computational-workbench-mcp

This Scientific Calculation Protocol (SCP) server furnishes AI agents, including advanced models like Claude, with capabilities for executing complex symbolic manipulation, performing high-precision numerical calculations, analyzing diverse datasets, and rendering graphical representations of results. It is optimally suited for domains like theoretical physics, advanced engineering simulation, and quantum information processing, all encapsulated within a reproducible Docker framework.

Core Capabilities

• Execute core numerical operations leveraging NumPy, SciPy, SymPy, and Pandas for data handling.
• Undertake formal mathematical resolution, including solving systems of ordinary and partial differential equations.
• Facilitate extensive linear algebraic transformations and multi-dimensional array manipulation.
• Support simulation and analysis relevant to quantum information science.
• Generate publication-quality data representations using Matplotlib and Seaborn.
• Implement and train predictive models via scikit-learn.
• Handle specialized tensor algebra and demanding floating-point matrix arithmetic.
• Conduct comprehensive statistical assessments on structured datasets.
• Ensure operational ubiquity across various host platforms (auto-detecting configurations for Windows, macOS, and Linux), with specific optimization for Apple Silicon (M-series) architectures.
• Native execution support across both traditional x86_64 (Intel/AMD) and modern ARM architectures.

Deployment Guide

Utilizing the Official Docker Artifact

bash

Acquire the latest build artifact from the registry

docker pull ychen94/computing-mcp:latest

Initiate the runtime container (auto-configures host sharing)

docker run -i --rm -v /tmp:/app/shared ychen94/computing-mcp:latest

For Windows command-line environments: powershell docker run -i --rm -v %env:TEMP%:/app/shared ychen94/computing-mcp:latest

Integration within Claude Desktop Application

1. Launch the Claude Desktop client.
2. Navigate to Settings ➝ Developer ➝ Configuration Editor.
3. Insert the pertinent JSON block below into your configuration file:

For Unix-like systems (macOS/Linux):

{ "mcpServers": { "computational-workbench": { "command": "docker", "args": [ "run", "-i", "--rm", "-v", "/tmp:/app/shared", "ychen94/computing-mcp:latest" ] } } }

For Windows systems:

{ "mcpServers": { "computational-workbench": { "command": "docker", "args": [ "run", "-i", "--rm", "-v", "%TEMP%:/app/shared", "ychen94/computing-mcp:latest" ] } } }

Operational Demonstrations

Tensor Product Computation

Execute the calculation and graphical rendering for the Kronecker product of two specified matrices. Instructions:

import numpy as np import matplotlib.pyplot as plt

Define initial tensors

A = np.array([[1, 2], [3, 4]]) B = np.array([[5, 6], [7, 8]])

Compute the tensor product using numpy's Kronecker function

tensor_product = np.kron(A, B)

Output results

print("Matrix A definition:") print(A) print("\nMatrix B definition:") print(B) print("\nResulting Tensor Product A ⊗ B:") print(tensor_product)

Generate a visual representation of the resultant matrix structure

plt.figure(figsize=(8, 6)) plt.imshow(tensor_product, cmap='viridis') plt.colorbar(label='Magnitude') plt.title('Visualization of Tensor Product A ⊗ B')

Symbolic Equation Solving

Determine the closed-form solution for the following second-order linear homogeneous ordinary differential equation. Instructions: import sympy as sp import matplotlib.pyplot as plt import numpy as np

Establish symbolic variable and dependent function

x = sp.Symbol('x') y = sp.Function('y')(x)

Define the ODE: y'' + 2y' + y = 0

diff_eq = sp.Eq(sp.diff(y, x, 2) + 2*sp.diff(y, x) + y, 0)

Obtain the general solution

solution = sp.dsolve(diff_eq) print("General Solution:") print(solution)

Isolate and print a specific solution instance (set arbitrary constants C1=1, C2=0)

solution_func = solution.rhs.subs({sp.symbols('C1'): 1, sp.symbols('C2'): 0}) print("Particular Solution Instance:") print(solution_func)

