. 选择工具：根据用户意图从下方工具列表中选择对应的工具函数
3. 提取参数：根据选中的工具，提取该工具需要的参数
4. 调用工具：使用关键字参数调用 scripts.tools 中的函数，例如 scripts.tools.search_schools(score='520', province='北京', category='综合')
5. 返回结果：将工具返回的 raw 数据整理后展示给用户

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工具选择规则

根据用户意图选择对应的工具函数：

用户意图	工具函数
Evaluate mathematical expressions using SymPy.

Supports: - Arithmetic: +, -, *, /, ^ - Trigonometry: sin, cos, tan, asin, acos, atan - Logarithms: log, ln, exp - Constants: pi, e - Functions: sqrt, abs

Examples:

SIMPLE ARITHMETIC: expression="2 + 2" Result: 4

TRIGONOMETRY: expression="sin(pi/2)" Result: 1.0

WITH VARIABLES: expression="x^2 + 2*x + 1", variables={"x": 3} Result: 16

MULTIPLE VARIABLES: expression="x^2 + y^2", variables={"x": 3, "y": 4} Result: 25 | scripts.tools.calculate | | Perform percentage calculations: of, increase, decrease, or change.

Examples:

PERCENTAGE OF: 15% of 200 operation="of", value=200, percentage=15 Result: 30

INCREASE: 100 increased by 20% operation="increase", value=100, percentage=20 Result: 120

DECREASE: 100 decreased by 20% operation="decrease", value=100, percentage=20 Result: 80

PERCENTAGE CHANGE: from 80 to 100 operation="change", value=80, percentage=100 Result: 25 (25% increase) | scripts.tools.percentage | | Advanced rounding operations with multiple methods.

Methods: - round: Round to nearest (3.145 → 3.15 at 2dp) - floor: Always round down (3.149 → 3.14) - ceil: Always round up (3.141 → 3.15) - trunc: Truncate towards zero (-3.7 → -3, 3.7 → 3)

Examples:

ROUND TO NEAREST: values=3.14159, method="round", decimals=2 Result: 3.14

FLOOR (DOWN): values=3.14159, method="floor", decimals=2 Result: 3.14

CEIL (UP): values=3.14159, method="ceil", decimals=2 Result: 3.15

MULTIPLE VALUES: values=[3.14159, 2.71828], method="round", decimals=2 Result: [3.14, 2.72] | scripts.tools.round | | Convert between angle units: degrees ↔ radians.

Examples:

DEGREES TO RADIANS: value=180, from_unit="degrees", to_unit="radians" Result: 3.14159... (π)

RADIANS TO DEGREES: value=3.14159, from_unit="radians", to_unit="degrees" Result: 180

RIGHT ANGLE: value=90, from_unit="degrees", to_unit="radians" Result: 1.5708... (π/2) | scripts.tools.convert_units | | Perform element-wise operations on arrays using Polars.

Supports array-array and array-scalar operations.

Examples:

SCALAR MULTIPLICATION: operation="multiply", array1=[[1,2],[3,4]], array2=2 Result: [[2,4],[6,8]]

ARRAY ADDITION: operation="add", array1=[[1,2]], array2=[[3,4]] Result: [[4,6]]

POWER OPERATION: operation="power", array1=[[2,3]], array2=2 Result: [[4,9]]

ARRAY DIVISION: operation="divide", array1=[[10,20],[30,40]], array2=[[2,4],[5,8]] Result: [[5,5],[6,5]] | scripts.tools.array_operations | | Calculate statistical measures on arrays using Polars.

Supports computation across entire array, rows, or columns.

Examples:

COLUMN-WISE MEANS: data=[[1,2,3],[4,5,6]], operations=["mean"], axis=0 Result: [2.5, 3.5, 4.5] (average of each column)

ROW-WISE MEANS: data=[[1,2,3],[4,5,6]], operations=["mean"], axis=1 Result: [2.0, 5.0] (average of each row)

OVERALL STATISTICS: data=[[1,2,3],[4,5,6]], operations=["mean","std"], axis=None Result: {mean: 3.5, std: 1.71}

MULTIPLE STATISTICS: data=[[1,2,3],[4,5,6]], operations=["min","max","mean"], axis=0 Result: {min: [1,2,3], max: [4,5,6], mean: [2.5,3.5,4.5]} | scripts.tools.array_statistics | | Perform aggregation operations on 1D arrays.

Examples:

SUMPRODUCT: operation="sumproduct", array1=[1,2,3], array2=[4,5,6] Result: 32 (1×4 + 2×5 + 3×6)

WEIGHTED AVERAGE: operation="weighted_average", array1=[10,20,30], weights=[1,2,3] Result: 23.33... ((10×1 + 20×2 + 30×3) / (1+2+3))

DOT PRODUCT: operation="dot_product", array1=[1,2], array2=[3,4] Result: 11 (1×3 + 2×4)

GRADE CALCULATION: operation="weighted_average", array1=[85,92,78], weights=[0.3,0.5,0.2] Result: 86.5 | scripts.tools.array_aggregate | | Transform arrays for ML preprocessing and data normalization.

Transformations: - normalize: L2 normalization (unit vector) - standardize: Z-score (mean=0, std=1) - minmax_scale: Scale to [0,1] range - log_transform: Natural log transform

Examples:

L2 NORMALIZATION: data=[[3,4]], transform="normalize" Result: [[0.6,0.8]] (3²+4²=25, √25=5, 3/5=0.6, 4/5=0.8)

STANDARDIZATION (Z-SCORE): data=[[1,2],[3,4]], transform="standardize" Result: Values with mean=0, std=1

MIN-MAX SCALING: data=[[1,2],[3,4]], transform="minmax_scale" Result: [[0,0.33],[0.67,1]] (scaled to [0,1])

LOG TRANSFORM: data=[[1,10,100]], transform="log_transform" Result: [[0,2.3,4.6]] (natural log) | scripts.tools.array_transform | | Comprehensive statistical analysis using Polars.

