Recent content by m4r35n357

Really?

I guess all Python devs know about PyCharm (commercial, but with a gratis (community) version) which has a really nice debugger built in. Perhaps you don't know about Eric. Eric is nice when you don't have an x86 based computer (Raspberry Pi), or an x86 not running one of the OSs supported by...

IMO learning by doing is the best way to approach this, so I'll give you some search terms. Most of these things involve systems of Ordinary Differential Equations (ODEs). Search for methods of solving them. Another related area is Hamiltonian Mechanics (also an ODE formulation), which is at...

Heh, I meant the third line of equations, so you got the right part! So if I get you the term just represents all the combinations requred to form the RHS. In that case I would agree it gets too big to handle (numerically) for large numbers of series. I am actually investigating whether there...

Hmm, not sure I understand. Are you saying that the term(s) within the product/sum ##\Pi \Sigma## on the third line do not represent a formula that I can implement myself, because that is my objective (I just don't know what the term means).

I'm sure there are degenerate/edge cases, but here is ##|x + 1|##: Yes there really are 12 derivatives here! Piecewise functions are fine as long as f() is defined at the jump (and derivatives set to zero - see next sentence!). However, this is nothing whatsoever to do with the order of...

Thanks for the feedback! ODEs are what got me involved with this method in the first place, and is the main reason I reverse-engineered the procedure for my own use. Turns out that the best way to verify the low level functions that I needed was to wrap them in Series objects and do those...

You bring up an interesting point, so make yourself comfortable ;) I am assuming that you use or have used RK4 for solving ODEs, which is by definition a finite difference approximation to a fourth order Taylor Series solver (because finding higher order derivatives is supposedly "difficult" or...

I am trying to make sense of the wikipedia article section regarding Cauchy product of several series. but am stuck right at the start because the notation used there is unfamiliar to me and not explained previously in the article. The commas in ##\Sigma a_1, k_1## etc. mean nothing to me. Am I...

Agreed, but as I mentioned above the "window" of intelligible output is finite. There is a subset of use cases for a CAS, where the symbolic output is translated to a more "familiar" language for execution. These are the use cases where my comparison is valid. Not because of the extra time...

Thought I would address this one separately. Here are the first twenty nineteen differentials of ##\exp (2.0)##: $ ipython3 Python 3.7.1 (default, Oct 22 2018, 11:21:55) Type 'copyright', 'credits' or 'license' for more information IPython 7.2.0 -- An enhanced Interactive Python. Type '?' for...

Not a major point to me, as in all practical cases where I've used symbolic differentiation (like calculating the einstein tensor from the metric in GR), the symbolic representations are a complete mess, even if the package is any good at simplification, but yes I suppose it is a benefit...

Well, the Wikipedia page is not a bad place to start . . .

So does AD; all the derivatives are derived from the function itself, at any point where the function is defined.

I thought I would give you guys some justification for why I keep pestering you with this odd numerical technique. I've mentioned its advantages over finite differences quite a few times, so now I am putting it up against symbolic differentiation. Here is a plot of the function ##x^2 /...