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28

This shows a way to parametrise a line using the method suggested by Rahul Narain in a comment, i.e. using Fourier to approximate the data with a set of sinusoids. I use Rationalize to convert all the reals back to rationals, this isn't necessary but it makes the expression look more like those used in Wolfram Alpha. param[x_, m_, t_] := Module[{f, n = ...


22

Perhaps this helps: The WolframAlpha function is limited to 1,000 API calls per day for professional Premier Service subscribers (500 API calls per day for student and classroom Premier Service subscribers), and 100 API calls per day for all other users, unless an API upgrade is purchased.


22

The idea The idea is that if we have $\log(a+b),\qquad a\gg b$ , then we can equivalently write this as $\log a + \log(1 + b/a)$ and the second part will be small, so that one can first compare the first part(s). The power towers with base numbers larger than 1 naturally lead to such logarithms when we repeatedly take the $\log$ of them. So, there ...


17

This now has been discussed in Wolfram blog posts by Michael Trott: Part 1: Making Formulas… for Everything — From Pi to the Pink Panther to Sir Isaac Newton Part 2: Using Formulas... for Everything — From Complex Analysis Class to Political Cartoons to Music Album Covers Here is one of the example apps from blog - go read it in full - fun! Don't miss the ...


12

Artes' guess seems basically right. Here is a way to reach the correct result. First, the antiderivative returned by Mathematica: i0 = FullSimplify[ Integrate[Sqrt[(2 t)^2 + (4 - 3 t^2)^2], t], t > 0] (* (2 (Sqrt[16 - 2 I (-5 I + Sqrt[11]) t^2] Sqrt[8 + I (5 I + Sqrt[11]) t^2] ( 5 (-5 I + Sqrt[11]) EllipticE[ArcSin[1/2 t Root[9 - 5 ...


9

Wolfram|Alpha is integrated in Mathematica. Integration based on function WolframAlpha. To learn basic interactive and programmatic usage see this question. In your case you can get formatted objects in Mathematica like: WolframAlpha["steam 135C", {{"PhaseDiagramTPPlot:ChemicalData", 1}, "Content"}, PodStates ...


8

This was supposed to be a comment to Simon's answer, but it's gotten too long. Still, I wanted to share a somewhat cleaned-up version of Simon's Fourier-fitting function param[] (which I have renamed to FourierCurve[]): FourierCurve[x_, m_, t_, tol_: 0.01] := Module[{rat = Rationalize[#, tol] &, fc}, fc = Take[Chop[Fourier[x, FourierParameters -> ...


8

The bug is probably with Wolfram Alpha, not Mathematica, since the Mathematica query and the Wolfram Alpha website results are consistent. (Edit: Bug is fixed as of 2012-11-26, I got a kind notification from the W|A team in response to my earlier feedback) It looks like they swapped longitude with latitude for Upper Austria (it works with good ole Austria ...


8

You can set the options for WolframAlpha in the usual way. The option to change is: SetOptions[WolframAlpha, PodStates -> {"Show metric"}] as for me (for whatever reason) it was the default to show metric units, I could verify with: SetOptions[WolframAlpha, PodStates -> {"Show non-metric"}] that this seems indeed to affect also the answers to the ...


8

Though WolframAlpha understands some basic Mathematica syntax, that is simply not it's first objective, namely to attempt to understand natural language input. Thus, rather than typing Integrate[x*Sin[x],{x,0,Pi}] one may type some variant of integrate xsinx x,0,pi The results, whether obtained via the web interface or right in notebook, are ...


7

You can access historical GPD data via the WolframAlpha command like so: gdpData = WolframAlpha["us gdp", {{"History:GrossDomesticProduct:EconomicData",1},"ComputableData"}]; This returns quarterly data going back to 1947 in a structured list. You can manipulate the data just as you would any data in Mathematica. Thus, you can get the data points at ...


7

I'm not sure whether this is what you seek, but you can use Trace to investigate in a call to Quantity. Then you extract the essence Quantity["Newtons"]; StringReplace[Names["CalculateUnits`UnitCommonSymbols`*"], "CalculateUnits`UnitCommonSymbols`" ~~ r_ :> r] and you get some kind of list ;-)


6

I'm using 8.0.4 and I get reasonable results (notice the constraint c>0) : nlm = NonlinearModelFit[data, {a + b Log[c x], c > 0}, {a, b, c}, x] ; nlm // Normal (* 0.0740508 - 0.00391526 Log[1.0714 x] *) FindFit[data, {a + b Log[c x], c > 0}, {a, b, c}, x] (* {a -> 0.0740508, b -> -0.00391526, c -> 1.0714} *) Show[Plot[nlm[x], {x, 10, ...


6

In Mathematica 10, this tells you the number of calls remaining in your cloud account if you are logged in: CloudAccountData["WolframAlphaCallsAvailable"] 2168


5

This does not really answer the question as to why Mathematica's Integrate yields an apparently wrong answer. But to simply state why the two answers are different. It seems Wolfram|Alpha does not attempt to do a symbolic integration (which is what your input asks for) before taking its numerical value. As I stated in my comment, using NIntegrate gives the ...


