GSoC : This week in SymPy #7

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

  Progress of Week 7

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
• PR #9666 : Equate S.Complexes with ComplexPlane(S.Reals*S.Reals)
• PR #9628 : [WIP] Make invert_real more robust
• PR #9587 : Add Linsolve Docs
• PR #9500 : Documenting solveset

That’s all for now, looking forward for week #8. :grinning: