Welcome to QBee’s documentation!

qbee is a package for transforming differential equations into polynomial and quadratic polynomial forms via introducing new variables. It includes functionality for:

• exact transformation of Ordinary Differential Equations (ODEs) into a form with a polynomial right-hand side (polynomialization).

• exact transformation of polynomial ODEs intro a form with right-hand side being quadratic polynomials (quadratization).

• obtaining a general (vectorized) form of new variables to quadratize linearly coupled polynomial ODEs given in vectorized form (dimension-agnostic quadratization)

• automatized transformation of polynomialized and quadratized systems of ODEs into a form suitable for numerical integrators.

Background - Why we created qbee

Lorem ipsum add articles and examples

Indices and tables

• Index

• Search Page

Contents:

• Installation
  • Pip / PyPI
  • Git
  • Run QBee
• Cheatsheet
• Quadratization
  • Quadratization by example
  • Formal definition
  • Monomial quadratization
  • Laurent monomials
• Inputs and Parameters
  • Inputs’ Derivatives
  • Existence of input-free quadratizations
  • Setting up possible derivatives of inputs
• Polynomialization
  • Polynomialization by example
  • Polynomialization and Laurent monomials
  • Optional: Polynomialization of rational powers
• Dimension-Agnostic Quadratization
• Numerical Integration
• Articles and Resources
• API Reference
  • polynomialize_and_quadratize()
  • quadratize()
  • polynomialize()
  • quadratize_dimension_agnostic()
  • pruning_by_nodes_processed()
  • pruning_by_vars_number()
  • pruning_by_declining_variables()
  • pruning_by_elapsed_time()
  • pruning_by_nodes_without_quadratization_found()
  • without_variables()
  • default_generation()
  • functions()
  • parameters()
  • qbee.INDEPENDENT_VARIABLE