Analysis types: - describe: Count, mean, std, min, max, median - quartiles: Q1, Q2, Q3, IQR - outliers: IQR-based detection (values beyond Q1-1.5×IQR or Q3+1.5×IQR)

Examples:

DESCRIPTIVE STATISTICS: data=[1,2,3,4,5,100], analyses=["describe"] Result: {count:6, mean:19.17, std:39.25, min:1, max:100, median:3.5}

QUARTILES: data=[1,2,3,4,5], analyses=["quartiles"] Result: {Q1:2, Q2:3, Q3:4, IQR:2}

OUTLIER DETECTION: data=[1,2,3,4,5,100], analyses=["outliers"] Result: {outlier_values:[100], outlier_count:1, lower_bound:-1, upper_bound:8.5}

FULL ANALYSIS: data=[1,2,3,4,5,100], analyses=["describe","quartiles","outliers"] Result: All three analyses combined | scripts.tools.statistics | | Create pivot tables from tabular data using Polars.

Like Excel pivot tables: reshape data with row/column dimensions and aggregated values.

Example:

SALES BY REGION AND PRODUCT: data=[ {"region":"North","product":"A","sales":100}, {"region":"North","product":"B","sales":150}, {"region":"South","product":"A","sales":80}, {"region":"South","product":"B","sales":120} ], index="region", columns="product", values="sales", aggfunc="sum" Result: product | A | B --------|------|------ North | 100 | 150 South | 80 | 120

COUNT AGGREGATION: Same data with aggfunc="count" Result: Count of entries per region-product combination

AVERAGE SCORES: data=[{"dept":"Sales","role":"Manager","score":85}, ...] index="dept", columns="role", values="score", aggfunc="mean" Result: Average scores by department and role | scripts.tools.pivot_table | | Calculate correlation matrices between multiple variables using Polars.

Methods: - pearson: Linear correlation (-1 to +1, 0 = no linear relationship) - spearman: Rank-based correlation (monotonic, robust to outliers)

Examples:

PEARSON CORRELATION: data={"x":[1,2,3], "y":[2,4,6], "z":[1,1,1]}, method="pearson", output_format="matrix" Result: { "x": {"x":1.0, "y":1.0, "z":NaN}, "y": {"x":1.0, "y":1.0, "z":NaN}, "z": {"x":NaN, "y":NaN, "z":NaN} }

PAIRWISE FORMAT: data={"height":[170,175,168], "weight":[65,78,62]}, method="pearson", output_format="pairs" Result: [{"var1":"height", "var2":"weight", "correlation":0.89}]

SPEARMAN (RANK): data={"x":[1,2,100], "y":[2,4,200]}, method="spearman" Result: Perfect correlation (1.0) despite non-linear relationship | scripts.tools.correlation | | Time Value of Money (TVM) calculations: solve for PV, FV, PMT, rate, IRR, or NPV.

The TVM equation has 5 variables - know 4, solve for the 5th: PV = Present Value (lump sum now) FV = Future Value (lump sum at maturity) PMT = Payment (regular periodic cash flow) N = Number of periods I/Y = Interest rate per period

Sign convention: negative = cash out (you pay), positive = cash in (you receive)

Examples:

ZERO-COUPON BOND: PV of £1000 in 10 years at 5% calculation="pv", rate=0.05, periods=10, future_value=1000 Result: £613.91

COUPON BOND: PV of £30 annual coupons + £1000 face value at 5% yield calculation="pv", rate=0.05, periods=10, payment=30, future_value=1000 Result: £845.57

RETIREMENT SAVINGS: FV with £500/month for 30 years at 7% calculation="fv", rate=0.07/12, periods=360, payment=-500, present_value=0 Result: £566,764

MORTGAGE PAYMENT: Monthly payment on £200k loan, 30 years, 4% APR calculation="pmt", rate=0.04/12, periods=360, present_value=-200000, future_value=0 Result: £954.83

INTEREST RATE: What rate grows £613.81 to £1000 in 10 years? calculation="rate", periods=10, present_value=-613.81, future_value=1000 Result: 0.05 (5%)

GROWING ANNUITY: Salary stream with 3.5% raises, discounted at 12% calculation="pv", rate=0.12, periods=25, payment=-45000, growth_rate=0.035 Result: £402,586 | scripts.tools.financial_calcs | | Calculate compound interest with various compounding frequencies.

Formulas: Discrete: A = P(1 + r/n)^(nt) Continuous: A = Pe^(rt)

Examples:

ANNUAL COMPOUNDING: £1000 at 5% for 10 years principal=1000, rate=0.05, time=10, frequency="annual" Result: £1628.89

MONTHLY COMPOUNDING: £1000 at 5% for 10 years principal=1000, rate=0.05, time=10, frequency="monthly" Result: £1647.01

CONTINUOUS COMPOUNDING: £1000 at 5% for 10 years principal=1000, rate=0.05, time=10, frequency="continuous" Result: £1648.72 | scripts.tools.compound_interest | | Calculate present value of a perpetuity (infinite series of payments).

A perpetuity is an annuity that continues forever. Common in: - Preferred stock dividends - Endowment funds - Real estate with infinite rental income - UK Consol bonds (historically)

Formulas: Level Ordinary: PV = C / r Level Due: PV = C / r × (1 + r) Growing: PV = C / (r - g), where r > g

Examples:

LEVEL PERPETUITY: £1000 annual payment at 5% payment=1000, rate=0.05 Result: PV = £20,000

GROWING PERPETUITY: £1000 payment growing 3% annually at 8% discount payment=1000, rate=0.08, growth_rate=0.03 Result: PV = £20,000

PERPETUITY DUE: £1000 at period start at 5% payment=1000, rate=0.05, when='begin' Result: PV = £21,000 | scripts.tools.perpetuity | | Core matrix operations using NumPy BLAS.

