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

*To*: mathgroup at smc.vnet.net*Subject*: [mg14670] using Upset for defining positive real values (Re: Can I get ComplexExpand to really work?)*From*: Maarten.vanderBurgt at icos.be*Date*: Sat, 7 Nov 1998 02:10:27 -0500*Sender*: owner-wri-mathgroup at wolfram.com

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 ___________________________________________________________________________ ____ Maarten van der Burgt R&D Department ICOS Vision Systems Esperantolaan 9 B-3001 Leuven Belgium tel. + 32 16 398220 direct + 32 16 398316 fax. + 32 16 400067 e-mail: maarten.vanderburgt at icos.be ___________________________________________________________________________ ____