# GSoC : This week in SymPy #7

Open Source · GSoC · SymPyHi there! It’s been seven weeks into GSoC and second half has started now. Here is the Progress so far.

### **Progress of Week 7**

</br>
This week I Opened #9628, which is basically an attempt to make `solveset`

more robust, as I mentioned in my last post.
The idea is to tell the user about the domain of solution returned.

Now, It makes sure that n is positive, in the following example:

```
In [3]: x = Symbol('x', real=True)
In [4]: n = Symbol('n', real=True)
In [7]: solveset(Abs(x) - n, x)
Out[7]: Intersection([0, oo), {n}) U Intersection((-oo, 0], {-n})
```

Otherwise it will return an `EmptySet()`

```
In [6]: solveset(Abs(x) - n, x).subs(n, -1)
Out[6]: EmptySet()
```

Earlier:

```
In [12]: solveset(Abs(x) - n, x)
Out[12]: {-n, n}
```

So, for this to happen, we needed to make changes in the `invert_real`

:

```
if isinstance(f, Abs):
g_ys = g_ys - FiniteSet(*[g_y for g_y in g_ys if g_y.is_negative])
return _invert_real(f.args[0],
Union(g_ys, imageset(Lambda(n, -n), g_ys)), symbol)
Union(imageset(Lambda(n, n), g_ys).intersect(Interval(0, oo)),
imageset(Lambda(n, -n), g_ys).intersect(Interval(-oo, 0))),
symbol)
```

So, we applied set operations on the invert to make it return non-EmptySet only when there is a solution.

### Now For more Complex Cases:

For the following case:

```
In [14]: invert_real(2**x, 2 - a, x)
Out[14]: (x, {log(-a + 2)/log(2)})
```

For the invert to be real, we must state that `a`

belongs to the Interval `(-oo, 2]`

otherwise it would be complex, but no set operation on `{log(-a + 2)/log(2)}`

can make the interval of `a`

to be in `(-oo, 2]`

.

Although, it does returns an `EmptySet()`

on substituting absurd values:

```
In [23]: solveset(2**x + a - 2, x).subs(a, 3)
Out[23]: EmptySet()
```

So, we need not make any changes to the `Pow`

handling in `invert_real`

& It’s almost done now, except for a couple of TODO’s:

- Document new changes
- Add More tests

Though, I will wait for final thumbs up from @hargup, regarding this.

**from __future__ import plan** Week #7:

This week I plan to complete PR #9628 & get it Merged & start working on replacing old `solve`

in the code base with `solveset`

.

**$ git log**

Below is the list of other PR’s I worked on:

PR #9671 : Simplify `ComplexPlane({x}*{y})`

to `FiniteSet(x + I*y)`

PR #9668 : Support solving for Dummy symbols in linsolve

</br>
PR #9666 : Equate S.Complexes with `ComplexPlane(S.Reals*S.Reals)`

PR #9628 : [WIP] Make invert_real more robust

</br> PR #9587 : Add Linsolve Docs

</br>
PR #9500 : Documenting `solveset`

</br> That’s all for now, looking forward for week #8. :grinning: