If I have the url to a page, how would I obtain the Infobox information on the right using MediaWiki webservices?
How to get the Infobox data from Wikipedia
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I'd use the wikipedia (wikimedia) API. You can get data back in JSON, XML, php native format, and others. You'll then still need to parse the returned information to extract and format the info you want, but the info box start, stop, and information types are clear.
Run your query for just rvsection=0, as this first section gets you the material before the first section break, including the infobox. Then you'll need to parse the infobox content, which shouldn't be too hard. See en.wikipedia.org/w/api.php for the formal wikipedia api documentation, and www.mediawiki.org/wiki/API for the manual.
Run, for example, the query: http://en.wikipedia.org/w/api.php?action=query&prop=revisions&rvprop=content&format=xmlfm&titles=fortran&rvsection=0
Another great MediaWiki parser is mwparserfromhell.
In [1]: import mwparserfromhell
In [2]: import pywikibot
In [3]: enwp = pywikibot.Site('en','wikipedia')
In [4]: page = pywikibot.Page(enwp, 'Waking Life')
In [5]: wikitext = page.get()
In [6]: wikicode = mwparserfromhell.parse(wikitext)
In [7]: templates = wikicode.filter_templates()
In [8]: templates?
Type: list
String Form:[u'{{Use mdy dates|date=September 2012}}', u"{{Infobox film\n| name = Waking Life\n| im <...> critic film|waking-life|Waking Life}}', u'{{Richard Linklater}}', u'{{DEFAULTSORT:Waking Life}}']
Length: 31
Docstring:
list() -> new empty list
list(iterable) -> new list initialized from iterable's items
In [10]: templates[:2]
Out[10]:
[u'{{Use mdy dates|date=September 2012}}',
u"{{Infobox film\n| name = Waking Life\n| image = Waking-Life-Poster.jpg\n| image_size = 220px\n| alt =\n| caption = Theatrical release poster\n| director = [[Richard Linklater]]\n| producer = [[Tommy Pallotta]]<br />[[Jonah Smith]]<br />Anne Walker-McBay<br />Palmer West\n| writer = Richard Linklater\n| starring = [[Wiley Wiggins]]\n| music = Glover Gill\n| cinematography = Richard Linklater<br />[[Tommy Pallotta]]\n| editing = Sandra Adair\n| studio = [[Thousand Words]]\n| distributor = [[Fox Searchlight Pictures]]\n| released = {{Film date|2001|01|23|[[Sundance Film Festival|Sundance]]|2001|10|19|United States}}\n| runtime = 101 minutes<!--Theatrical runtime: 100:40--><ref>{{cite web |title=''WAKING LIFE'' (15) |url=http://www.bbfc.co.uk/releases/waking-life-2002-3|work=[[British Board of Film Classification]]|date=September 19, 2001|accessdate=May 6, 2013}}</ref>\n| country = United States\n| language = English\n| budget =\n| gross = $3,176,880<ref>{{cite web|title=''Waking Life'' (2001)|work=[[Box Office Mojo]] |url=http://www.boxofficemojo.com/movies/?id=wakinglife.htm|accessdate=March 20, 2010}}</ref>\n}}"]
In [11]: infobox_film = templates[1]
In [12]: for param in infobox_film.params:
print param.name, param.value
name Waking Life
image Waking-Life-Poster.jpg
image_size 220px
alt
caption Theatrical release poster
director [[Richard Linklater]]
producer [[Tommy Pallotta]]<br />[[Jonah Smith]]<br />Anne Walker-McBay<br />Palmer West
writer Richard Linklater
starring [[Wiley Wiggins]]
music Glover Gill
cinematography Richard Linklater<br />[[Tommy Pallotta]]
editing Sandra Adair
studio [[Thousand Words]]
distributor [[Fox Searchlight Pictures]]
released {{Film date|2001|01|23|[[Sundance Film Festival|Sundance]]|2001|10|19|United States}}
runtime 101 minutes<!--Theatrical runtime: 100:40--><ref>{{cite web |title=''WAKING LIFE'' (15) |url=http://www.bbfc.co.uk/releases/waking-life-2002-3|work=[[British Board of Film Classification]]|date=September 19, 2001|accessdate=May 6, 2013}}</ref>
country United States
language English
budget
gross $3,176,880<ref>{{cite web|title=''Waking Life'' (2001)|work=[[Box Office Mojo]] |url=http://www.boxofficemojo.com/movies/?id=wakinglife.htm|accessdate=March 20, 2010}}</ref>
Don't forget that params are mwparserfromhell objects too!
Best Answer
Use the Mediawiki API through this Python library: https://github.com/siznax/wptools
Usage:
Output: