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Topic: How on Earth?
Replies: 6   Last Post: Sep 12, 2012 3:29 AM

 Messages: [ Previous | Next ]
 Bill Rowe Posts: 1,647 Registered: 3/14/08
Re: 2 Assumptions for one parameter?
Posted: Sep 12, 2012 3:29 AM

On 9/11/12 at 2:32 AM,
=?ISO-8859-1?Q?Andreas_Talmon_l=27Arm=E9e?=@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

Date Subject Author
9/10/12 Chris Arthur
9/10/12 Bob Hanlon
9/11/12 Andreas Talmon l'Armée
9/12/12 Bill Rowe
9/12/12 Bob Hanlon