Usage Examples

April 2, 2026 · View on GitHub

Available Tools

calc_expression

Safely evaluate mathematical expressions with support for basic operations and math functions.

Parameters:

expression (string, required, max 500 chars): Mathematical expression to evaluate

Supported operations: +, -, *, /, **, ()
Supported functions: sin, cos, tan, log, sqrt, abs, pow

Examples:

"2 + 3 * 4" → 14.0
"sqrt(16)" → 4.0
"sin(3.14159/2)" → 1.0
"pow(2, 3)" → 8.0

calc_statistics

Perform statistical calculations on a list of numbers.

Parameters:

numbers (array of floats, required, max 10000 elements): List of numbers to analyze
operation (string, required): Statistical operation to perform

Available operations: mean, median, mode, std_dev, variance

Examples:

numbers=[85, 92, 78, 96, 88], operation="mean" → 87.8
numbers=[1, 2, 3, 4, 5], operation="median" → 3.0
numbers=[1, 1, 2, 3], operation="mode" → 1.0

calc_interest

Calculate compound interest for investments.

Parameters:

principal (float, required): Initial investment amount
rate (float, required): Annual interest rate as decimal (e.g., 0.045 for 4.5%)
time (float, required): Time period in years
compounds_per_year (integer, optional, default: 1): Compounding frequency

Formula: A = P(1 + r/n)^(nt)

Example:

principal=5000, rate=0.045, time=10, compounds_per_year=12
→ Final: \$7814.17, Interest: \$2814.17

calc_units

Convert between different units of measurement.

Parameters:

value (float, required): Value to convert
from_unit (string, required): Source unit
to_unit (string, required): Target unit
unit_type (string, required): Type of conversion

Supported unit types:

temperature: c, f, k (Celsius, Fahrenheit, Kelvin)
length: mm, cm, m, km, in, ft, yd, mi
weight: g, kg, oz, lb

Examples:

value=25, from_unit="c", to_unit="f", unit_type="temperature" → 77.0 f
value=5, from_unit="mi", to_unit="km", unit_type="length" → 8.047 km
value=1, from_unit="kg", to_unit="lb", unit_type="weight" → 2.205 lb

workspace_save

Save calculation to persistent workspace (survives server restarts).

Parameters:

name (string, required, max 50 chars): Variable name (alphanumeric, underscore, hyphen only)
expression (string, required, max 500 chars): Mathematical expression
result (float, required): Calculated result

Example:

name="portfolio_return", expression="10000 * 1.$07^{5}$", result=14025.52
→ Saved successfully

workspace_load

Load previously saved calculation from workspace.

Parameters:

name (string, required): Variable name to load

Example:

name="portfolio_return"
→ Returns: expression="10000 * 1.$07^{5}$", result=14025.52, timestamp

plot_function

Generate mathematical function plots (requires matplotlib).

Parameters:

expression (string, required, max 500 chars): Function to plot (use x as variable)
x_range (tuple, required): (min, max) for x-axis
num_points (integer, optional, default: 100, range: 2-10000): Number of points to plot

Examples:

expression="x**2", x_range=(-5, 5) → Parabola plot
expression="sin(x)", x_range=(-3.14, 3.14) → Sine wave plot
expression="log(x)", x_range=(0.1, 10) → Logarithm plot

plot_histogram

Create statistical histogram (requires matplotlib).

Parameters:

data (array of floats, required, max 10000 elements): Numerical values
bins (integer, optional, default: 20): Number of histogram bins
title (string, optional, max 100 chars): Chart title

Returns: PNG image with mean and median lines

Example:

data=[1, 2, 2, 3, 3, 3, 4, 4, 5], bins=5, title="Score Distribution"

plot_line_chart

Create line chart from data points (requires matplotlib).

Parameters:

x_data (array of floats, required, max 10000 elements): X-axis values
y_data (array of floats, required, max 10000 elements): Y-axis values
title (string, optional, max 100 chars): Chart title
x_label (string, optional, max 100 chars): X-axis label
y_label (string, optional, max 100 chars): Y-axis label
color (string, optional, max 100 chars): Line color (name or hex)
show_grid (boolean, optional, default: true): Display grid lines

Example:

x_data=[1, 2, 3, 4], y_data=[1, 4, 9, 16], title="Squares", color="blue"

plot_scatter

Create scatter plot for correlation analysis (requires matplotlib).

Parameters:

x_data (array of floats, required, max 10000 elements): X-axis values
y_data (array of floats, required, max 10000 elements): Y-axis values
title (string, optional, max 100 chars): Chart title
x_label (string, optional, max 100 chars): X-axis label
y_label (string, optional, max 100 chars): Y-axis label
color (string, optional, max 100 chars): Point color
point_size (integer, optional, default: 50): Size of points

Example:

x_data=[1, 2, 3, 4], y_data=[2, 4, 5, 8], title="Correlation Study"

plot_box_plot

Create box plot for distribution comparison (requires matplotlib).

Parameters:

data_groups (array of arrays, required, max 100 groups): Data groups to compare
group_labels (array of strings, optional): Labels for each group
title (string, optional, max 100 chars): Chart title
y_label (string, optional, max 100 chars): Y-axis label
color (string, optional, max 100 chars): Box color

Example:

data_groups=[[1,2,3,4], [2,3,4,5], [3,4,5,6]], group_labels=["A", "B", "C"]

plot_financial_line

Generate synthetic financial price data with trends (requires matplotlib).