Convert the symbolic expression to a callable numeric function

solution_lambda = sp.lambdify(x, solution_func)

Plot the function across a defined range

x_vals = np.linspace(0, 5, 100) y_vals = [float(solution_lambda(x_val)) for x_val in x_vals]

plt.figure(figsize=(10, 6)) plt.plot(x_vals, y_vals, label='y(x)') plt.grid(True, linestyle='--') plt.title("Solution Plot for y''(x) + 2*y'(x) + y(x) = 0") plt.xlabel('Independent Variable x') plt.ylabel('Function Value y(x)') plt.show()

Exploratory Data Cluster Analysis

Analyze the provided synthetic dataset to delineate intrinsic groupings. Instructions:

import numpy as np import pandas as pd import matplotlib.pyplot as plt from sklearn.cluster import KMeans from sklearn.preprocessing import StandardScaler

Generate synthetic data points distributed in three distinct regions

np.random.seed(42) n_points = 300

Define cluster centroids and variances

cluster_a = np.random.normal(loc=[2, 2], scale=0.5, size=(n_points//3, 2)) cluster_b = np.random.normal(loc=[7, 7], scale=0.5, size=(n_points//3, 2)) cluster_c = np.random.normal(loc=[2, 7], scale=0.5, size=(n_points//3, 2))

Aggregate features

Features = np.vstack([cluster_a, cluster_b, cluster_c])

Create a structured data container

df = pd.DataFrame(Features, columns=['Metric_A', 'Metric_B']) print("Initial Data Snapshot:") print(df.head())

Normalize data for distance-based algorithms

processor = StandardScaler() X_normalized = processor.fit_transform(Features)

Execute K-Means algorithm with k=3

kmeans_model = KMeans(n_clusters=3, random_state=42, n_init='auto') df['Group_ID'] = kmeans_model.fit_predict(X_normalized)

Visualization of the discovered groupings

plt.figure(figsize=(10, 6)) for group_id in range(3): subset = df[df['Group_ID'] == group_id] plt.scatter(subset['Metric_A'], subset['Metric_B'], label=f'Cluster {group_id}', alpha=0.7)

Revert cluster centers to original scale for plotting

cluster_centers_original_scale = processor.inverse_transform(kmeans_model.cluster_centers_) plt.scatter(cluster_centers_original_scale[:, 0], cluster_centers_original_scale[:, 1], s=200, c='red', marker='X', label='Centroids')

plt.title('K-Means Partitioning of Feature Space') plt.xlabel('Metric A Value') plt.ylabel('Metric B Value') plt.legend() plt.grid(True, alpha=0.5)

Quantum Information Processing

Demonstration Gallery

Laser Physics Simulation Results:

Elliptic Integral Evaluation:

Debugging and Support

Common Operational Difficulties

1. Volume Mapping Access Denied

2. Confirm the existence of the host directory specified for mounting and verify necessary read/write permissions.

3. Missing Output Visualizations

4. Inspect the mounted host location (/tmp on non-Windows hosts or the system temporary directory on Windows).
5. Verify that Docker possesses the requisite file system write privileges.

6. Examine the raw output payload from the mcp tool execution. Once located, use standard terminal commands or image viewers to inspect the file.

   💡 💡 Integration with specialized terminal extensions like iterm-mcp-server or equivalent features in other terminals allows for seamless, non-disruptive handling of generated artifacts. 💡 💡

Assistance Request Protocol

Should an unforeseen error occur, please initiate a new issue on GitHub, providing: 1. Complete traceback or error output. 2. Details of your operating system and the installed Docker version. 3. Step-by-step procedure to reliably reproduce the fault.

Licensing Terms

Distribution and use of this software are governed by the MIT License. Refer to the LICENSE file within the primary source repository located here for comprehensive legal details.

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