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Re: Uniform design

  • To: mathgroup at
  • Subject: [mg48107] Re: Uniform design
  • From: ab_def at (Maxim)
  • Date: Thu, 13 May 2004 00:08:47 -0400 (EDT)
  • References: <c7nnc7$dm5$>
  • Sender: owner-wri-mathgroup at

Here's a couple of more 'mathematical' examples along the same lines:

0*Interval[{0, Infinity}]
Infinity*Interval[{0, Infinity}]
Interval[{0, 0}]*Interval[{0, Infinity}]
Interval[{0, Infinity}]*Interval[{0, Infinity}]

Infinity::indet: Indeterminate expression 0*Infinity encountered.

Interval[{0, Indeterminate}]

Interval[{0, Infinity}]

Infinity::indet: Indeterminate expression 0*Infinity encountered.

Interval[{0, Indeterminate}]

Interval[{0, Infinity}]

This also leads to the more general question of whether we need to
distinguish between open and closed intervals or the endpoints can
simply be neglected. But in any case there should be one uniform
convention for dealing with such issues, otherwise we won't be able to
get consistent results:

Interval[{0, Infinity}]*(x*Interval[{0, Infinity}] + 1) // D[#, x]&
Interval[{0, Infinity}]*(x*Interval[{0, Infinity}] + 1) // Expand //
D[#, x]&

Infinity::indet: Indeterminate expression 0*Infinity encountered.

x*Interval[{0, Indeterminate}] + Interval[{0, Infinity}]

Interval[{0, Infinity}]

Also, it's strange that Solve accepts intervals (Mathematica Help for
Interval even gives such an example), but doesn't really support them:

Solve[1/(x - 1) == Interval[{-1, 1}]]

{{x -> Interval[{-Infinity, Infinity}]}}

Not much point in treating this equation as Solve[1/(x-1)==a,x] and
giving incorrect result.

Another question is related to Laplace transform. Mathematica mixes
the use of generalized functions with formulas like L[f']=p*F(p)-f(0),
which are only valid for ordinary functions. Because of this, we get
results like the following:

LaplaceTransform[f'[t], t, p] /. f -> UnitStep


Maxim Rytin
m.r at

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