Parameters:

days (integer, optional, default: 30, range: 2-1000): Number of days
trend (string, optional, default: "bullish"): Market trend
start_price (float, optional, default: 100.0): Starting price
color (string, optional, max 100 chars): Line color

Available trends: bullish, bearish, volatile

Note: Generates synthetic data for educational purposes only, not real market data.

Example:

days=60, trend="bullish", start_price=150.0, color="green"

matrix_multiply

Multiply two matrices using NumPy (requires [scientific] extra).

Parameters:

matrix_a (array of arrays, required): First matrix
matrix_b (array of arrays, required): Second matrix

Examples:

matrix_a=[[1, 2], [3, 4]], matrix_b=[[5, 6], [7, 8]]
→ [[19 22]
   [43 50]]

matrix_a=[[1, 2, 3], [4, 5, 6]], matrix_b=[[7, 8], [9, 10], [11, 12]]
→ [[58  64]
   [139 154]]

matrix_a=[[1, 2], [3, 4]], matrix_b=[[1, 0], [0, 1]]
→ [[1 2]
   [3 4]]  (identity property)

Error handling:

matrix_a=[[1, 2], [3, 4]], matrix_b=[[1, 2, 3]]
→ Error: Incompatible matrix dimensions for multiplication

matrix_transpose

Transpose a matrix (swap rows and columns).

Parameters:

matrix (array of arrays, required): Matrix to transpose

Examples:

matrix=[[1, 2, 3], [4, 5, 6]]
→ [[1 4]
   [2 5]
   [3 6]]

matrix=[[1, 2], [3, 4]]
→ [[1 3]
   [2 4]]

matrix=[[1, 2, 3, 4]]
→ [[1]
   [2]
   [3]
   [4]]

matrix_determinant

Calculate determinant of a square matrix.

Parameters:

matrix (array of arrays, required): Square matrix

Examples:

matrix=[[4, 6], [3, 8]]
→ 14.0

matrix=[[1, 2, 3], [0, 1, 4], [5, 6, 0]]
→ 1.0

matrix=[[1, 2], [2, 4]]
→ 0.0 (singular matrix)

Error handling:

matrix=[[1, 2, 3], [4, 5, 6]]
→ Error: Matrix must be square

matrix_inverse

Compute the inverse of a square matrix.

Parameters:

matrix (array of arrays, required): Square matrix to invert

Examples:

matrix=[[4, 7], [2, 6]]
→ [[ 0.6  -0.7 ]
   [-0.2   0.4 ]]

matrix=[[1, 0], [0, 1]]
→ [[1. 0.]
   [0. 1.]]  (identity inverse)

Error handling:

matrix=[[1, 2], [2, 4]]
→ Error: Matrix is singular and cannot be inverted

matrix=[[1, 2, 3], [4, 5, 6]]
→ Error: Matrix must be square

matrix_eigenvalues

Calculate eigenvalues of a square matrix.

Parameters:

matrix (array of arrays, required): Square matrix

Examples:

matrix=[[4, 2], [1, 3]]
→ [5.0, 2.0]

matrix=[[3, 0, 0], [0, 5, 0], [0, 0, 7]]
→ [3.0, 5.0, 7.0]  (diagonal elements)

matrix=[[1, 0, 0], [0, 1, 0], [0, 0, 1]]
→ [1.0, 1.0, 1.0]  (identity matrix)

Note: Output may include complex eigenvalues for some matrices.

Available Resources

math://test

Simple test resource for verifying MCP connectivity.

Returns: Success message confirming resource access is working.

Example:

math://test
→ "Test resource working successfully!"

math://constants/{constant}

Get mathematical constants with descriptions.

Available constants:

pi - Ratio of circle's circumference to diameter (3.14159...)
e - Euler's number, base of natural logarithm (2.71828...)
golden_ratio - Golden ratio φ (1.61803...)
euler_gamma - Euler-Mascheroni constant γ (0.57721...)
sqrt2 - Square root of 2 (1.41421...)
sqrt3 - Square root of 3 (1.73205...)

Example:

math://constants/pi
→ Returns: value and description

math://functions

List all available mathematical functions with syntax and examples.

Returns: Complete reference including:

Function signatures
Parameter descriptions
Usage examples
Common patterns

math://workspace

Get persistent calculation workspace summary.

Returns:

All saved variables with expressions and results
Total calculation count
Last access timestamp

math://history

Get chronological calculation history from workspace.

Returns: Last 10 calculations with timestamps (most recent first)

Available Prompts

math_tutor

Generate a math tutoring prompt for explaining concepts.

Arguments:

topic (string, required): Mathematical topic to explain
level (string, optional, default: "intermediate"): Difficulty level (beginner, intermediate, advanced)
include_examples (boolean, optional, default: true): Include worked examples

Example:

topic="derivatives", level="beginner", include_examples=true
→ Returns structured teaching prompt

formula_explainer

Generate a prompt for explaining mathematical formulas.

Arguments:

formula (string, required): Mathematical formula to explain
context (string, optional, default: "general mathematics"): Mathematical context

Example:

formula="A = πr²", context="geometry"
→ Returns detailed formula breakdown