SAGE tip: More about Differential Forms

In a previous post we discuss the definition of the coordinated patch on a manifold, how to define differential forms, wedge them or calculate their exterior derivative… even simplify’em. This time a zero form will be defined and a list of forms will be created… So, let’s begin! Define a 0-form Once created the coordinated [...]

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SAGE tip: GRmodule. Day 07.

This code is supposed to be (if some one does the work in the future) located in sage.tensor.differential_form_element. The code presented below is a slight modification of Joris code for differential forms manipulation on SAGE. Needed modules from sage.symbolic.ring import SymbolicRing, SR from sage.rings.ring_element import RingElement from sage.algebras.algebra_element import AlgebraElement from sage.rings.integer import Integer from [...]

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SAGE tip: GRmodule. Day 06.

I’ve just updated the SAGE worksheet which uses the definitions described in the previous posts. There are some explanations in text format The code has been hidden… because is long. Moreover… I’ve discover something really amazing! Joris Vankerschaver‘s code of the differential form package in SAGE. Thus, I could use some ideas from Joris’ code [...]

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SAGE tip: GRmodule. Day 05

Hi everyone! This time the Christoffel connection will be defined. The code As usual, here is the code: class Christoffel(Tensor): ”’The class to represent Christoffel Symbols of the second kind. Please note that while it inherits from Tensor, Christoffel symbols are NOT tensors”’ def __init__(self,metr,symbol=’C',rank=(1,2),sh=(1,-1,-1)): # The metric self.g_down = metr # Since we have [...]

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SAGE tip: Working with Differential Forms.

A few weeks ago I realize there is a package for working with differential forms in SAGE. So, I’ve tried to take advantage of that! This is what I’ve learnt so far. Define your manifold If you work with differential forms you should know (probably better than me), that you define forms in a coordinate [...]

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