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I want to plot the following:

Plot[{Sqrt[x], Sum[HeavisideTheta[x - n^2], {n, 1, Floor[x]}]}, {x, 0,50}]

which looks like

sum of heaviside step functions

Is there a simple way to get this same plot with vertical lines at the jumps between steps?

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  • $\begingroup$ I'm not sure what happened but I was messing around and suddenly the steps appeared, I'm not sure why, the code is exactly the same, but now it is throwing this error: Plot::exclul: {Sin[\[Pi] Re[x]]-0,Sin[\[Pi] Im[x]]-0,Im[-n^2+x]-0,(-n^2+x)-0} must be a list of equalities or real-valued functions. $\endgroup$ – Kai Dec 3 '17 at 3:10
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See the option Exclusions:

Plot[{Sqrt[x], Sum[HeavisideTheta[x - n^2], {n, 1, Floor[x]}]}, {x, 0, 50},
 Exclusions -> None]

Mathematica graphics

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The only easy method I'm aware of is to make it a parametric plot instead.

wrapper[f_] := {#1, f[#1]} &;
ParametricPlot[
    {wrapper[Sqrt][x], 
    wrapper[Sum[HeavisideTheta[# - n^2], {n, 1, Floor[#]}] &][x]}
    , {x, 0, 50}
]

Produces the output:

enter image description here

I also receive this error you mention in your comment. I don't understand why; maybe ParametricPlot thinks the functions may not have real values. If you're confident there's no problem with your input, you can wrap ParametricPlot in Quiet[ ... , ParametricPlot:exclul to prevent this message from appearing.

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