MathGroup Archive 2010

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: How to assume that a function is positive?


On 30 Nov, 10:04, 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

This fact is even more puzzling after observing the following results:

Clear[f];

Simplify[Sqrt[f[x]^2], f[x] > 0]
Out[]= f[x]

Simplify[Sqrt[f[x]^2],  !f[x] < 0]
Out[]= f[x]


f/:f[_]>0=True;

Simplify[Sqrt[f[x]^2], f[x]>0]
Out[]= Sqrt[f[x] ^2]


f/:f[_]<0=False;

Simplify[Sqrt[f[x]^2],  !f[x] < 0]
Out[]= Sqrt[f[x] ^2]


In other terms, not only any way to impose the positivity of f appears
to fail, but it also *breaks* Mathematica (8) capability to perform
the simplifications!

Can anyone explain this behavior?

ADL


  • Prev by Date: Re: basic pattern matching
  • Next by Date: Re: basic pattern matching
  • Previous by thread: Re: How to assume that a function is positive?
  • Next by thread: Re: How to assume that a function is positive?