Lab 5 - Quaternions

1. Open your homework 4 in IntelliJ (or other IDE, so that it can be changed), be sure that unit testing works.
2. If you do not have the latest version of your work on bitbucket (or github), create a commit and push it. If necessary, refer to the materials of the first lab. The test file QuaternionTest.java must also be included in the version control.
3. The teacher will assign you a partner for this lab.
4. Show that all the tests pass on your computer (if necessary, check the materials of the first lab), that the work has been submitted by the deadline and the teachers comments (must contain "ok"). The partner does the same
5. Divide the roles: developer and tester. One partner ("developer") is responsible for the file Quaternion.java, the other partner ("tester") is responsible for the file QuaternionTest.java.
6. Development: Add a new method pow for raising a quaternion to a given integer power (by multiplication):
          q.pow(0) is 1: new Quaternion(1, 0, 0, 0)
          q.pow(1) is equal to (but not identical to) q
          q.pow(-1) is q.inverse()
          q.pow(n) is defined for n > 1 by the rule: q.times(q.pow(n-1))
          q.pow(-n) is q.pow(n).inverse()
7. Testing: Write about 5-7 test cases for pow that cover all the rules in the previous item and add them to existing tests (use the junit4 framework, see the test file QuaternionTest.java for an example). Zero quaternion on negative power must raise an exception, zero on power zero is 1. Check that pow(1) creates a new quaternion.
   
8. Share your result with the partner and test the new solution in both computers.
9. Make a new commit  "Developer: name, Tester: name" and upload it to bitbucket (or github), the partner will do the same with their code. Do this after the testing part is finished.
10. Show the commit, the tests and running examples to the teacher. You can also run tests from the command line if there is a problem with the IDE.
11. Challenge: Extend the valueOf method so that it accepts input with minus signs and abbreviated strings of the form:
    "-1-2i-3j-4k" (does not include plus signs for negative components)
    "-1-2i" means -1-2i+0j+0k (missing some part means that the corresponding component is 0), for example: "-1-2i-3j" means -1-2i-3j+0k and "-1" means -1+0i+0j+0k
    "i" means 0+1i+0j+0k (missing the imaginary part coeficient means that this coeficient is 1), for example "i-j-k" means 0+1i-1j-1k
    
12. The teacher will discuss, ask questions and grade your work.