       Re: using Upset for defining positive real values (Re: Can I get ComplexExpand to really work?)

• To: mathgroup at smc.vnet.net
• Subject: [mg14672] Re: [mg14670] using Upset for defining positive real values (Re: Can I get ComplexExpand to really work?)
• From: "Kevin J. McCann" <kevinmccann at Home.com>
• Date: Sun, 8 Nov 1998 21:15:33 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```My guess is that Solve doesn't "ask" Sign, nor does it do things with
Re,Im. Hence, those functions do not get to tell Solve these things.
Try your Solve below with a "+1", and you will see that solve gives +I,
-I in spite of the Upsets.  I have found that the Upsets are good with
algebraic stuff (load Algebra`ReIm`) and with integrals.  The latter
because of the conditionals that often result in the output.

Kevin

-----Original Message-----
From: Maarten.vanderBurgt at icos.be <Maarten.vanderBurgt at icos.be> To:
mathgroup at smc.vnet.net
Subject: [mg14672] [mg14670] using Upset for defining positive real values (Re:
Can I get ComplexExpand to really work?)

>
>Hello,
>
>In functions like Solve and Simplify there is no option like the
>Assumptions option in Integrate.
>an alternative to the Assumptions option in Integrate. I thought this
>might work as well for Solve, Simplify etc.
>
>In the example below I want A to be positive real number. I use Upset to
>give A the right properties.
>I was hoping Solve[A^2-1 == 0, A] would come up with the only possible
>solution given that A is a positive real: {A -> 1}. Same for
>Simplify[Sqrt[A^2]]: I would expect the result to be simply A (instead
>of Sqrt[A^2]) when A is set to be positive and real.
>
>Upset does not seem to work here.
>
>1st question: why?
>
>2nd question: is there a way you can introduce simple assumptions about
>variables in order to rule out some solutions or to reduce the number
>of solutions from functions like Solve, or to get a more simple answer
>from manipulation fuctions like Simplify.
>
>In:= Sign[a]^=1;
>         Re[a]^=a;
>         Im[a]^=0;
>In:= ?a
>     "Global`a"
>     Im[a] ^= 0
>     Re[a] ^= a
>     Sign[a] ^= 1
>In:= Solve[a^2-1 == 0, a]
>Out= {{a -> -1},{a -> 1}}
>In := Simplify[Sqrt[a^2]]
>Out= Sqrt[a^2]
>
>
>thanks for any help
>
>Maarten van der Burgt
>
>
>

```

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