
From:  Paul Kienzle 
Subject:  Re: Symbolic expand function doesn't always do anything 
Date:  Tue, 14 Sep 2004 20:32:14 0400 
How about: if (floor(d) == d && d+1 != d) number = GiNaC::numeric(int(d)); else number = GiNaC::numeric(d);  Paul On Sep 14, 2004, at 11:22 AM, Benjamin Sapp wrote:
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 thatthe only other gotcha? I don't feel confident enough in my knowledge offloating point representation to say for sure. Thanks, Ben. On Mon, 20040913 at 19:36, Paul Kienzle wrote:Ben,My understanding of IEEE 754 is that integers are exactly representableup 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 thevalue is meant to be an approximation? I think this would capture moreof 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 isconverted 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 exactlya 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( (xvpa("1"))^vpa("3")) ans = 1+x^33*x^2+3*x It's a bit cumbersome but I don't think there's a better solution. Good luck, Ben. On Mon, 20040913 at 08:28, edAqa mortoray 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( (x1)^2 ) ans = (x1)^2 I want to get ans = 1 + x^2  2*x If you do this form, it works: >expand( (x1) * (x1) ) ans = 1.0+x^2(2.0)*xUsing ginsh with expand produces the desired results, so I'm assumingit is an Octave integration peculariaty: ginsh> expand( (x1)^3 ); 13*x^2+x^3+3*x Octave is freely available under the terms of the GNU GPL. Octave's home on the web: http://www.octave.org How to fund new projects: http://www.octave.org/funding.html Subscription information: http://www.octave.org/archive.html 
 Octave is freely available under the terms of the GNU GPL. Octave's home on the web: http://www.octave.org How to fund new projects: http://www.octave.org/funding.html Subscription information: http://www.octave.org/archive.html 
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