Examples:

MATRIX MULTIPLICATION: operation="multiply", matrix1=[[1,2],[3,4]], matrix2=[[5,6],[7,8]] Result: [[19,22],[43,50]]

MATRIX INVERSE: operation="inverse", matrix1=[[1,2],[3,4]] Result: [[-2,1],[1.5,-0.5]]

TRANSPOSE: operation="transpose", matrix1=[[1,2],[3,4]] Result: [[1,3],[2,4]]

DETERMINANT: operation="determinant", matrix1=[[1,2],[3,4]] Result: -2.0

TRACE: operation="trace", matrix1=[[1,2],[3,4]] Result: 5.0 (1+4) | scripts.tools.matrix_operations | | Solve systems of linear equations (Ax = b) using SciPy's optimised solver.

Examples:

SQUARE SYSTEM (2 equations, 2 unknowns): coefficients=[[2,3],[1,1]], constants=[8,3], method="direct" Solves: 2x+3y=8, x+y=3 Result: [x=1, y=2]

OVERDETERMINED SYSTEM (3 equations, 2 unknowns): coefficients=[[1,2],[3,4],[5,6]], constants=[5,6,7], method="least_squares" Finds best-fit x minimizing ||Ax-b|| Result: [x≈-6, y≈5.5]

3x3 SYSTEM: coefficients=[[2,1,-1],[1,3,2],[-1,2,1]], constants=[8,13,5], method="direct" Result: [x=3, y=2, z=1] | scripts.tools.solve_linear_system | | Matrix decompositions: eigenvalues/vectors, SVD, QR, Cholesky, LU.

Examples:

EIGENVALUE DECOMPOSITION: matrix=[[4,2],[1,3]], decomposition="eigen" Result: {eigenvalues: [5, 2], eigenvectors: [[0.89,0.45],[0.71,-0.71]]}

SINGULAR VALUE DECOMPOSITION (SVD): matrix=[[1,2],[3,4],[5,6]], decomposition="svd" Result: {U: 3×3, singular_values: [9.5, 0.77], Vt: 2×2}

QR FACTORISATION: matrix=[[1,2],[3,4]], decomposition="qr" Result: {Q: orthogonal, R: upper triangular}

CHOLESKY (symmetric positive definite): matrix=[[4,2],[2,3]], decomposition="cholesky" Result: {L: [[2,0],[1,1.41]]} where A=LL^T

LU DECOMPOSITION: matrix=[[2,1],[4,3]], decomposition="lu" Result: {P: permutation, L: lower, U: upper} where A=PLU | scripts.tools.matrix_decomposition | | Compute symbolic and numerical derivatives with support for higher orders and partial derivatives.

Examples:

FIRST DERIVATIVE: expression="x^3 + 2x^2", variable="x", order=1 Result: derivative="3x^2 + 4*x"

SECOND DERIVATIVE (acceleration/concavity): expression="x^3", variable="x", order=2 Result: derivative="6*x"

EVALUATE AT POINT: expression="sin(x)", variable="x", order=1, point=0 Result: derivative="cos(x)", value_at_point=1.0

PRODUCT RULE: expression="sin(x)*cos(x)", variable="x", order=1 Result: derivative="cos(x)^2 - sin(x)^2"

PARTIAL DERIVATIVE: expression="x^2*y", variable="y", order=1 Result: derivative="x^2" (treating x as constant) | scripts.tools.derivative | | Compute symbolic and numerical integrals (definite and indefinite).

Examples:

INDEFINITE INTEGRAL (antiderivative): expression="x^2", variable="x" Result: "x^3/3"

DEFINITE INTEGRAL (area): expression="x^2", variable="x", lower_bound=0, upper_bound=1 Result: 0.333

TRIGONOMETRIC: expression="sin(x)", variable="x", lower_bound=0, upper_bound=3.14159 Result: 2.0 (area under one period)

NUMERICAL METHOD (non-elementary): expression="exp(-x^2)", variable="x", lower_bound=0, upper_bound=1, method="numerical" Result: 0.746824 (Gaussian integral approximation)

SYMBOLIC ANTIDERIVATIVE: expression="1/x", variable="x" Result: "log(x)" | scripts.tools.integral | | Compute limits and series expansions using SymPy.

Examples:

CLASSIC LIMIT: expression="sin(x)/x", variable="x", point=0, operation="limit" Result: limit=1

LIMIT AT INFINITY: expression="1/x", variable="x", point="oo", operation="limit" Result: limit=0

ONE-SIDED LIMIT: expression="1/x", variable="x", point=0, operation="limit", direction="+" Result: limit=+∞ (approaching from right)

REMOVABLE DISCONTINUITY: expression="(x^2-1)/(x-1)", variable="x", point=1, operation="limit" Result: limit=2

MACLAURIN SERIES (at 0): expression="exp(x)", variable="x", point=0, operation="series", order=4 Result: "1 + x + x^2/2 + x^3/6 + O(x^4)"

TAYLOR SERIES (at point): expression="sin(x)", variable="x", point=3.14159, operation="series", order=4 Result: expansion around π | scripts.tools.limits_series | | Execute multiple math operations in a single request with automatic dependency chaining.

USE THIS TOOL when you need 2+ calculations where outputs feed into inputs (bond pricing, statistical workflows, multi-step formulas). Don't make sequential individual tool calls.

