xby-math

Xby Math

A high-performance mathematical computing protocol server providing comprehensive mathematical computation capabilities, from basic arithmetic to advanced calculus and linear algebra.

Target profile

The plugin will be installed here. Keep web if you are unsure.

npx -y @deepseek-ai/dsh plugin --profile web add github:xby-skill/xby-math#d1a2a24f4c526ad90d407b967f7d2bb3f8afb261

Compatibility and provenance

Xby Math is published as xby-math and currently resolves to version 1.0.0. The Hub verifies its manifest and preserves the exact installation source for reproducible installs.

DSH compatibility: *
Runtime surfaces: any
Release source: github
Registry updated: 8/28/2026

Versions

1.0.0stable

8/28/2026

README

xby-math

DeepSeek Harness (DSH) 的插件：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。

功能

set_xby_apikey — 在聊天中设置 API 密钥（自动持久化，重启有效）
calculate — 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

percentage — 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)

round — 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]

convert_units — 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)

array_operations — 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]]

array_statistics — 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]}

array_aggregate — 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

array_transform — 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)

statistics — 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

pivot_table — 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

correlation — 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

financial_calcs — 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

compound_interest — 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

perpetuity — 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

matrix_operations — 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)

solve_linear_system — 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]

matrix_decomposition — 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

derivative — 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)

integral — 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)"

limits_series — 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

batch_execute — 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.

安装

方式一：从 GitHub 直接安装（推荐）

# 格式: dsh plugin --profile <profile> add github:<owner>/<repo>
dsh plugin --profile web add github:xby_skill/xby-math

方式二：从本地目录安装（开发模式）

# 仅用于本地开发调试
dsh plugin --profile web add /absolute/path/to/xby-math

方式三：通过 cordis.patch.yml 开发调试

dsh web --profile web --patch /absolute/path/to/dsh-ocr-plugin/cordis.patch.yml

配置

获取 API 密钥

前往小笨羊官网注册并获取 API 密钥。

README

xby-math

DeepSeek Harness (DSH) 的插件：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。

功能

set_xby_apikey — 在聊天中设置 API 密钥（自动持久化，重启有效）
calculate — 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

percentage — 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)

round — 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]

convert_units — 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)

array_operations — 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]]

array_statistics — 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]}

array_aggregate — 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

array_transform — 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)

statistics — 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

pivot_table — Create pivot tables from tabular data using Polars.

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

Example:

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

correlation — 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:

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

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

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

compound_interest — 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

perpetuity — 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

matrix_operations — 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)

solve_linear_system — 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]

matrix_decomposition — 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

derivative — 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)

integral — 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)"

limits_series — 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

batch_execute — 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

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.

安装

方式一：从 GitHub 直接安装（推荐）

# 格式: dsh plugin --profile <profile> add github:<owner>/<repo>
dsh plugin --profile web add github:xby_skill/xby-math

方式二：从本地目录安装（开发模式）

# 仅用于本地开发调试
dsh plugin --profile web add /absolute/path/to/xby-math

方式三：通过 cordis.patch.yml 开发调试

dsh web --profile web --patch /absolute/path/to/dsh-ocr-plugin/cordis.patch.yml

配置

获取 API 密钥

前往小笨羊官网注册并获取 API 密钥。