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The following takes you step-by-step. These instructions assume you're working with trunk. If you're working with a different version of SAMigo (like, say 2-7-x), just make sure that the version of SAMigo you checkout and the version Sakai thinks it's using agree. Otherwise, Sakai will keep using it's vanilla version and ignore your custom version and you won't see any changes!
1. Download samigo-trunk
cd samigo/trunk
mvn clean install
The above step puts samigo 2.8-SNAPSHOT into your local repo. You should see the .war file in /samigo-app. You should see an assembly .zip in samigo-assembly (among other samigo stuff).
2. Build sakai-trunk
mvn clean install -Dmaven.test.skip=true sakai:deploy
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So the Sakai core-deploy pom handles the Samigo deployment. So in step 1 above you do not need to do mvn clean install sakai:deploy from samigo-trunk to get Samigo into Tomcat before building and deploying Sakai.
3. Start Tomcat
Once, you have Samigo deploying correctly locally, you might want to use the -o param to tell Maven not to look beyond your local repo (which implies that you need to make sure it is fully stocked with required artifacts first).
mvn -o clean install -Dmaven.test.skip=true sakai:deploy
4. Modifying Samigo
So assuming you have Samigo trunk deploying properly to Tomcat I'll assume you want to edit the code. Easy enough, edit it and perform a mvn clean install sakai:deploy to update your local samigo artifacts as well as deploy samigo to Tomcat. I don't think you will need to delete the existing samigo artifacts in Tomcat beforehand. Then stop and restart Tomcat.
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You may want to consider setting up your own external maven repo to store your institutional artifacts (if one does not already exist).
5. Gotcha: signing the audio-jar (specific to SAMigo, not relevant for other indie releases)
If you don't already know, SAMigo's audio does need to be signed. As of 2.7.x, the audio jar can be signed as part of the build process. HOWEVER, if you are building SAMigo seperately, as these instructions have you do, then it won't get signed and you need to do it the old-fashioned way. Detailed instructions are here: http://confluence.sakaiproject.org/display/SAM/2.6+Release+Notes
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