Benefits: 90-95% token reduction, single API call, highly flexible workflows

Quick Start

Available tools (20): • Basic: calculate, percentage, round, convert_units • Arrays: array_operations, array_statistics, array_aggregate, array_transform • Statistics: statistics, pivot_table, correlation • Financial: financial_calcs, compound_interest, perpetuity • Linear Algebra: matrix_operations, solve_linear_system, matrix_decomposition • Calculus: derivative, integral, limits_series

Result referencing:

Pass $op_id.result directly in any parameter:

• $op_id.result - Use output from prior operation
• $op_id.result[0] - Array indexing
• $op_id.metadata.field - Nested fields

Example: "payment": "$coupon.result" or "variables": {"x": "$op1.result"}

Example - Bond valuation:

{
  "operations": [
    {"id": "coupon", "tool": "calculate",
     "context": "Calculate annual coupon payment",
     "arguments": {"expression": "principal * 0.04", "variables": {"principal": 8306623.86}}},
    {"id": "fv", "tool": "financial_calcs",
     "context": "Future value of coupon payments",
     "arguments": {"calculation": "fv", "rate": 0.04, "periods": 10,
                   "payment": "$coupon.result", "present_value": 0}},
    {"id": "total", "tool": "calculate",
     "context": "Total bond maturity value",
     "arguments": {"expression": "fv + principal",
                   "variables": {"fv": "$fv.result", "principal": 8306623.86}}}
  ],
  "execution_mode": "auto",
  "output_mode": "minimal",
  "context": "Bond A 10-year valuation"
}

When to Use

✅ Multi-step calculations (financial models, statistics, transformations) ✅ Data pipelines where step N needs output from step N-1 ✅ Any workflow requiring 2+ operations from the tools above

❌ Single standalone calculation ❌ Need to inspect/validate intermediate results before proceeding

Execution Modes

• auto (recommended): DAG-based optimization, parallel where possible
• sequential: Strict order
• parallel: All concurrent (only if truly independent)

Output Modes

• full: Complete metadata (default)
• compact: Remove nulls/whitespace
• minimal: Basic operation objects with values
• value: Flat {id: value} map (~90% smaller) - use this for most cases
• final: Sequential chains only, returns terminal result (~95% smaller)

Structure

Each operation:

• tool: Tool name (required)
• arguments: Tool parameters (required)
• id: Unique identifier (auto-generated if omitted)
• context: Optional label for this operation

Batch-level context parameter labels entire workflow across all output modes.

Response includes: per-operation status, result/error, execution_time_ms, dependency wave, summary stats. | scripts.tools.batch_execute |

如果参数不完整，使用 AskUserQuestion 向用户询问缺失的参数。

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工具函数说明

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scripts.tools.calculate

工具描述：Evaluate mathematical expressions using SymPy.

Supports: - Arithmetic: +, -, *, /, ^ - Trigonometry: sin, cos, tan, asin, acos, atan - Logarithms: log, ln, exp - Constants: pi, e - Functions: sqrt, abs

Examples:

SIMPLE ARITHMETIC: expression="2 + 2" Result: 4

TRIGONOMETRY: expression="sin(pi/2)" Result: 1.0

WITH VARIABLES: expression="x^2 + 2*x + 1", variables={"x": 3} Result: 16

MULTIPLE VARIABLES: expression="x^2 + y^2", variables={"x": 3, "y": 4} Result: 25

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
expression	string	true		Mathematical expression (e.g., '2+2', 'sin(pi/2)', 'x^2+1')
variables	null	false		Variable substitutions (e.g., {'x': 5, 'y': 10})

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scripts.tools.percentage

工具描述：Perform percentage calculations: of, increase, decrease, or change.

Examples:

PERCENTAGE OF: 15% of 200 operation="of", value=200, percentage=15 Result: 30

INCREASE: 100 increased by 20% operation="increase", value=100, percentage=20 Result: 120

DECREASE: 100 decreased by 20% operation="decrease", value=100, percentage=20 Result: 80

PERCENTAGE CHANGE: from 80 to 100 operation="change", value=80, percentage=100 Result: 25 (25% increase)

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
operation	string	true		Type of calculation
value	number	true		Base value
percentage	number	true		Percentage amount (or new value for 'change')

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scripts.tools.round

工具描述：Advanced rounding operations with multiple methods.

Methods: - round: Round to nearest (3.145 → 3.15 at 2dp) - floor: Always round down (3.149 → 3.14) - ceil: Always round up (3.141 → 3.15) - trunc: Truncate towards zero (-3.7 → -3, 3.7 → 3)

Examples:

ROUND TO NEAREST: values=3.14159, method="round", decimals=2 Result: 3.14

FLOOR (DOWN): values=3.14159, method="floor", decimals=2 Result: 3.14

CEIL (UP): values=3.14159, method="ceil", decimals=2 Result: 3.15

MULTIPLE VALUES: values=[3.14159, 2.71828], method="round", decimals=2 Result: [3.14, 2.72]

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
values	null	true		Single value or list (e.g., 3.14159 or [3.14, 2.71])
method	string	false	"round"	Rounding method
decimals	integer	false	0.0	Number of decimal places

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scripts.tools.convert_units

工具描述：Convert between angle units: degrees ↔ radians.

Examples:

DEGREES TO RADIANS: value=180, from_unit="degrees", to_unit="radians" Result: 3.14159... (π)

RADIANS TO DEGREES: value=3.14159, from_unit="radians", to_unit="degrees" Result: 180

RIGHT ANGLE: value=90, from_unit="degrees", to_unit="radians" Result: 1.5708... (π/2)

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
value	number	true		Value to convert (e.g., 180, 3.14159)
from_unit	string	true		Source unit
to_unit	string	true		Target unit

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scripts.tools.array_operations

工具描述：Perform element-wise operations on arrays using Polars.

Supports array-array and array-scalar operations.

