Preface

The design philosophy of DeepSeek Harness (DSH) is “everything is a plugin,” allowing developers to extend an agent’s toolbox through plugins. When dealing with problems related to geometry, physics, or tensor fields, symbolic-level differential geometry computations are often required. This plugin wraps SymPy’s diffgeom module, integrating differential geometry symbolic computing capabilities into DSH and enabling agents to directly handle manifolds, tensor fields, and differential operators in code.

Plugin Overview

  • Name: dsh-diffgeom
  • Purpose: A DSH plugin for computing geometric problems
  • Owner: hatter123
  • License: MIT

Core Features

The plugin provides basic operators and objects for differential geometry symbolic computation:

  • Basic geometric objects: manifolds, patches, coordinate systems
  • Field theory tools: scalar fields and tensor fields (supports abstract, coordinate-free representations)
  • Differential operators: exterior derivative d (Differential), wedge product ∧ (Wedge), Lie derivative
  • Riemannian geometry: covariant derivative, metric → Christoffel symbols → Ricci/Riemann components

Installation and Activation

Before installing, make sure Python 3 is installed and SymPy has been installed via pip:

python -m pip install sympy

Use the following command to install:

dsh plugin --profile web add "D:/VSCode_/Project/dsh/dsh-diffgeom"

After installation is complete, DSH registers a tool named diffgeom, which can be called directly in code.

Typical Usage

The plugin includes a Euclidean manifold environment and provides 2D and 3D objects and operators by default. The following are some basic usage examples:

# 外导数：计算标量场 x*y 的外导数
d(x*y)

# 楔积：计算基 1-形式 ex 和 ey 在基向量上的楔积，结果为 1
Wedge(ex, ey)(e_x, e_y)

# 李导数：计算标量场 x*y 沿向量场 e_x 的李导数
LieDerivative(e_x, x*y)

Technical Details

  • Dependencies: Python 3 with SymPy installed.
  • Runtime mechanism: index.js calls python diffgeom_backend.py "<code>" using Node’s child_process, captures standard output, and returns the result.
  • Preloaded objects:
  • 2D environment: m, p, r2 (manifold/patch/coordinate system); coordinates x, y; basis 1-forms ex, ey; basis vectors e_x, e_y; metric g.
  • 3D environment: m3, p3, r3; coordinates x3, y3, z3; basis ex3, ey3, ez3; vectors e_x3, e_y3, e_z3; metric g3.
  • Available constructors: Manifold, Patch, CoordSystem, TensorProduct, Wedge, LieDerivative, Differential, metric_to_Christoffel_2nd, metric_to_Ricci_components, metric_to_Riemann_components, symbols, Function, simplify.

Notes

  • This plugin runs with the permissions of the current DSH process. Please ensure it is installed from a trusted source and review the source code and license.
  • Since the plugin depends on a Python environment, make sure your workspace is correctly configured with Python 3 and SymPy.

Summary

dsh-diffgeom provides a direct entry point for differential geometry symbolic computation in DeepSeek Harness. With the preloaded Euclidean manifold environment, developers can quickly compute exterior derivatives, Lie derivatives, Christoffel symbols, and more without creating separate Python scripts.