Re: 2 Assumptions for one parameter?

*To*: mathgroup at smc.vnet.net*Subject*: [mg128053] Re: 2 Assumptions for one parameter?*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Wed, 12 Sep 2012 02:58:04 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

On 9/11/12 at 2:32 AM, =?ISO-8859-1?Q?Andreas_Talmon_l=27Arm=E9e?= at smc.vnet.net wrote: >What is the right typing to make two assumptions for one parameter? >Something like this: >$Assumptions={a>0&&Element[a,Reals]} either what you have or: $Assumpitions={a>0, Element[a,Reals]} but note, by default Mathematica makes a variable as general as possible. So, since a>0 isn't meaningful for complex a, it follows: $Assumptions={a>0&&Element[a,Reals]} $Assumptions={a>0, Element[a,Reals]} $Assumptions={a>0} all achieve exactly the same thing. >And is there a way to to control my assumptions made for the >parameters I use something like >?a It is unclear to me what you are trying to do here. Setting the value of $Assumptions impacts those functions that look at the value of $Assumptions when you use them but has no effect on the value of other symbols such as a. That is you can do: In[6]:= Clear[a]; $Assumptions = {a > 0}; Simplify@Element[Sqrt[a], Reals] Out[7]= True then assign a value to a that contradicts your assumptions and work with it In[8]:= a = -2; Element[Sqrt[a], Reals] Out[9]= False but this definitely causes problems for functions that look at the value of $Assumptions since now In[10]:= Simplify@Element[Sqrt[a], Reals] Out[10]= True and generates an warning stating one or more assumptions evaluated to False