make heaviside and step play nicely together.

[kcrisman]

The heaviside built-in function and the step symbolic method are not the same at zero.

sage: heaviside(0)
heaviside(0)
sage: SR(0).step()
1/2

And the documentation seems to indicate that heaviside should be undefined (?) at zero, though it's not definitive.

In addition to reconciling these, we should probably unify notation or something.

Depends on #22838

CC: @mforets @rwst

Component: symbolics

Author: Ralf Stephan

Branch/Commit: bbc921e

Reviewer: Travis Scrimshaw, Marcelo Forets

Issue created by migration from https://trac.sagemath.org/ticket/10070

[kcrisman]

comment:1

See also #10071 for how this would allow step(hold=True) to be evaluated post hoc.

[mforets]

comment:7

the problem is that in many contexts (that is, university courses and books), the heaviside step function is not assigned the value 1/2 at 0, as was the choice in SR(0).step(). if seen as a distribution, there is no need for such choice indeed, since this would be a difference by a set of measure 0.

let me mention in passing that a proper class of distributions with some flesh in it would be a (cool!) feature.

compare to:

• heaviside has a similar behaviour to Mathematica's HeavisideTheta function.

• unit_step has a similar behaviour to Mathematica's UnitStep function.

in sum, this is to suggest:

• writing "See also" blocks, where it is missing
• allowing the possibility to assign a value to heaviside at 0 (as in sympy)