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: Exponentiate a Matrix

From time to time when one works with operators, such as in Quantum mechanics, something like an exponential of the operator appears (this is also the case in many areas of Mathematics like group theory of differential geometry). This exponentiation of a matrix should be understood as the series expansion of the exponential. SAGE knows [...]

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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: Series Expansion

Two days ago I was trying to expand in series a lot of functions… so I ask myself, Could it be done in SAGE? It should be possible… but, How? So I ask on google group. Solution by Andrzej Chrzeszczyk sage: var(‘r’); sage: f=2*r/sinh(2*r) sage: f.taylor(r,0,5) 14/45*r^4 – 2/3*r^2 + 1 sage: maxima(f).powerseries(‘r’,0) -4*r*’sum((2^(2*i2-1)-1)*2^(2*i2-1)*bern(2*i2)*r^(2*i2-1)/ (2*i2)!,i2,0,inf) [...]

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