There are already some implementations of Gosper's algorithms. For example here:
http://contfrac.sourceforge.net/
What are the problems with Gosper's algorithms that you are primarily trying to solve?
Also, which programming language are you using? Just curious.
I'm not sure you can guarantee termination in cases such as computing f(g(x)) where x is integer and f(g(x)) is also integer, but g(x) is transcendental...
There seems to be a conclusion in the literature that CF-based methods are slower than other methods for exact arithmetic.
If you have...
a new free e-book about linear algebra using exterior products; explains all about determinants and also Pfaffians, gives specific examples of calculations.
http://homepages.physik.uni-muenchen.de/~winitzki/Linear_algebra_exterior.pdf
hello, jostpuur. You seem to be interested in the lack of rigorous mathematics in physics. I am trying to show examples where physicists proceed regardless of nonrigorous mathematics. The examples I showed are not simply mistakes in calculations but mistakes that originated from lack of...
What you are saying is that an approximation is used beyond the range of its validity, just because a more precise computation is too complicated. This is a different story. What I meant to say is that the "black magic" of renormalization is not even presented as anything different from the...
Then I would give the example of renormalization in quantum field theory. It is an accepted standard practice to perform renormalization using totally unjustified mathematical steps (Feynman integral, perturbative expansion, cutoffs, counterterms, etc.). These unjustified mathematical steps are...
Somebody asked whether there are actual examples when insufficient knowledge of mathematics gave wrong results in physics.
There certainly exist many examples where physicists have arrived to incorrect conclusions due to wrong understanding of some mathematical issues. However, these examples...
I think Birrell-Davies is pretty much unreadable for a beginning graduate student. If you already have a PhD and have working knowledge of quantum field theory then you can understand Birrell-Davies with considerable effort. In my view this is the case with almost any advanced monograph. Another...
titous
The problem is that people here have no clue what is a "global 2nd order field" or "B:E" or "alpha * K". People here know standard mathematics, but you are using mathematical terminology that is highly nonstandard (although maybe everyone in your field uses it). So you won't be able to...
The LaTeX is entered as [ tex ] \ alpha [ / tex ] (remove spaces).
I think you are trying to invent a generalization of spinors. A spinor changes sign when you rotate by 2\pi. But a spinor is not multiplied by \exp(\imath \pi/2) under rotation by \pi. And also inversion just leaves a spinor...
I felt that this was a bit offensive, - don't you think? Especially considering that most GR books do things this way. For example, Landau&Lifschitz Classical theory of fields.
smallphi
try this set of lecture notes (I already posted a link in another thread), maybe you will like it better.
http://www.theorie.physik.uni-muenchen.de/~serge/T7/
I would also agree with Chris Hillman's comment about your expectations being too high. The kind of book you are looking for...
I think it's quite possible to avoid "physical arguments" when dealing with pure mathematics. A student just needs to understand why a new notion is being introduced. For example, in functional analysis: one is supposed to learn a large number of definitions; an operator can be closed...
The second law is the most useful for calculations, but the other two laws are needed conceptually. Here is an interpretation of Newton's laws:
First law: There exist "objects not acted upon by outside forces", i.e. isolated bodies very far from all other bodies. Also, there exist reference...