On Tue, 26 Aug 2008 08:29:33 +0200
"Ondrej Certik" <[EMAIL PROTECTED]> wrote:
>
> On Tue, Aug 26, 2008 at 12:49 AM, William Stein <[EMAIL PROTECTED]> wrote:
> >
> >> BTW, one important warning: ginac and sympycore are missing
> >> assumptions and sympy only has very trivial ones, like positive,
> >> negative, integer, even, odd, etc. This is really important for any
> >> nontrivial things in a CAS and I changes to the core may be needed. I
> >> really want to have assumptions in sympy first before saying -- yes,
> >> this approach to do the core is the best.
> >>
> >> Ondrej
> >
> > Why are assumptions "really important for any nontrivial things in a CAS"?
> > In my entire life I've only ever used assumptions to get maxima to do
> > a symbolic integration. I've never used them in any other context.
> > Can you please educate me on why they are so important? Thanks.
>
> Basically all more nontrivial simplifications. Things like to simplify
> sqrt(1-sin(x)**2) etc. Or acos(cos(x)). All of those are things that
> are needed to be automatic, but only work sometimes, e.g. if 0 < x <
> pi, or -pi/2 < x < pi/2 etc. This is obivously needed in integration
> and in solvers and also just when the user wants to simplify the
> expression. So in particular this is done inside ginac, so ginac need
> some way to handle these. Do you have any ideas how to do it?
Looking briefly at the MMA documentation, I can't find any reference to
a general assumption context, which can be queried to get information
on variables/expressions.
It seems that you can give assumptions only for specific functions,
such as
In[]:= Simplify[ArcCos[Cos[x]],{0<x,x<Pi/2}]
Out[]= x
same goes for Refine, FullSimplify and FunctionExpand (whatever that
is).
As already mentioned in another thread, the automatic evaluation (basic
simplification) in GiNaC is meant to be a cheap operation. MMA doesn't
do automatic simplification of this statement either,
In[]:= Assuming[0<x, Assuming[x<Pi/2 ,ArcCos[Cos[x]]]]
Out[]= ArcCos[Cos[x]]
Cheers,
Burcin
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