Humm, I am open to suggestions on something

I need to plot some map, and color (with some opacity) the region that is nearer some distance to any of a set of points

So, the union of disks with different centers and some constant radius (say 50 kilometers)

If one plots GeoDisks their opacities add up

@Rojo Do regions support geo? You could also draw the disks separately as an opaque layer, rasterize, then overlay with adjusted opacity I think.

@MichaelHale yeah, thanks, probably some GeoStylingImageFunction thing will work

Looks like someone got sufficiently annoyed at WRI not fixing bugs that they actually published a paper on a bug in Mathematica

@acl I, for one, am surprised that the Notices of the AMS would publish an article whose essential content is - "when using a computer algebra system, you should check your results".

@acl Who uses Table[Table[RandomInteger[{-99, 99}], {i, 1, 14}], {j, 1, 14}] ?!? :-D

@MarkMcClure That's basically what one of the developers said at WTC last week in a presentation. But (I think) your point was that "output" is not the same as a rational argument.

Q: Anyone having trouble with Safari cacheing SE pages and always showing the cached page when using the back button? I have to reload every time. Emptying the cache works once; then the page gets cached again. It just started a couple of week ago. (Maybe after a software update.)

Also my comments are formatted so that my name overlaps the end of the comment. (Started about the same time as the cacheing problem). Any fixes?

@MarkMcClure I agree that this should be standard procedure. However, this type of bug seems never to get fixed in the kernel. I don't like what this implies about how priorities are set.

This does indeed look curious: mathematica.stackexchange.com/q/64318/12

@acl Is boosting one's paper count that easy? I should write a paper like that every month!

@MarkMcClure Some people really don't seem to get that point. This looks like the outshoot of the open source propaganda that Sage people have been doing. Honestly I find this disgusting and this attitude is what keeps me away from Sage.

The argument is that no one should ever use a non-open source system for research because a closed-source program cannot be peer review, therefore its results cannot be trusted.

The fallacy here is the implicit claim that open source can be trusted to produce correct results. Wrong! Results can only be trusted if they have been verified by independent methods. I'm not going to take anyone seriously if they say otherwise.

If the software gave me eigenvectors, I'll multiply them again by the matrix to see if they change. Verifying is easy most of the time. If it's not easy, then use another software to compare.

I understand that the Sage project needed to get funding (including NSF funding) and needed to argue why they should get it, but just because there's a big competition for grants, saying just about anything (including fallacies) to get them is not fair game.

Fortunately most open source projects (including the culture of their communities) are not like this. I don't constantly bump into open-source-fanaticism and badmouthing competitors when I search for R-solutions or Python-solutions.

@acl Can that function plot the social network of your Facebook friends, do an EdgeDetect on it, blend it and tweet it to @wolframtap? No? Sorry, no bug fixes for you!

@rm-rf getting more cynical by the day, are we?

@Szabolcs they overdo it a bit, that's true

@acl No, just trying to displace all the Rojos on the star board :P

@Szabolcs I could double my paper count: for each paper published, I could publish one on the bugs I uncovered in mma on the way!

@rm-rf Star ;)

(well, I am exaggerating a bit, but I could probably get .5 bug papers/real paper)

@acl No, you're not exaggerating unfortunately.

:18357252 For the record, the issue does appear to have been addressed in V10.0.1.  The following yielded no problems for me:
powersMatrix = DiagonalMatrix[
   {10^123, 10^152, 10^185, 10^220, 10^397, 10^449, 10^503, 10^563,
    10^979, 10^1059, 10^1143, 10^1229, 10^1319, 10^1412}];
Do[
 SeedRandom[k];
 basicMatrix =
  Table[Table[RandomInteger[{-99, 99}], {i, 1, 14}], {j, 1, 14}];
 smallMatrix =
  Table[Table[RandomInteger[{-999, 999}], {i, 1, 14}], {j, 1, 14}];
 bigMatrix = basicMatrix.powersMatrix + smallMatrix;

The same computation yielded an error every time in V9.0.1.

On the other hand, the notebooks they linked in their paper still seem to have problems. I know nothing of the math there, though, so I don't know that it's really a problem!

@Szabolcs Agreed! I actually tried Sage for quite some time and, if it were awesome, I'd probably still use it. Honestly, though, it just doesn't seem to be very good software. Part X rarely works well with part Y. As such, it's much less than the sum of its parts.