Examples:

SCALAR MULTIPLICATION: operation="multiply", array1=[[1,2],[3,4]], array2=2 Result: [[2,4],[6,8]]

ARRAY ADDITION: operation="add", array1=[[1,2]], array2=[[3,4]] Result: [[4,6]]

POWER OPERATION: operation="power", array1=[[2,3]], array2=2 Result: [[4,9]]

ARRAY DIVISION: operation="divide", array1=[[10,20],[30,40]], array2=[[2,4],[5,8]] Result: [[5,5],[6,5]]

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
operation	string	true		Element-wise operation to perform
array1	array	true		First 2D array (e.g., [[1,2],[3,4]])
array2	null	true		Second array, scalar, or JSON string

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scripts.tools.array_statistics

工具描述：Calculate statistical measures on arrays using Polars.

Supports computation across entire array, rows, or columns.

Examples:

COLUMN-WISE MEANS: data=[[1,2,3],[4,5,6]], operations=["mean"], axis=0 Result: [2.5, 3.5, 4.5] (average of each column)

ROW-WISE MEANS: data=[[1,2,3],[4,5,6]], operations=["mean"], axis=1 Result: [2.0, 5.0] (average of each row)

OVERALL STATISTICS: data=[[1,2,3],[4,5,6]], operations=["mean","std"], axis=None Result: {mean: 3.5, std: 1.71}

MULTIPLE STATISTICS: data=[[1,2,3],[4,5,6]], operations=["min","max","mean"], axis=0 Result: {min: [1,2,3], max: [4,5,6], mean: [2.5,3.5,4.5]}

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
data	array	true		2D array (e.g., [[1,2,3],[4,5,6]])
operations	array	true		Statistics to compute (e.g., ['mean','std'])
axis	null	false		Axis: 0=column-wise, 1=row-wise, None=overall

---

scripts.tools.array_aggregate

工具描述：Perform aggregation operations on 1D arrays.

Examples:

SUMPRODUCT: operation="sumproduct", array1=[1,2,3], array2=[4,5,6] Result: 32 (1×4 + 2×5 + 3×6)

WEIGHTED AVERAGE: operation="weighted_average", array1=[10,20,30], weights=[1,2,3] Result: 23.33... ((10×1 + 20×2 + 30×3) / (1+2+3))

DOT PRODUCT: operation="dot_product", array1=[1,2], array2=[3,4] Result: 11 (1×3 + 2×4)

GRADE CALCULATION: operation="weighted_average", array1=[85,92,78], weights=[0.3,0.5,0.2] Result: 86.5

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
operation	string	true		Aggregation operation
array1	array	true		First 1D array (e.g., [1,2,3])
array2	null	false		Second 1D array for sumproduct/dot_product
weights	null	false		Weights for weighted_average (e.g., [1,2,3])

---

scripts.tools.array_transform

工具描述：Transform arrays for ML preprocessing and data normalization.

Transformations: - normalize: L2 normalization (unit vector) - standardize: Z-score (mean=0, std=1) - minmax_scale: Scale to [0,1] range - log_transform: Natural log transform

Examples:

L2 NORMALIZATION: data=[[3,4]], transform="normalize" Result: [[0.6,0.8]] (3²+4²=25, √25=5, 3/5=0.6, 4/5=0.8)

STANDARDIZATION (Z-SCORE): data=[[1,2],[3,4]], transform="standardize" Result: Values with mean=0, std=1

MIN-MAX SCALING: data=[[1,2],[3,4]], transform="minmax_scale" Result: [[0,0.33],[0.67,1]] (scaled to [0,1])

LOG TRANSFORM: data=[[1,10,100]], transform="log_transform" Result: [[0,2.3,4.6]] (natural log)

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
data	array	true		2D array to transform (e.g., [[1,2],[3,4]])
transform	string	true		Transformation type
axis	null	false		Axis: 0=column-wise, 1=row-wise, None=overall

---

scripts.tools.statistics

工具描述：Comprehensive statistical analysis using Polars.

Analysis types: - describe: Count, mean, std, min, max, median - quartiles: Q1, Q2, Q3, IQR - outliers: IQR-based detection (values beyond Q1-1.5×IQR or Q3+1.5×IQR)

Examples:

DESCRIPTIVE STATISTICS: data=[1,2,3,4,5,100], analyses=["describe"] Result: {count:6, mean:19.17, std:39.25, min:1, max:100, median:3.5}

QUARTILES: data=[1,2,3,4,5], analyses=["quartiles"] Result: {Q1:2, Q2:3, Q3:4, IQR:2}

OUTLIER DETECTION: data=[1,2,3,4,5,100], analyses=["outliers"] Result: {outlier_values:[100], outlier_count:1, lower_bound:-1, upper_bound:8.5}

FULL ANALYSIS: data=[1,2,3,4,5,100], analyses=["describe","quartiles","outliers"] Result: All three analyses combined

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
data	array	true		List of numerical values (e.g., [1,2,3,4,5,100])
analyses	array	true		Types of analysis to perform

---

scripts.tools.pivot_table

工具描述：Create pivot tables from tabular data using Polars.

Like Excel pivot tables: reshape data with row/column dimensions and aggregated values.

Example:

SALES BY REGION AND PRODUCT: data=[ {"region":"North","product":"A","sales":100}, {"region":"North","product":"B","sales":150}, {"region":"South","product":"A","sales":80}, {"region":"South","product":"B","sales":120} ], index="region", columns="product", values="sales", aggfunc="sum" Result: product | A | B --------|------|------ North | 100 | 150 South | 80 | 120

COUNT AGGREGATION: Same data with aggfunc="count" Result: Count of entries per region-product combination

AVERAGE SCORES: data=[{"dept":"Sales","role":"Manager","score":85}, ...] index="dept", columns="role", values="score", aggfunc="mean" Result: Average scores by department and role

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
data	array	true		List of row dictionaries
index	string	true		Column name for row index
columns	string	true		Column name for pivot columns
values	string	true		Column name to aggregate
aggfunc	string	false	"sum"	Aggregation function

---

scripts.tools.correlation

工具描述：Calculate correlation matrices between multiple variables using Polars.

