Re: Symbolic expand function doesn't always do anything

[Benjamin Sapp]

Paul, 

What the best way of doing that?  Here's an idea,  

double d;          
int id;  
if (ceil(d) == floor(d)) {
        id = (int)d; 
        number = GiNaC::numeric(id); 
        // printf("it's an integer: %d\n", id); 
}else{
        // printf(" not an integer: %f\n", d); 
        number = GiNaC::numeric(d); 
}

The problem with this is what happens when we get very large numbers? 
If the number is large enough then the number will always fall on an
integer value...  right?  Should we also check how large the value is
and only do it for small numbers?  where is that cutoff? (The 2^53 you
referred to maybe?)  Maybe I need to go look at the standard.  Is that
the only other gotcha?  I don't feel confident enough in my knowledge of
floating point representation to say for sure.  

Thanks, 
Ben.    
 
On Mon, 2004-09-13 at 19:36, Paul Kienzle wrote:
> Ben,
> 
> My understanding of IEEE 754 is that integers are exactly representable 
> up
> to about 2^53.  Couldn't the symbolic package treat integer values as
> exact vpa values, and only force the user to mark the cases where the
> value is meant to be an approximation?  I think this would capture more
> of the common cases correctly.
> 
> - Paul
> 
> 
> On Sep 13, 2004, at 12:01 PM, Benjamin Sapp wrote:
> 
> > Hi,
> >
> > Indeed, you are correct it is an octave integration peculiarity.  You
> > see, octave interprets any thing that can be a number as a double
> > first.  Then, when a double is used in a symbolic expression it is
> > converted to the exact form like in ginsh.  By that time it's too late
> > because a 1 is already double approximation of a 1 rather than exactly 
> > a
> > 1.   You can perform your example from ginsh in octave by surrounding
> > each exact number with quotes and vpa().  For example on my computer:
> >
> > octave:47> expand( (x-vpa("1"))^vpa("3"))
> > ans =
> >
> > -1+x^3-3*x^2+3*x
> >
> > It's a bit cumbersome but I don't think there's a better solution.
> >
> > Good luck,
> > Ben.
> >
> > On Mon, 2004-09-13 at 08:28, edA-qa mort-ora-y wrote:
> >> I'm using the OctaveForge integration of the GiNaC symbolic library 
> >> and
> >> having some trouble using the "expand" function.
> >>
> >> I want is to perform the polynomial expansion:
> >>
> >>    >x = sym( "x" )
> >>    >expand( (x-1)^2 )
> >>    ans = (x-1)^2
> >>
> >>    I want to get
> >>    ans = 1 + x^2 - 2*x
> >>
> >> If you do this form, it works:
> >>    >expand( (x-1) * (x-1) )
> >>    ans = 1.0+x^2-(2.0)*x
> >>
> >> Using ginsh with expand produces the desired results, so I'm assuming 
> >> it
> >> is an Octave integration peculariaty:
> >>
> >>    ginsh>  expand( (x-1)^3 );
> >>    -1-3*x^2+x^3+3*x
> >>
> >
> >
> >
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