ciao

@Szabolcs Makes sense to me (if a bit weird way to do it). As plotpoints goes up, resolution of hypotenuse increases as an aside. In any case, the evaluations for the plot produce a sequence that when fed to ListPlot generates the same result, though obviously with no concept of the "region" and concomitant filling...

Given a (simple but large number of terms) polynomial in a few dozen variables, is Replace[poly, Power[x_, _] -> x, {2}] the quickest way to set all exponents to one, or is there something faster (i.e., an internal function or some such means)?

@VitaliyKaurov Version 1 on Apple. Probably still have it laying around in my old software boxes.

<Soapbox On> I am seriously getting tired of the "do my work for me", zero effort, photograph/image of a textbook exercise questions.<Soapbox Off>

@rcollyer Cool. It's even worse - that example, after opening and checking CPU use in task manager, doing some scrolling, etc. then just hangs. I have to kill Mathematica to get out...

@rcollyer Sent an example.

@rcollyer Might be impractical to supply notebook I'm currently working on, but give me an hour or so and I'll try to simplify it and/or find example elsewhere.

@rcollyer Yes, just the FE. Scrolling gets pretty chunky too when this is going on.

@rcollyer Windows 10

@Silvia And on the other side of that coin, a buddy was in Arizona for spring training, which was cancelled. His kids implored him not to fly back. So he rented a car. It only cost him $15 a day - they had so many car cancellations they just wanted to move them.

@halirutan Sorry for tardy reply - seems I did not get notification of your response. In any case - the long pauses resolved themselves after a few complete exit/start of MMA - beats me what was going on. Thanks again for taking the time to reply...

I have been suffering with long pauses/hangs when entering lines in the frontend. There was a question in the past year related to this, thought I'd bookmarked it, had not, searched to no avail. Had to do with deleting a system file (IIRC a history of commands used, for completion/hinting), which I'd done before and it fixed the issue. Anyone recall the question and/or file name?

@SjoerdC.deVries Not a word in English - but used to mean something that performs (i.e. efficient)

@J.M. Oh, of course - I've done so on occasion for specific cases, but to have such things as built-ins (and a wider range of statistical tests) would be sweet - MMA already has breadth/depth (at least in probability) beyond any product I'm aware of. I held off going to 10 , then surprised to see significant performance improvements in some probability functionality (and close to speed of work-arounds I'd posted) that was completely undocumented in release notes...

The day a new version of MMA is touted, and instead of boasting of things like "...two man-years of effort resulting in significantly improved image recognition for dog collars..." there's "...built-in functionality for Edgeworth and saddle-point approximations for probability distributions..." I'll probably have a coronary from surprise and delight...

@Kuba some patch on the part of the globe where it's below the horizon gets paint, and the patch where the cone exits the globe toward moon gets paint. Imagine pointing a flashlight that has a beam that expands to size of moon at the moon (and magically passes through earth) - you'd light up some ground (small patch) where moon's not visible, bigger patch where beam exits globe. My guess is rotation of Earth + orbit of Moon over time results in pinched band around globe.

@J.M. - Perhaps, I loath "do this for me" questions, but the whole geospatial aspect is way out of my field, so a question there might precipitate a "oh, that's easy, look here..." answer, so I'll probably do so.

Any 3D Geospatial plot wizards: I'd like to make an animation of the globe, rotating, but with a certain shading done first - I want to pick a point on the Earth, use it as the peak of a cone, the large end of the cone being the Moon's disk. Anywhere that cone intersects the surface over some selected time period, shade. I'd imagine over a long time span, it's a wide band. I've done nothing with the Geo/Astro features of MMA, will be learn-as-go. Is this going to be simple with MMA features?

@E.Doroskevic What are you expecting? The returned object is the representation, which you can then operate on, e.g. with Volume, etc.

@Szabolcs: I use SparseArray[Unitize[Subtract[arr, Max@arr]], Automatic, 1]["NonzeroPositions"] for multi-dimensional cases, pretty quick...

@Szabolcs Pick[Range@Length@#, #, Max@#] &@list ?

@AliHashmi: Ping him at his personal blog - listed in his profile...

Is it me, or has the number of "I want this, do it for me and make sure you fully explain/comment the code" questions gone way up in the past half year or so?

@OleksandrR. Agreed, seems to be a trend over last year - Raspberry Pi/ University courses I suppose...

@belisarius Ah, sorry I missed you - just popped in to scan for interesting code snippets...

@Guesswhoitis. Of course - and the interesting generalizations by Kupin and Pudwell. I don't have to tell you (if you've viewed their implementations), they're mathematicians, not coders :-) , so was just checking if anyone had seen an mma implementation before I start on one.

