nijenhuis-toolkit 0.1.1

A toolkit to simplify working with Nijenhuis and Haantjes tensors

Nijenhuis toolkit

Symbolic computation of Nijenhuis and Haantjes tensors for integrability analysis of hydrodynamic-type systems.

Features

• Nijenhuis and Haantjes tensor objects in python
• Symbolic computation using SymPy
• Checking of diagonalisability and zero elements
• Easy to read tensor summaries
• Direct LaTeX translation functions for tensors and matrices

Installation

If using pip: pip install nijenhuis-toolkit

Examples

# Define coordinates and a matrix as an operator
u, v = sp.symbols('u v')

L = Operator(
    [[v,1],
    [0,v]],coords=[u,v])

# Compute the Nijenhuis and Haantjes tensors
N = L.nijenhuis_tensor()
H = L.haantjes_tensor()

# Prouce a tensor summary
print(tensor_summary(N,symbol="N"))
>>> N: 2 components total, 0 non-zero
    

#Check if the Nijenhuis tensor is identically zero
print(L.is_nijenhuis())
>>> True