**GSoC 2020 Week-4**

The first phase of GSoC is over. We can now integrate the scalar or vector field over a parametrically defined region.

The PR for `ParametricIntegral`

class has been merged. In my last post, I mentioned about a weird error. It turns out that I was importing `pi`

as a symbol instead of as a number. Due to this, the expressions were returned unevaluated causing tests to fail.

## The route ahead

I had a detailed discussion with Francesco about the route ahead. My plan has drifted from my proposal because we have decided not to implement new classes for special regions like circles and spheres. The geometry module already has classes to represent some of these regions. We have decided to use these classes.

Francesco reminded me that we have to complete the documentation of these changes. I was planning to complete the documentation in the last phase. But I will try completing it soon as I may forget some details.

We also discussed adding support to perform integral transformation using Stoke’s and Green’s theorem. In many cases, such transformation can be useful but adding them may be outside the scope of this project.

I have convinced Francesco on adding classes to represent implicitly defined regions. It might be the most difficult part of the project but hopefully, it will be useful to SymPy users.

### Next week’s goal

My next week’s goal is to make a PR for adding suppor to integrate over objects of the geometry module.