In the previous MaplePrimes, one could check the tally of a user's Posts, Answers, Replies, and favorites. That information is now gone, and I miss it. One can still see Posts, etc., but not a count of them.

@jessica99 But the equations in this Answer are not the same as those in the Question. This system is linear; the other is nonlinear. (I see now that you've changed the equations in the original Question to match those in this Answer.)

Do you have any initial conditions? I've tried various combinations, but I encounter possible singularities in the interval -5...5 for every nontrivial triple that I've tried.

Also, I'm amazed that you can compute the solution to this nonlinear system manually. Can you post your solution? Perhaps we have different concepts of what is meant by a "solution".

@Matt C Anderson Well, the name pi is certainly not obvious, so you'd have difficulty searching for it. That name, or rather the Greek letter, is the standard in number theory for the function. Having assessed your interests from your several postings, I suggest that you browse the help page of every command in the numtheory package. There's not that many. Many are related to prime numbers.

@sand15 Why would you want to suppress the Question? Your technique of examining the error messages is very useful and creative. I was just about to mention it myself.

I'd say that deleting a Question that has been Answered is frowned upon. It is extremely frowned upon by me, especially when one of the Answers is mine! However, I seem to be the only one here that speaks out vehemently against the practice, so I'm curious what others think, especially if it's their Answer that's being deleted.

The vast majority of Question-deleters that I've seen are those who want to hide the fact that they've posted their homework problem. This makes me furious when I've spent hours of effort and several days of back-and-forth discussion crafting an Answer. In the case of this Question, I don't care about my Answer, but I see no reason why your useful Reply should be deleted.

I don't want to start any bad habits among the posters. I am a moderator and you are not. My judgement is that the Question cannot be deleted. The only Answered Questions that I would allow to de deleted are those that are objectionable, illegal, nonsensical, or irrelevant to Maple. Other moderators may disagree and still have the power to delete.

@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