Read their TOS: http://www.wolframalpha.com/termsofuse.html, specifically their Attribution and Licensing section.
If you incorporate results from Wolfram Alpha in any work without attribution meeting their standards you will have breached your TOS and they suggest you also will have committed copyright violations and academic plagiarism. If your work is not personal (unshared?) or academic, then they demand you negotiate a license.
Google seems happy to let you know sin(x) is wiggly and send you on your way.
(If you don't see the "play sound" link, refresh the page.)
Edit: Phew, -2 and dropping. I was worried there for a second.
And on top of that, it also gives you the result right there on the page: http://cl.ly/0a3L0K3T2a0E350d300n
Clickable and brings you to wolfram alpha:
zero-click search is an awesome feature of DuckDuckGo
No, I don't see a fast interactive graph when I clicked on that link.
Hopefully WA will do something similar in the near future.
Agreed regards zoom and such.
"Try to pan or zoom the function to a different region. The plotting algorithm detected one of the following:
- Too many asymptotes
- Too many transitions of the function from defined to undefined regions
- Too many points on the graph that might not represent the function value currently due to high volatility"
It looks like can actually detect when their graphing algo starts to break down.
One way is to set a threshold for whether or not to join the dots, if it's above the threshold perform a search between those points to see if they are between the dots or if they diverge, this search can be complicated or simple, google seems to use a fair bit of cpu power when zooming out on tan(x) so I'm guessing they're using a search here rather than some alternative 'clever' induction from the nature of the curve itself.
This would produce a list of X values for which the overall function is not defined. When your pixel plotting passes one or more of those X values, don't draw a line. If you pass several in a single pixel, give up.
Related is also navigation in maps-software. Not many programs do this right even though it's so simple.
It also formats the equations nicely and lets you copy them as PDF. Makes a decent formula editor for Pages (with simple formulas).
Yup, that works.
Not to say it is uncommon to call Stephen Wolfram egotistic, I swear there was a thread about Wolfram remembering Turing and people counting how many times Wolfram mentioned himself but it may have been killed as I can't find it.
(Wolfram on Steve Jobs)