Undetermined gauges (Help in mathematica)()

  • Context: Mathematica 
  • Thread starter Thread starter MathematicalPhysicist
  • Start date Start date
  • Tags Tags
    Mathematica
Click For Summary
SUMMARY

This discussion focuses on extracting undetermined gauges from Mathematica, specifically in the context of perturbation theory. The user seeks guidance on coding methods to derive coefficients (x_i's) and the corresponding gauges (deltas) from a polynomial equation using the undetermined gauges approach. The discussion references two methods for solving polynomial roots: power series expansion and the undetermined gauges method. A specific Mathematica file format change from .txt to .nb is also highlighted as necessary for proper code execution.

PREREQUISITES
  • Understanding of perturbation theory in mathematical physics.
  • Familiarity with Mathematica programming language and its syntax.
  • Knowledge of polynomial equations and their roots.
  • Experience with series expansions in mathematical analysis.
NEXT STEPS
  • Research the implementation of undetermined gauges in Mathematica.
  • Learn about perturbation theory applications in polynomial root finding.
  • Explore Mathematica's capabilities for symbolic computation.
  • Study the differences between .txt and .nb file formats in Mathematica.
USEFUL FOR

Mathematicians, physicists, and researchers working with perturbation theory and Mathematica, particularly those focused on polynomial equations and symbolic computation.

MathematicalPhysicist
Science Advisor
Gold Member
Messages
4,662
Reaction score
372
I want to be able to extract from mathematica, an undertermined gauges, like in pertubation theory:

$$\delta_0(\epsilon)x_0+\delta_1(\epsilon)x_1+\cdots+\delta_k(\epsilon)x_k $$

And to extract the guages (deltas) and the coefficients (x_i's) from the code, how do you propose me to code this?To clarify what I mean. In pertubation theory for solving polynomial roots, we have two methods either to expand in a power series of epsilons, and then plug back to the pertubed polynomial equation, or to use the method above of undetermined gauges.

In the attachment there's example for power series, I want to use this to an equation where only undtermined gauges will work, so I neet to change the first root and second to find coefficients $x_1,x_2$ and the suitable gauges.Anyway here's the term undetermined gauges:
http://books.google.co.il/books?id=...6AEwAw#v=onepage&q=undetermined gauge&f=false

P.S you need to change after the .txt, to .nb, so that mathematica will read it.
 

Attachments

Physics news on Phys.org
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?