UnitStep bugs remain in ver. 5.01
- To: mathgroup at smc.vnet.net
- Subject: [mg53026] UnitStep bugs remain in ver. 5.01
- From: jackgold at umich.edu
- Date: Mon, 20 Dec 2004 06:34:51 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
I am using Mac OS 10.3 and have just upgraded to ver 5.1. Many versions ago I
took an interest in how Mathematica handles the unit step function. Up until
recently it was an add-on but now (and perhaps earlier) it is a built in
function. One would have expected that some of the minor bugs would have been
removed, but they have not. I record here for your study this particular bug:
UnitStep[x^2]/.x->0 returns 1, as it should.
UnitStep[x^2]//FunctionExpand returns UnitStep[-x]+UnitStep[x]
This is inconsistent with the first (correct) result at x = 0, since
UnitStep[-x]+UnitStep[x]/.x->0 returns 2.
IMO this inconsistency is due to a failure of FunctionExpand. The correct
expansion should contain a term - DiscreteDelta[x] which is zero everywhere
except at x=0 at which point it is -1. The example of the use of Function
Expand in the Help fails for the same reason but this time at x = 2.
I have written Wolfram about this many years ago and did so again yesterday.
The problem in general is this: FunctionExpand[UnitStep["any polynomial"]]
fails at some of the zeros of "any polynomial". For most uses, I suppose this
in a triviality, but one might be able to construct a use for which this error
turns out to be important. Oh well, maybe next year ...
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