SymFields: An Open Source Symbolic Fields Analysis Tool for General Curvilinear Coordinates in Python

TL;DR

SymFields is an open source Python tool that enables vector field analysis in general curvilinear coordinates, simplifying complex calculations for physicists by using real physical values and metric tensor-based differential operators.

Contribution

It introduces a symbolic Python module that extends scalar analysis to vector fields in arbitrary curvilinear coordinates, regardless of orthogonality.

Findings

Supports analysis in non-orthogonal curvilinear coordinates

Uses real physical values for differential operators

Simplifies vector field calculations in complex coordinate systems

Abstract

An open source symbolic tool for vector fields analysis 'SymFields' is developed in Python. The SymFields module is constructed upon Python symbolic module sympy, which could only conduct scaler field analysis. With SymFields module, you can conduct vector analysis for general curvilinear coordinates regardless whether it is orthogonal or not. In SymFields, the differential operators based on metric tensor are normalized to real physical values, which means your can use real physical value of the vector fields as inputs. This could greatly free the physicists from the tedious calculation under complicated coordinates.