The Heaviside step function implicitly expands to a piecewise function:
UnitStep[t - 3] // PiecewiseExpand
$$ \begin{cases} 1 & t\geq 3 \\ 0 & \text{True} \\ \end{cases} $$
But the Heaviside step with strict inequalities does not have an implicit expansion:
HeavisideTheta[t - 3] // PiecewiseExpand
$$ \theta (t-3) $$
and the expansion must be given explicitly (Solution from this answer):
% /. {
HeavisideTheta[x_] :> Piecewise[{{1, x > 0}, {0, x < 0}}]
} // PiecewiseExpand
$$ \begin{cases} 1 & t>3 \\ 0 & \text{True} \\ \end{cases} $$
Is this just an oversight in the implementation or is there a more nuanced distinction?
Related:
Converting HeavisideTheta[]s and Sign[]s functions to a single Piecewise[]
D[HeavisideTheta[x], x]
evaluates toDiracDelta[x]
. IfHeavisideTheta
converted to aPiecewise
expression this relation toDiracDelta
would be obscured. $\endgroup$