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GSoC 2018: Week 6

Here is the brief work done for rubi in the 6th week of GSoC period.

Last week almost 70 % of the miscellaneous algebra was tested. In the start of the week, the miscellaneous algebra testing was completed. The miscellaneous algebra test cases have been pushed in this PR.

After this, I moved on to load exponential rules and test them. While loading the exponential rules, there were some parsing issues. Those were fixed. On start of the testing, it was found that some integrals depend upon the logarithmic and special_function rules. Those too needed to be loaded. There were some undefined or wrongly defined utility_functions like `CancelCommonFactors`, `Gamma (gammainc)`, `PolyGamma`, `ProductLog` and few more small functions. These didn't take much time. I fixed all these.

Soon I realised a major issue of `exp` and `Pow`. Sympy doesn't identify exp as Pow. The rubi rules are defined in such a way that exp needs to be realised as Pow. I tried to process an expression to replace exp with Pow. These are the major methods I tried :
  • Pow(E, z, evaluate=False) . This does not work well, an expression containing Mul is evaluated to exp. I tried to fix it. I found that `flatten` of Mul causes the evaluation. I found the code messy. These can be solved but requires more time.
  • Pow(Dummy('E', z, evaluate=False) .This was suggested by Aaron. The matching part has no issues in this. But functions which use the property of `E` does not work properly. Like `Log(E)` should evaluate to 1.
  • Pow(UnevaluatedExpr(E), z) . In this the matching was as expected. I modified `Log` as `return log(z).doit()` . But then also there were some issues. I made a new subclass `rubi_unevaluated_expr`. To solve the commutative issue, I defined a property in this new subclass.
I think the last one is the best solution for now. Another issue was some rules which caused recursion errors like one in the image 

To solve it I checked that if last 5 rules applied are same then return a Function `Integrate` and replace it at last while returning. This works fine.

In this week, I was unable to do much testing. But I am sure the upcoming week will be better in this respect. I have tested a small part of exponential rules. In the upcoming week, I will try to finish exponential rules within 2-3 days and soon move to logarithmic rules. 


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We completed the testing of logarithmic test cases. Some of the tests are failing as they depend on trigonometric rules. The rules and tests have been updated in this PR.

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Then I moved on to implementing appellf1 in sympy. Progress can be seen in this PR.

We will be updating our utility_functions to the latest version of RUBI.