@sigl1982 AFAIK, I finest time resolution that you'll get on any system is 1/256 s. You don't weigh individual atoms on a pan scale, yet the mass of most atoms is known to several digits accuracy. Indirect aggregate methods must be used to measure very small things.

I understand that theta(t) represents the angular displacement at time t. But why are there two differential equations for theta(t)? What do deG and deL represent?

Please show an example of this computation worked out by hand for one matrix. I'm having some trouble understanding the steps. And does "direct neighbor" include diagonals, so that each entry could have as many an as eight direct neighbors?

@Christopher2222 I think that the number is sequential (i.e., that it increases by one each time that it increases) but not that it's directy related to the labor hours. Rather, I'd guess that the number is increased each time the system is recompiled. That seems indirectly, although closely, related to the labor.

It's interesting from a marketing standpoint. I wonder if any objective meaning could be ascribed to the number on the vertical axis---the version number---or if it's purely a subjective marketing gimmick. Being more precise by using the terminology of statistical data types (Wikipedia link), I wonder whether this number is merely an ordinal scale rather than a ratio scale. I think that more ratio-scale meaning could be ascribed to the number returned by version(), which is currently set at 1,133,417. I suspect that this number may be closely related to the number of person-hours of labor that's been put into the product.

@Christopher2222 wrote:

• What value could someone get out of determining that a dataset contains two particular distributions?

Well, for example, if you were to sample the heights of a population of adult humans, you'd likely find that the data were not normally distributed, which may be contrary to your expectation. Why? It's because of the different distributions of the heights of men and women. A computer analysis of the dataset could show that it's a combination of two normal distributions.

@Christopher2222 Your method has this flaw:

has(ifactor(2^7), 7);

      true

It's also extremely inefficient compared to the other methods. Compare using
n:= nextprime(2^(2^6))*nextprime(2^(2^7)).

What does it mean to "solve" a derivative?

@taro I'm having a bit of trouble understanding your English. The word "could" makes no sense to me in this context.

Regarding the effect of restart: If the random order of things is based on the explicit use of the random number generator, then restart will cause the same order to be used. However, if the random order is based on the memory addresses where things are stored, then restart won't fix the order.

It may be possible to enforce a certain order of the parts of an expression by using sort, but I have tried this several times before, and although it is possible, I decided that it wasn't worth the effort.

@roman_pearce By what algorithm do you expect to get a 30-fold improvement? I can get a 7-8-fold improvement with chrem. I don't know a better algorithm than that.

restart:

n:= 100:

A:= Matrix((n$2), ()-> rand(), order= C_order):

#Naive method:
CodeTools:-Usage(1/A):
memory used=5.68GiB, alloc change=164.00MiB, cpu time=78.91s, real time=77.12s, gc time=3.44s
#Use casting to select the method:
CodeTools:-Usage(1/Matrix(A, datatype= integer)):
memory used=5.46GiB, alloc change=360.00MiB, cpu time=14.78s, real time=12.78s, gc time=2.95s
#My best quick attempt at a faster integer inverse:
IntInv:= (A::Matrix(square, integer))-> 
   (n-> LinearAlgebra:-Modular:-IntegerLinearSolve(
      <A | LinearAlgebra:-IdentityMatrix(n)>, n, _rest
   ))
      (op([1,1], A), _rest)
:
CodeTools:-Usage(IntInv(A)):
memory used=1.57GiB, alloc change=0 bytes, cpu time=25.89s, real time=24.38s, gc time=2.08s
CodeTools:-Usage(IntInv(A, method= chrem)):
memory used=1.84GiB, alloc change=0 bytes, cpu time=13.16s, real time=10.25s, gc time=3.75s

@YasH How can one use your function and also effectively use plot option discont; i.e., how can one avoid the vertical lines at the discontinuities? There seems to be a subtle distinction---which I can't yet make precise---between functions for which discont will work and those for which it won't. I can't make it work with your function.

Another thing that I like about the new editor is that I can copy-and-paste plots direct from a worksheet. That's much easier than uploading a file.

@nika The chi-squared test won't tell you a suitable distribution. It'll only tell you whether or not the normal distribution is suitable. If the test fails, it tells you nothing.

@vahid65 How about

plots:-animate(
    plots:-polarplot,
    [[[r, 0, r= 0..1], [r, 9*Pi/4*k/50, r= 0..1]], color= magenta],
    k= 0..50, thickness= 6
);

@Mihrab Oops, I changed the parentheses from your original. My command should've been

plot([seq(-arctan(2*m*x/(1-x^2)), m= 1..10)], x= 0..10, discont);