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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)
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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




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