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WolframAlpha["query"] - https://reference.wolfram.com/language/ref/WolframAlpha.html

Free-form input - https://reference.wolfram.com/language/workflow/EnterFreeFormInput.html

For example:

WolframAlpha["Solve[x^2+5x+6==0, x]"]

and

= and after

Solve[x^2+5x+6==0, x]

Both have have pretty similar output (cannot include it here because of sophisticated formatting).

Questions:

  1. Does the both use WolframAlpha?
  2. Is there any difference between them? If yes, what is the difference?
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  • $\begingroup$ They both should be using wolfram alpha as of version 8. See "With the new Mathematica 8, you can access the Wolfram|Alpha engine directly from within Mathematica. Inside a Mathematica notebook document, just type == at the beginning of a line; you’ll get an orange Spikey icon indicating that Mathematica is ready to perform a Wolfram|Alpha query. " blog.wolframalpha.com/2010/12/06/… $\endgroup$
    – Nasser
    Feb 21, 2020 at 20:17

1 Answer 1

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Here is the summary from original M8 release page:

enter image description here

This guide should also be useful: Free-Form & External Input. While both things you mentioned are a part of integration of Wolfram|Alpha (W|A) and Wolfram Language (WL), the difference is in the interface, goal and type of output they give you. Free-form input (FFI) via CTRL+= is great, for example, for quick-typing of FFI and its quick automatic conversion into entities, units, and other Wolfram Knowledgebase things. Hence CTRL+= is great for quick discovering of various numerous built-in quantities and other bits of knowledge that is so large it is very hard to grasp via some general overview. CTRL+= attempts to give the best semantic interpretation of the specified free-form string as a WL expression and can be used inside other WL expressions. In that sense it is a quick-interface embodiment of its programatic form SemanticInterpretation (do not confuse with Interpreter, which is another wonderful related function working a bit differently). As they seek a WL expression as an output you can quickly test the boundaries and see the difference with WolframAlpha[...] function. For instance, try this out:

In[]:=SemanticInterpretation["tell me a joke"]
Out[]=$Failed

and similarly:

enter image description here

As expected no WL expression form is found as there is none to find. On the other hand behold

enter image description here

This works as full W|A output is returned. WolframAlpha[...] interface embodiment is double-equal tap:

enter image description here

WolframAlpha[...] is great for controlled programmatic yield of various outputs, for instance

data= WolframAlpha["sun spots",
{{"SunspotsFullTimeSeries:SpaceWeatherData",1},"TimeSeriesData"}];
DateListPlot[data]

enter image description here

the code for which is automatically generated as explained HERE

enter image description here

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    $\begingroup$ Thank you for great answer! Also "SemanticInterpretation" link (or maybe it should be inline code?) is broken. $\endgroup$
    – vasili111
    Feb 23, 2020 at 15:43
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    $\begingroup$ @vasili111 thank you, fixed thee link. $\endgroup$
    – Vitaliy Kaurov
    Feb 23, 2020 at 15:49

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