Recent content by Identity

Thx, that works. I guess it's a shortcoming of mathematica. Oh, and the vectors aren't like usual vectors, they're just maps from R^2 to R^2.

Here's an example. You can keep shift+entering the output until it fully simplifies, but I can't get it to simplify immediately

I've defined A and B to be two affine transformations on \mathbb{R}^2. Then, I defined C and D to be some kinds of compositions of A and B, for example: C = Composition[A,B,B,A,A][{x,y}] D = Composition[B,A,B,A,B][{x,y}] Now, I want to evaluate expressions like: X =...

I'll have to try it out when i get back tonight, but that looks very promising, thanks :)

I can't do that, because B has a translation vector

I want to define something like: A\left(\begin{matrix} x \\ y\end{matrix}\right) = \left(\begin{matrix} 1 & -1 \\ -1 & 1 \end{matrix}\right)\left(\begin{matrix} x \\ y\end{matrix}\right) B\left(\begin{matrix} x \\ y\end{matrix}\right) = \left(\begin{matrix} 0 & 1 \\ 2 & -1...

Cheers quasar :)

Thanks... so for the example I gave, if \theta_{(x,y)}(a,b) = (xa-yb,xb+ya), then (\theta_{(x,y)})_* = \left[\begin{matrix} x & -y \\ y & x \end{matrix}\right] so X_{(x,y)} = \left[\begin{matrix} x & -y \\ y & x \end{matrix}\right]\left[\begin{matrix} 1 \\ 0\end{matrix}\right] =...

I need help calculating the exponential map of a general vector. Definition of the exponential map For a Lie group G with Lie algebra \mathfrak{g}, and a vector X \in \mathfrak{g} \equiv T_eG, let \hat{X} be the corresponding left-invariant vector field. Then let \gamma_X(t) be the maximal...

Great answer Adrian, thanks :)

What are the general features you should look for when classifying an arbitrary particle interaction according to strong, weak, or electromagnetic forces? Cheers

A black hole is just a collapsed star, so the gravitational field of a black hole is just like any star really. If we were a safe enough distance away from a black hole, Earth could orbit a black hole as if it were just another star. So to say that a black hole would consume all the matter and...

Thanks, yeah I also thought that having a maximal atlas wouldn't be that important as long as you had compatible charts. But anyway every text I read has it as a condition, which I thought was interesting: "A (smooth) differential manifold M^m of dimension m is a topological manifold of...

I've been looking in various books in differential geometry, and usually when they show that a smooth manifold has a differentiable structure, they just show that the atlas is C^\infty compatible, and forget about showing it is maximal. Which got me thinking. Given an atlas, how DOES one show...

Does anyone have any recommendations for software, or perhaps a programming language that specialises in creating animations/simulations in maths and physics? For example, "Turning a sphere inside out" "Mobius transformations revealed" "Klein bottle"