Want to pass your GAP generated Cayley graph to NetworkX or Sage's native graph package - good luck. More basically, try integrating x^n - it doesn't work because Maxima generates questions that Sage interface can't handle. Those are fundamental examples that have been part of the software for years.

@MarkMcClure Eh!

Eh??

Integrating x^n not working. :)

Ah yeah - a good one! Seriously, though.

Here's a Maxima session:

Note the question: "Is n+1 zero or nonzero?" I typed "nonzero;", then the answer appeared. Although, now that I look at it....

Here's a sage session:

Not good.

Now, it seems that a number of folks here are less and less happy with Mathematica. Honestly, it has it's strengths and weaknesses. Perhaps, it's not as fast at some tasks as it could be and perhaps the hyperbole coming from the top is a bit much. However, it's overall design is amazingly coherent and consistent (due, in no small part to the control from said top), its symbolic library can't be beat in terms of speed, scope or correctness, and the integration between parts is amazing.

As far as it's original mission goes - as a system for doing mathematics by computer, I believe it has no equal.

@Szabolcs Incidentally, the NSF generally does not fund open source software whose intention is to directly compete with commercial software - and with good reason. Mathematica and Matlab both started, in part, with NSF funding. They are success stories - why undermine that?

The NSF funding that the Sage project does receive has, as I understand it, to fund research into elliptic curves and related topics - not to fund a viable alternative to the Ms.

@MarkMcClure I don't think anybody disagrees with these advantages; that's why most of us stick to it. However, it is difficult to not notice that bugs do not get fixed. I was joking earlier, but actually the fact is that in about half the papers I write I discover one more bug in mma. I reported a couple but, as far as I can tell, nothing has been done.

eg, try

MathieuS[MathieuCharacteristicA[
  1, -(1/4)], -0.25`, 15.707963267948966`]
MathieuS[MathieuCharacteristicA[
  1, -(1/4)], -0.25`, 15.707963267948966`]

And if you look at what gets added over time, some of it is added and just left to rot. And while interesting things have been added in v10, some feel unfinished (and probably are). That's OK if they do get improved, but I will believe this when I see it.

@acl Weird bug, for sure - and it seems impervious to N[...]! Perhaps I've been lucky (or maybe it's because I've known a number of people at the company for a while and have worked there myself) but I've reported quite a few bugs myself that have been fixed.

And, as I said, the bug that initiated this very discussion appears to have been addressed, at least in part.

I must say that it is unbearable to wait full two-year release cycle for a bug fix, and just notice it's not there. Maybe if I would be paying tens of thousands per year on licenses they would take me seriously, but still.

I must say initial response tends to be swift, but that's it.

@kirma Perhaps that situation will improve with Mathematica Online? You'll be able to check weekly. :)

I wonder what exactly prevents WRI from making regular maintenance releases where they actually attempt to fix most pressing bugs several times a year. It is certainly possible to handle, I've been working on such a product for past five years or so.

@kirma Presumably the bugs we are discussing are considered low-priority. And I am guessing there are not hundreds of kernel developers, so...

Also, lack of proper maintenance release notes seems a bit odd to me.

@acl Most of them are the "well, I can avoid that" sort. But not all.

One of the most baffling oddities (a v10 regression) I've ran into recently was this (evaluate it): Integrate[Integrate[2^-(x + y), {x, 0, a - y}], {y, 0, a}, Assumptions -> a > 0]

I can't believe how many times I've done this:

SortBy[{{"a", 1}, {"b", 4}, {"c", 3}, {"d", 2}},
  Last][[-1 ;; -2 ;; -1]]

Or this:

SortBy[{{"a", 1}, {"b", 4}, {"c", 3}, {"d", 2}}, -Last@# &][[;; 2]]

And I just realized now I can do this:

MaximalBy[{{"a", 1}, {"b", 4}, {"c", 3}, {"d", 2}}, Last, 2]

@MichaelHale MaximalBy was introduced in v10. (Well, I guess you know that.:)

Yeah, it just took me until now to notice the optional 3rd argument, and now I'll use it a lot more.

:)

The computer beat me at my own game in 12 minutes with a few lines of code.