Methods: - pearson: Linear correlation (-1 to +1, 0 = no linear relationship) - spearman: Rank-based correlation (monotonic, robust to outliers)

Examples:

PEARSON CORRELATION: data={"x":[1,2,3], "y":[2,4,6], "z":[1,1,1]}, method="pearson", output_format="matrix" Result: { "x": {"x":1.0, "y":1.0, "z":NaN}, "y": {"x":1.0, "y":1.0, "z":NaN}, "z": {"x":NaN, "y":NaN, "z":NaN} }

PAIRWISE FORMAT: data={"height":[170,175,168], "weight":[65,78,62]}, method="pearson", output_format="pairs" Result: [{"var1":"height", "var2":"weight", "correlation":0.89}]

SPEARMAN (RANK): data={"x":[1,2,100], "y":[2,4,200]}, method="spearman" Result: Perfect correlation (1.0) despite non-linear relationship

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
data	object	true		Dict of variable names to values (e.g., {'x':[1,2,3],'y':[2,4,6]})
method	string	false	"pearson"	Correlation method
output_format	string	false	"matrix"	Output format: 'matrix' or 'pairs'

---

scripts.tools.financial_calcs

工具描述：Time Value of Money (TVM) calculations: solve for PV, FV, PMT, rate, IRR, or NPV.

The TVM equation has 5 variables - know 4, solve for the 5th: PV = Present Value (lump sum now) FV = Future Value (lump sum at maturity) PMT = Payment (regular periodic cash flow) N = Number of periods I/Y = Interest rate per period

Sign convention: negative = cash out (you pay), positive = cash in (you receive)

Examples:

ZERO-COUPON BOND: PV of £1000 in 10 years at 5% calculation="pv", rate=0.05, periods=10, future_value=1000 Result: £613.91

COUPON BOND: PV of £30 annual coupons + £1000 face value at 5% yield calculation="pv", rate=0.05, periods=10, payment=30, future_value=1000 Result: £845.57

RETIREMENT SAVINGS: FV with £500/month for 30 years at 7% calculation="fv", rate=0.07/12, periods=360, payment=-500, present_value=0 Result: £566,764

MORTGAGE PAYMENT: Monthly payment on £200k loan, 30 years, 4% APR calculation="pmt", rate=0.04/12, periods=360, present_value=-200000, future_value=0 Result: £954.83

INTEREST RATE: What rate grows £613.81 to £1000 in 10 years? calculation="rate", periods=10, present_value=-613.81, future_value=1000 Result: 0.05 (5%)

GROWING ANNUITY: Salary stream with 3.5% raises, discounted at 12% calculation="pv", rate=0.12, periods=25, payment=-45000, growth_rate=0.035 Result: £402,586

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
calculation	string	true		What to solve for: pv, fv, pmt, rate, irr, or npv
rate	null	false		Interest/discount rate per period (e.g., 0.05 for 5% annual)
periods	null	false		Number of compounding periods
payment	null	false		Regular periodic payment (negative=pay out, positive=receive)
present_value	null	false		Single lump sum at time 0 (negative=pay, positive=receive)
future_value	null	false		Single lump sum at maturity (negative=owe, positive=receive)
cash_flows	null	false		Series of cash flows for IRR/NPV (e.g., [-100, 30, 30, 130])
when	string	false	"end"	Payment timing: 'end' (ordinary) or 'begin' (annuity due)
growth_rate	number	false	0.0	Payment growth rate per period (0.0 for level annuity)

---

scripts.tools.compound_interest

工具描述：Calculate compound interest with various compounding frequencies.

Formulas: Discrete: A = P(1 + r/n)^(nt) Continuous: A = Pe^(rt)

Examples:

ANNUAL COMPOUNDING: £1000 at 5% for 10 years principal=1000, rate=0.05, time=10, frequency="annual" Result: £1628.89

MONTHLY COMPOUNDING: £1000 at 5% for 10 years principal=1000, rate=0.05, time=10, frequency="monthly" Result: £1647.01

CONTINUOUS COMPOUNDING: £1000 at 5% for 10 years principal=1000, rate=0.05, time=10, frequency="continuous" Result: £1648.72

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
principal	number	true		Initial principal amount (e.g., 1000)
rate	number	true		Annual interest rate (e.g., 0.05 for 5%)
time	number	true		Time period in years (e.g., 10)
frequency	string	false	"annual"	Compounding frequency

---

scripts.tools.perpetuity

工具描述：Calculate present value of a perpetuity (infinite series of payments).

A perpetuity is an annuity that continues forever. Common in: - Preferred stock dividends - Endowment funds - Real estate with infinite rental income - UK Consol bonds (historically)

Formulas: Level Ordinary: PV = C / r Level Due: PV = C / r × (1 + r) Growing: PV = C / (r - g), where r > g

Examples:

LEVEL PERPETUITY: £1000 annual payment at 5% payment=1000, rate=0.05 Result: PV = £20,000

GROWING PERPETUITY: £1000 payment growing 3% annually at 8% discount payment=1000, rate=0.08, growth_rate=0.03 Result: PV = £20,000

PERPETUITY DUE: £1000 at period start at 5% payment=1000, rate=0.05, when='begin' Result: PV = £21,000

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
payment	number	true		Periodic payment amount (e.g., 1000)
rate	number	true		Discount rate per period (e.g., 0.05)
growth_rate	null	false		Payment growth rate (None or 0 for level, e.g., 0.03 for growing)
when	string	false	"end"	Payment timing: 'end' or 'begin'

---

scripts.tools.matrix_operations

工具描述：Core matrix operations using NumPy BLAS.

