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MathGroup Archive 1998

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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.
>In a recent message ([mg14634]) Kevin McCann(?) suggested usign Upset as
>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[1]:= Sign[a]^=1;
>         Re[a]^=a;
>         Im[a]^=0;
>In[2]:= ?a
>     "Global`a"
>     Im[a] ^= 0
>     Re[a] ^= a
>     Sign[a] ^= 1
>In[3]:= Solve[a^2-1 == 0, a]
>Out[4]= {{a -> -1},{a -> 1}}
>In[5] := Simplify[Sqrt[a^2]]
>Out[5]= Sqrt[a^2]
>
>
>thanks for any help
>
>Maarten van der Burgt
>
>
>



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