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

*To*: mathgroup at smc.vnet.net*Subject*: [mg14711] Re: using Upset for defining positive real values (Re: Can I get ComplexExpand to really work?)*From*: Rolf Mertig <rolf at mertig.com>*Date*: Tue, 10 Nov 1998 01:21:03 -0500*Organization*: Mertig Research & Consulting*References*: <720tjl$1vs@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Maarten.vanderBurgt at icos.be wrote: > > 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? Because Simplify and Solve are obviously not written to recognize Upset values. > > 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[3]:= Solve[a^2-1 == 0, a] > Out[4]= {{a -> -1},{a -> 1}} > In[5] := Simplify[Sqrt[a^2]] > Out[5]= Sqrt[a^2] > Some possibilities are: In[1]:= PosSolve[eqs_, vars_] := Select[Solve[eqs, vars], Last[Last[#]] > 0&] In[2]:= PosSolve[a^2-1 == 0, a] Out[2]= {{a -> 1}} In[3]:= PowerExpand[Sqrt[a^2]] Out[3]= a -- Dr. Rolf Mertig Mertig Research & Consulting Mathematica training and programming Development and distribution of FeynCalc Amsterdam, The Netherlands http://www.mertig.com