       Simplify with If and UnitStep

• To: mathgroup at smc.vnet.net
• Subject: [mg31286] Simplify with If and UnitStep
• From: gg at hugo.doemaarwat.nl (Hugo Buddelmeijer)
• Date: Fri, 26 Oct 2001 04:28:37 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```I finally understand how I can create a 'piecewise' function with
mathematica with UnitStep, but somewhere further in my calculations it
doesn't Simplify it at all.
This is what I've got as a result now (I removed the ugly pieces

If[ 1/(32*t^0.3) > 1 && t^(-0.3) > 32,
62000*UnitStep[-0.1 + 32]*UnitStep[-0.1 + 1/t^0.3],
Integrate[M^2.55*UnitStep[M - 0.1, -M + 32],
{M, 0.1, 1/t^0.3}]]

There are a couple of annoying things here that I can't solve...

1) On the first line there are 2 conditions which are exactly the same
only the 32 is on the other site of the >, how can I turn this into
just 1 condition? (preferable the latter)

2) On the second line there is a UnitStep[-0.1+32] which is certainly
1. The second UnitStep is also 1 because the last part there is always
larger then 32, that's what the If statement implies. How can I get
these UnitStep's to be 1?

3) On the 3th and 4th line it Integrate's over M in between 0.1 and a
number lower then 32 (as the If statement implies), so the last
UnitStep should also be 1.

So what I want to see is actualy

If[t^(-0.3) > 32, 62000, -0.00007939 + 0.281/t^1.065]

Which looks way nicer then the upper statement, but essentially the
same. (I rounded the numbers somewhat, but you get the idea.)

If anyone can give me a hint about what I should do I will be very
gratefull :-)

Groetjes,
Hugo

```

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