Examples:

MATRIX MULTIPLICATION: operation="multiply", matrix1=[[1,2],[3,4]], matrix2=[[5,6],[7,8]] Result: [[19,22],[43,50]]

MATRIX INVERSE: operation="inverse", matrix1=[[1,2],[3,4]] Result: [[-2,1],[1.5,-0.5]]

TRANSPOSE: operation="transpose", matrix1=[[1,2],[3,4]] Result: [[1,3],[2,4]]

DETERMINANT: operation="determinant", matrix1=[[1,2],[3,4]] Result: -2.0

TRACE: operation="trace", matrix1=[[1,2],[3,4]] Result: 5.0 (1+4)

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
operation	string	true		Matrix operation
matrix1	array	true		First matrix (e.g., [[1,2],[3,4]])
matrix2	null	false		Second matrix for multiplication

---

scripts.tools.solve_linear_system

工具描述：Solve systems of linear equations (Ax = b) using SciPy's optimised solver.

Examples:

SQUARE SYSTEM (2 equations, 2 unknowns): coefficients=[[2,3],[1,1]], constants=[8,3], method="direct" Solves: 2x+3y=8, x+y=3 Result: [x=1, y=2]

OVERDETERMINED SYSTEM (3 equations, 2 unknowns): coefficients=[[1,2],[3,4],[5,6]], constants=[5,6,7], method="least_squares" Finds best-fit x minimizing ||Ax-b|| Result: [x≈-6, y≈5.5]

3x3 SYSTEM: coefficients=[[2,1,-1],[1,3,2],[-1,2,1]], constants=[8,13,5], method="direct" Result: [x=3, y=2, z=1]

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
coefficients	array	true		Coefficient matrix A in Ax=b system (2D list, e.g., [[2,3],[1,1]])
constants	array	true		Constants vector b in Ax=b system (1D list, e.g., [8,3])
method	string	false	"direct"	Solution method: direct=exact (square systems), least_squares=overdetermined systems

---

scripts.tools.matrix_decomposition

工具描述：Matrix decompositions: eigenvalues/vectors, SVD, QR, Cholesky, LU.

Examples:

EIGENVALUE DECOMPOSITION: matrix=[[4,2],[1,3]], decomposition="eigen" Result: {eigenvalues: [5, 2], eigenvectors: [[0.89,0.45],[0.71,-0.71]]}

SINGULAR VALUE DECOMPOSITION (SVD): matrix=[[1,2],[3,4],[5,6]], decomposition="svd" Result: {U: 3×3, singular_values: [9.5, 0.77], Vt: 2×2}

QR FACTORISATION: matrix=[[1,2],[3,4]], decomposition="qr" Result: {Q: orthogonal, R: upper triangular}

CHOLESKY (symmetric positive definite): matrix=[[4,2],[2,3]], decomposition="cholesky" Result: {L: [[2,0],[1,1.41]]} where A=LL^T

LU DECOMPOSITION: matrix=[[2,1],[4,3]], decomposition="lu" Result: {P: permutation, L: lower, U: upper} where A=PLU

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
matrix	array	true		Matrix to decompose as 2D nested list (e.g., [[4,2],[1,3]])
decomposition	string	true		Decomposition type: eigen=eigenvalues/vectors, svd=singular value, qr=QR, cholesky=symmetric positive definite, lu=LU factorisation

---

scripts.tools.derivative

工具描述：Compute symbolic and numerical derivatives with support for higher orders and partial derivatives.

Examples:

FIRST DERIVATIVE: expression="x^3 + 2x^2", variable="x", order=1 Result: derivative="3x^2 + 4*x"

SECOND DERIVATIVE (acceleration/concavity): expression="x^3", variable="x", order=2 Result: derivative="6*x"

EVALUATE AT POINT: expression="sin(x)", variable="x", order=1, point=0 Result: derivative="cos(x)", value_at_point=1.0

PRODUCT RULE: expression="sin(x)*cos(x)", variable="x", order=1 Result: derivative="cos(x)^2 - sin(x)^2"

PARTIAL DERIVATIVE: expression="x^2*y", variable="y", order=1 Result: derivative="x^2" (treating x as constant)

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
expression	string	true		Mathematical expression to differentiate (e.g., 'x^3 + 2*x^2', 'sin(x)')
variable	string	true		Variable to differentiate with respect to (e.g., 'x', 't')
order	integer	false	1.0	Derivative order (1=first derivative, 2=second, etc.)
point	null	false		Optional point for numerical evaluation of the derivative

---

scripts.tools.integral

工具描述：Compute symbolic and numerical integrals (definite and indefinite).

Examples:

INDEFINITE INTEGRAL (antiderivative): expression="x^2", variable="x" Result: "x^3/3"

DEFINITE INTEGRAL (area): expression="x^2", variable="x", lower_bound=0, upper_bound=1 Result: 0.333

TRIGONOMETRIC: expression="sin(x)", variable="x", lower_bound=0, upper_bound=3.14159 Result: 2.0 (area under one period)

NUMERICAL METHOD (non-elementary): expression="exp(-x^2)", variable="x", lower_bound=0, upper_bound=1, method="numerical" Result: 0.746824 (Gaussian integral approximation)

SYMBOLIC ANTIDERIVATIVE: expression="1/x", variable="x" Result: "log(x)"

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
expression	string	true		Mathematical expression to integrate (e.g., 'x^2', 'sin(x)')
variable	string	true		Integration variable (e.g., 'x', 't')
lower_bound	null	false		Lower bound for definite integral (omit for indefinite)
upper_bound	null	false		Upper bound for definite integral (omit for indefinite)
method	string	false	"symbolic"	Integration method: symbolic=exact/analytical, numerical=approximate (requires bounds)

---

scripts.tools.limits_series

工具描述：Compute limits and series expansions using SymPy.