5

For indefinite integrals where "Show Steps" is available, the pod state is "IndefiniteIntegral__Step-by-step solution". The following works for cases where W|A can show the steps. showSteps[query_] := WolframAlpha[ "integrate " <> ToString[query], {{"IndefiniteIntegral", 2}, "Content"}, PodStates -> {"IndefiniteIntegral__Step-by-step ...


5

1) Tap twice = on a new line 2) After orange Spiky type: city in orange county, california 3) Press button MORE till you get al cities 4) Click little cross in the right top corner of the cities panel and choose from the sub-menu: Commutable Data This is what you get (it may look cumbersome but the point is you don't have to type it - the code is ...


5

I can't say that all the Alpha Pro features are available through V8 of Mathematica, but certainly many are. Here are three examples: Type "derivative of x^2" into Alpha. If you are not logged into the Pro version, you will be unable to access the result, other than as a visual image. In particular, you can't easily copy and paste results. Or try, just ...


5

If you don't want Mathematica to use Wolfram | Alpha for correcting incorrect units, you can just set $AllowInternet = False. The downside of this is that it also blocks internet access for the curated data functions such as WeatherData, FinancialData, etc. You can also use Block to disallow internet only within your function.


5

Calling Wolfram|Alpha is not generally an efficient way to retrieve bulk data; where possible, it is better to use a built in data function. Part of the problem is figuring out what to submit to Wolfram|Alpha. In the code you supplied, the issue begins with Wolfram|Alpha returning Missing[NotAvailable]. WolframAlpha["AAPL ...


4

WeatherData[] can give you what you want: startdate = DateList[]; city = "Amsterdam" startpoint = 5 (*hours ago: for amsterdam, the most recent data was not available...*) range = 48 (*in hours*) data = WeatherData[city,"Temperature", #] & /@ (DatePlus[DateList[], {-#, "Hour"}][[1 ;; 4]] & /@ Range[startpoint, range]); For some reason WeatherData ...


4

Oh, I was going to say the same thing. Here's a picture instead of me clicking in the little screw icon... This pastes the query into your document (and runs it too): WolframAlpha["Sunrise june 25, 2013", {{"DaylightInformation", 1}, "ComputableData"}] Then I assigned the results to a symbol for further processing.


4

WolframAlpha["Sunrise june 25, 2013", {{"DaylightInformation", 1}, "ComputableData"}, PodStates -> {"DaylightInformation__More"}] gives {{"begin astronomical twilight", "3:56 am PDT"}, {"begin nautical twilight", "4:40 am PDT"}, {"begin civil twilight", "5:18 am PDT"}, {"sunrise", "5:49 am PDT"}, {"sunset", "8:33 pm PDT"}, {"end ...


4

Well, let's look at the limited good news first. While I don't believe there's any way to specify a single simple parameter indicating that you want to return all the data available, it is possible to programatically specify the number of pushes that you want using Table["More ...",{k}]. Typically, you can simulate lots of pushes and the output will be ...


4

For limitations on many times you can use W/Aplha please see this


4

I can offer some ideas but it would take work to put together into a package. I'll illustrate with the example sqrt(3)+sqrt(5)pi. val = Sqrt[3] + Sqrt[5]*Pi; Set up an vector of values involving powers of both pi and val. We will work at fairly high precision (300 digits). I chose to go to degree 6 in each, which is overkill for this example but of course ...


4

Here is how you attack this: First click on the little "+" in the right upper corner. Then you select either "Subpod content" or directly "Formula data". Both will result in a more specific request which gives you the hint you need: {WolframAlpha[ "6.38905609893065", {{"PossibleClosedForm", 1}, "FormulaData"}], WolframAlpha[ "6.38905609893065", ...


4

A properly formatted Quantity expression should work just fine, without trying to connect to WolframAlpha servers for conversion. For example, Quantity[1, "Feet"] + Quantity[2, "Inches"] should run with or without internet connectivity. In contrast, Quantity[1, "Foot"] + Quantity[2, "Inches"] will attempt to contact WA servers in an attempt to ...


3

I observed this behavior while at a training session at Wolfram Headquarters, and there seems to be an issue with using Integers here: Integrate[Sqrt[(2. t)^2 + (4. - 3. t^2)^2], {t, 0, 2}] // N (* 7.847 *) Specifying Real numbers yields the correct result. I can only assume that Wolfram Alpha is performing this calculation with Real numbers as well.


3

For your specific example, the following does what you want: = List plot of {1,2,3,4,5} But in general don't send WolframAlpha inputs as though you're using Mathematica. Just send free-form linguistic input i.e. plain English (or other languages it understands). For example, to plot the Sine function don't type Plot[Sin[x],{x,-3,3}] just type "plot sin ...



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