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Re: How to assume that a function is positive?

• To: mathgroup at smc.vnet.net
• Subject: [mg114311] Re: How to assume that a function is positive?
• From: Valeri Astanoff <astanoff at gmail.com>
• Date: Tue, 30 Nov 2010 06:23:06 -0500 (EST)
• References: <id2emr$d88$1@smc.vnet.net>

On Nov 30, 10:04 am, Sam Takoy <sam.ta... at yahoo.com> wrote:
> Hi,
>
> Who do I let Mathematica know that a function f is positive for all
> arguments? For example, how do I make the following work (I think my
> intention is clear):
>
> Assuming[f[x] > 0, (f[x + y]^2)^(1/2) // Simplify]
>
> Many thanks in advance,
>
> Sam

Good day,

You could use this [laborious!] trick :

In[1]:= pos[fun_, ex_] := And @@ (fun[#] > 0 & /@
 (Identity @@@ Extract[ex, Position[ex, fun[__]] ]) )

In[2]:= z = (f[x + y]^2)^(1/2) + (f[x]^2)^(1/2);

In[3]:= Assuming[pos[f, z], z // Simplify]

Out[3]= f[x] + f[x + y]

hth

--
Valeri