Examples:

CLASSIC LIMIT: expression="sin(x)/x", variable="x", point=0, operation="limit" Result: limit=1

LIMIT AT INFINITY: expression="1/x", variable="x", point="oo", operation="limit" Result: limit=0

ONE-SIDED LIMIT: expression="1/x", variable="x", point=0, operation="limit", direction="+" Result: limit=+∞ (approaching from right)

REMOVABLE DISCONTINUITY: expression="(x^2-1)/(x-1)", variable="x", point=1, operation="limit" Result: limit=2

MACLAURIN SERIES (at 0): expression="exp(x)", variable="x", point=0, operation="series", order=4 Result: "1 + x + x^2/2 + x^3/6 + O(x^4)"

TAYLOR SERIES (at point): expression="sin(x)", variable="x", point=3.14159, operation="series", order=4 Result: expansion around π

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
expression	string	true		Mathematical expression to analyse (e.g., 'sin(x)/x', 'exp(x)')
variable	string	true		Variable for limit/expansion (e.g., 'x', 't')
point	null	true		Point for limit/expansion (number, 'oo' for infinity, '-oo' for -infinity)
operation	string	false	"limit"	Operation: limit=compute limit, series=Taylor/Maclaurin expansion
order	integer	false	6.0	Series expansion order (number of terms)
direction	string	false	"+-"	Limit direction: +=from right, -=from left, +-=both sides

---

scripts.tools.batch_execute

工具描述：Execute multiple math operations in a single request with automatic dependency chaining.

USE THIS TOOL when you need 2+ calculations where outputs feed into inputs (bond pricing, statistical workflows, multi-step formulas). Don't make sequential individual tool calls.

Benefits: 90-95% token reduction, single API call, highly flexible workflows

Quick Start

Available tools (20): • Basic: calculate, percentage, round, convert_units • Arrays: array_operations, array_statistics, array_aggregate, array_transform • Statistics: statistics, pivot_table, correlation • Financial: financial_calcs, compound_interest, perpetuity • Linear Algebra: matrix_operations, solve_linear_system, matrix_decomposition • Calculus: derivative, integral, limits_series

Result referencing:

Pass $op_id.result directly in any parameter:

• $op_id.result - Use output from prior operation
• $op_id.result[0] - Array indexing
• $op_id.metadata.field - Nested fields

Example: "payment": "$coupon.result" or "variables": {"x": "$op1.result"}

Example - Bond valuation:

{
  "operations": [
    {"id": "coupon", "tool": "calculate",
     "context": "Calculate annual coupon payment",
     "arguments": {"expression": "principal * 0.04", "variables": {"principal": 8306623.86}}},
    {"id": "fv", "tool": "financial_calcs",
     "context": "Future value of coupon payments",
     "arguments": {"calculation": "fv", "rate": 0.04, "periods": 10,
                   "payment": "$coupon.result", "present_value": 0}},
    {"id": "total", "tool": "calculate",
     "context": "Total bond maturity value",
     "arguments": {"expression": "fv + principal",
                   "variables": {"fv": "$fv.result", "principal": 8306623.86}}}
  ],
  "execution_mode": "auto",
  "output_mode": "minimal",
  "context": "Bond A 10-year valuation"
}

When to Use

✅ Multi-step calculations (financial models, statistics, transformations) ✅ Data pipelines where step N needs output from step N-1 ✅ Any workflow requiring 2+ operations from the tools above

❌ Single standalone calculation ❌ Need to inspect/validate intermediate results before proceeding

Execution Modes

• auto (recommended): DAG-based optimization, parallel where possible
• sequential: Strict order
• parallel: All concurrent (only if truly independent)

Output Modes

• full: Complete metadata (default)
• compact: Remove nulls/whitespace
• minimal: Basic operation objects with values
• value: Flat {id: value} map (~90% smaller) - use this for most cases
• final: Sequential chains only, returns terminal result (~95% smaller)

Structure

Each operation:

• tool: Tool name (required)
• arguments: Tool parameters (required)
• id: Unique identifier (auto-generated if omitted)
• context: Optional label for this operation

Batch-level context parameter labels entire workflow across all output modes.

Response includes: per-operation status, result/error, execution_time_ms, dependency wave, summary stats.

参数定义

参数名称	参数类型	是否必填	默认值	描述
context	null	false		Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_mode	string	false	"full"	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.
operations	array	true		List of operations to execute. Each operation MUST include: tool (name), arguments (dict). Optional: id (UUID/string), context, label, timeout_ms (int)
execution_mode	string	false	"auto"	Execution strategy: sequential (order), parallel (concurrent), auto (DAG-based)
max_concurrent	integer	false	5.0	Maximum concurrent operations (applies to parallel/auto modes)
stop_on_error	boolean	false	false	Whether to stop execution on first error. If False, independent operations continue even if others fail.

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返回值处理

工具函数返回 dict 对象：

• result["raw"] - API 原始返回数据（JSON），直接将此数据整理后展示给用户
• result["success"] - 是否成功（True/False）
• result["message"] - 状态消息

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项目结构

xiaobenyang_gaokao_skill/
├── scripts/
│   ├── __init__.py
│   ├── config.py       # 配置管理 + set_api_key()
│   ├── call_api.py      # API 客户端 + call_api()
│   └── tools.py         # 工具函数（直接调用）
├── requirements.txt
└── SKILL.md

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注意事项

1. API 密钥是必需的，无密钥时必须通过 AskUserQuestion 询问用户
2. 禁止在缺少 API 密钥时自行搜索或编造数据