Summation with Piecewise not computed

[asmeurer]

Based on https://stackoverflow.com/questions/46966198/how-to-set-index-as-variables. I believe the loops reduce to

>>> summation(Piecewise((a_x**2 + a_x, (j**2 - j > 1) & (k/2 > 20)), (0, True)), (j, 0, 1000-1), (k, 0, 10000-1), (i, 0, 10000-1))
Sum(Piecewise((a_x**2 + a_x, (k/2 > 20) & (j**2 - j > 1)), (0, True)), (j, 0, 999), (k, 0, 9999), (i, 0, 9999))

which doesn't evaluate or simplify at all. Even if you replace a_x with a number it doesn't evaluate

>>> summation(Piecewise((a_x**2 + a_x, (j**2 - j > 1) & (k/2 > 20)), (0, True)), (j, 0, 1000-1), (k, 0, 10000-1), (i, 0, 10000-1)).subs(a_x, 2).doit()
Sum(Piecewise((6, (k/2 > 20) & (j**2 - j > 1)), (0, True)), (j, 0, 999), (k, 0, 9999), (i, 0, 9999))
>>> summation(Piecewise((a_x**2 + a_x, (j**2 - j > 1) & (k/2 > 20)), (0, True)), (j, 0, 1000-1), (k, 0, 10000-1), (i, 0, 10000-1)).subs(a_x, 2).evalf()
Sum(Piecewise((6, (k/2 > 20) & (j**2 - j > 1)), (0, True)), (j, 0, 999), (k, 0, 9999), (i, 0, 9999))

The answer on the SO post claims it should be 995900780000*(a_x**2 + a_x), which I have not verified.

[smichr]

Ahh. piecewise_fold gets this wrong, too, because it doesn't consider the interaction between the summation and the conditions.

[smichr]

Seems to me it should reduce to

summation(a_x**2 + a_x, (j, 2, 1000-1), (k, 41, 10000-1), (i, 0, 10000-1))
99390820000*(a_x**2 + a_x)

[vishalg2235]

Summation limits of 'j' is limiting to total 100 iterations. like, it is computing for (j,0,99),(j,1,100),(j,10,109) and not computing for (j,0,100),(j,10,110) where 'j' iterations are going more than 100 times.

>>>summation(Piecewise((a_x**2 + a_x, (j**2 - j > 1) & (k/2 > 20)), (0, True)), (j, 0, 100-1), (k, 0, 10000-1), (i, 0, 10000-1))
9759820000*a_x**2 + 9759820000*a_x
>>>summation(Piecewise((a_x**2 + a_x, (j**2 - j > 1) & (k/2 > 20)), (0, True)), (j, 0, 1000-1), (k, 0, 10000-1), (i, 0, 10000-1))
Sum(Piecewise((a_x**2 + a_x, (k/2 > 20) & (j**2 - j > 1)), (0, True)), (j, 0, 999), (k, 0, 9999), (i, 0, 9999))
>>>summation(Piecewise((a_x**2 + a_x, (j**2 - j > 1) & (k/2 > 20)), (0, True)), (j, 0, 101-1), (k, 0, 10000-1), (i, 0, 10000-1))
Sum(Piecewise((a_x**2 + a_x, (k/2 > 20) & (j**2 - j > 1)), (0, True)), (j, 0, 100), (k, 0, 9999), (i, 0, 9999))
>>> summation(Piecewise((a_x**2 + a_x, (j**2 - j > 1) & (k/2 > 20)), (0, True)), (j, 1, 101-1), (k, 0, 10000-1), (i, 0, 10000-1))
9859410000*a_x**2 + 9859410000*a_x
>>> summation(Piecewise((a_x**2 + a_x, (j**2 - j > 1) & (k/2 > 20)), (0, True)), (j, 10, 111-1), (k, 0, 10000-1), (i, 0, 10000-1))
Sum(Piecewise((a_x**2 + a_x, (k/2 > 20) & (j**2 - j > 1)), (0, True)), (j, 10, 110), (k, 0, 9999), (i, 0, 9999))
>>> summation(Piecewise((a_x**2 + a_x, (j**2 - j > 1) & (k/2 > 20)), (0, True)), (j, 10, 110-1), (k, 0, 10000-1), (i, 0, 10000-1))
9959000000*a_x**2 + 9959000000*a_x
>>> summation(Piecewise((a_x**2 + a_x, (j**2 - j > 1) & (k/2 > 20)), (0, True)), (j, 10, 120-1), (k, 0, 10000-1), (i, 0, 10000-1))
Sum(Piecewise((a_x**2 + a_x, (k/2 > 20) & (j**2 - j > 1)), (0, True)), (j, 10, 119), (k, 0, 9999), (i, 0, 9999))

Also seems to me it must reduce to

>>>summation(a_x**2 + a_x, (j, 2, 1000-1), (k, 42, 10000-1), (i, 0, 10000-1))
99380840000*a_x**2 + 99380840000*a_x

because :

>>> k = 41
>>> k/2
20

[vishalg2235]

ping @asmeurer @smichr

[BananaOrbit]

I'm not sure if this is related but there is also an issue with plotting Piecewise. #13320

[smichr]

dup of #12631