When looking for hardware, I often try to find out if the manufacturer employs open source developers and things like that. I know Canonical has relations with a couple of big computer companies, but who, apart from Canonical, is supporting the community effort directly? Is there a list?
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I know of employees of the following companies who are tasked with improvements to Ubuntu as a primary job responsibility, including maintenance or delivery of software in the archive, bugfixing, and other development work performed on and in Ubuntu. This list is necessarily incomplete, as it is exceedingly likely that many folk have not decided to disclose their employment and/or job responsibilities to me (or I forgot). Some of these may not meet your definition of "big", others are indisputably so.
I am also aware of employees of many other firms who provide publicity or support services (magazine publishers, book publishers, event organisers, on- or off-site systems support services, deployment services, etc.) for Ubuntu or Ubuntu Derivatives (including the remixes typically deployed for pre-installed systems) who consider themselves to be part of the Ubuntu community, although their output is often not in the form of patches or uploads directly to Ubuntu.
Further, there are a number of companies that look favorably on contributions by their employees into Ubuntu, and whose staff hold significant positions within the Ubuntu community, but who have not explicitly tasked their staff with improvements to Ubuntu as a primary responsibility.
Beyond that, there exists a significant number of individual or small consultancies that provide services which sometimes include delivery or improvement of software in Ubuntu or delivery of Ubuntu into some environment, for which necessary modifications are applied directly to Ubuntu. While these are surely not "big", they not infrequently perform services for clients that meet most definitions of "big". As these relationships are typically confidential between the parties concerned, they may necessarily not be listed here.
Additionally, there is the list of companies that have commercial relationships with all those above, with the intent of delivering Ubuntu to users or supporting Ubuntu. While these companies may not be directly funding Ubuntu Development, without their assistance, few of the aforementioned firms would be as interested in funding that development.
Firstly, please correct me if I'm wrong, and understand that English is not my first language.
Firstly, can we define what "big computer companies" are? Are we talking about the "big-ness" like Canonical (whose name is most probably unfamiliar to most people) or big like Intel, AMD/ATI, nVidia (whose name is synonymous to processors and graphic cards respectively).
From what I know, the Ubuntu Project is solely funded by one "big computer company": Canonical. I'm sure there are many other smaller companies and instances funding the project, but most of those are typically donations. I've asked this question many times -- often rephrased to, "how do open source companies make profit?" -- and a majority of people will almost always answer through sponsorships, adverts, merchandise and such.
Open source-promoting companies, like IBM, Intel, Novell, Red Hat, etc., don't particularly focus their funding onto one opensource project, unless its their own, like Intel's MeeGo for example.
Please feel free to criticize my answer; I know there is a strong possibility of something being incorrect there.
Cheers, :)
The twice-yearly Ubuntu Developer Summit (UDS) or yearly Debconf are a location where it is easy to see direct funding for Ubuntu: companies sending their own employees (or for individuals, sending themselves). When you see people from Intel, HP, Dell, … at UDS (or another Linux conference) it's probably a fairly good confirmation that their attendance is being funded to some degree directly by their employer:
launchpad.net/sprints/uds-m/+attendees-csvlaunchpad.net/sprints/uds-n/+attendees-csvlaunchpad.net/sprints/uds-o/+attendees-csvGoogle themselves have hosted UDS twice at their Mountain View campus (2006, 2008). In addition, if you're eating a meal in the evening at UDS and it says "sponsored by Amazon AWS" then it's probably a further indication of contribution (but for practical reasons, the sponsorship likely went via the the conference/summit organisers).
In the case of Ubuntu, it's easier for a company to approach Canonical Ltd because Canonical have the best contacts and know-how when it comes to the Ubuntu project.
There is a list of OEMs who submit their hardware for certification here.
Individual components are also certified here.
There is also a list of Ubuntu "partners" here. These are software or service providers who specifically support Ubuntu. It's a big list ;-)
Ubuntu certification is very thorough, as detailed on the official page here and Dell's blog here.
While these may not be purely financial donations to the Ubuntu project, hardware and software certification is far better .. it's really best sort of practical support for Ubuntu you can give IMHO. Who doesn't want to see these logos on the latest cool hardware or software?
Linagora is one of those companies. They count 160 employees and have offices in France, Belgium and the United States.
Their first way of supporting Ubuntu is by writing and publishing documents, scripts and more. See their community website for more info (in French). Their second way of supporting is by contributing to FLOSS code including Ubuntu. All their commitments are even listed on a dedicated site (in English and in French), sorted by project.
A short version of Paul's answer is simply "All of Canonical's customers".
IBM does: http://www-03.ibm.com/linux/community.html