On another note, is anyone aware of a MMA implementation of the Goulden-Jackson clustering method for pattern-avoiding words? I'd rather grab an existing package vs reinvent the wheel...

@OleksandrR. Disagree with site getting "downvote happy" - ref'd question is one of several by same that seem to show little if any effort in utilizing and understanding documentation. Myself, I will downvote many "be my automated documentation source" questions.

Considering the cost of license and extensions to have dozens of subkernels licensed, you must have support from Wolfram, yes? This is clearly a question better directed there, particularly so if it's a licensing issue.

Anyway, semi-interesting problem, but pretty clear large cases / performance does not matter to OP , since accepted answer gets agonizingly slow for such things compared to other simpler answers posted. Thanks for interchange!

Since the subsets rapidly grow to non-single elements, this avoids traversing the list sequentially, and a quick cobbled-up test showed it much faster for large cases...

@LeonidShifrin: Shall I spoil the ending, or do you want the "ah-ha!" yourself? Hint: Look at the pattern of positions in the accumulation of the target list vs where the subset breaks happen...

@LeonidShifrin: Fair enough (depends on the what definition of "is" is, eh? ;-} ) - btw -cool way to do this for large lists is via bin search - quite fast...

@LeonidShifrin: Range[-3,3] trivial example - s/b 7 distinct sets, but output is just the range...

Neat, but fails when negatives present. +1 though. Interestingly, dramatic slowdown with reals.

@juror: That really added nothing - I can get the equation(s) from the code - that does not answer the fundamental question: WHAT does this conglomeration represent? You have not even specified the possible values for the parameters. My interest in code-tuning drops A.S. to zero if it's just code with no meaning. Nonetheless, simply changing the b[n, b0, t] term in f to bv, and surrounding the function body with With[{bv = b[n, b0, t]},...] nets a big boost... And I'll repeat - if you know characteristics of roots, using FindRoot will net several orders of magnitude improvement.

@juror: As in, what is this calculating? Is it some made-up distribution, or does the underlying problem have some realization that might lend itself to intrinsic MMA functionality (like, "I'm tying to calculate the distribution of Pokemons blown by a plasma beam at 2^8 km/sec..." or something. What do the parameters to your function represent, etc. In any case, barring that, if you can use FindRoot etc. (given you can roughly guess some position for the minimal root) you'll get orders of magnitude speed-up in the time-consuming part of your example.

With the wonderfully descriptive variable names (BTW, don't use uppercase initials for your own symbols, bad idea), how is one supposed to figure out what this does? Nor should one have to - why not add what precisely the goal is (as in the probabilistic arena this is playing in)?

@martin: One more query - does N imply the number of variables in each term? That is, does your goal of 20 mean 20 variables? (Sorry, I've not taken much time at reversing your code to figure that part out). If so, you're going to run into problems where number of permutations needed for calculations could be huge/blow memory limits, else they need to be done "iteratively" with a huge performance hit. Let me know...

So, assuming I can come up with a reasonably efficient step 2 (I think I can), this could be good. But, if you're "done", will relegate to spare-spare-time thinking. Let me know...

a nine term set with internal powers ranging from 1 to 9 and external powers ranging from 1 to 10 with a few duplicates thrown in. Using CoefficientRules took nearly five minutes on the netbook. New step took... 0 seconds (below timer resolution). I gave up trying bigger tests to get timings, CR just takes too long.

@martin: However, I've made the "a-ha!" on the earlier truncated products idea. The basic idea is to get coeffs. for each of the terms (where each (a^x+b^x...)^z is a "term"), and then use those to get the ultimate result. Now, even though CoefficientRules is fairly fast on individual simple terms like that (it probably has some magic sauce internally), I tested step 1 of this idea (getting those coeff. sets) on...

@martin: Are you still on this, or is the current state of solution "good enough"? Here's where I'm at: Method of "flash" mentioned earlier is a mixed bag. Sometimes blindingly fast (as in handily beats CoefficientRules for getting all distinct), sometimes a dog, slower than current getCoeff. I kind of expected that from the method, but... bummer.

Glad to here it. Had a flash as I fell to sleep last night that might be a fast way to gen valid exp sets... will ponder today and update you.

Working on some ideas today ... stay tuned.

. If I can get it to work (right now most coeff. are fine, some are < than actual from truncation, so need to figure out correction) this c/b quite fast.

@martin Whoa! That's a lotta code ;-) I'll be lounging later, will ponder this, my gut tells me there's an efficient way of doing this, though I'm not sure so efficient that getting all for all valid sets will be nearly as fast as the earlier simpler case. I'm also playing with "truncating" results - that is, doing one poly multiplication, pulling distinct terms, multiplying by next, pulling distinct... rinse and repeat