[sage-devel] Re: Testing and Verification of Sage + Mathematica

2009-05-27 Thread rjf
I'm not saying every polynomial multiplication program can be shown to be correct; just the method I suggested happens to be pretty simple. If you write a polynomial multiplication program that has certain breakpoints, e.g. switching to a different method like Karatsuba or FFT at size 3000, then

[sage-devel] Re: Testing and Verification of Sage + Mathematica

2009-05-26 Thread William Stein
On Tue, May 26, 2009 at 3:55 PM, rjf wrote: > > Disregarding the obvious " marketing fluff" of Wolfram's statement, it > seems to me plausible that some programs are more likely to be correct > (at least in well-understood basic components) than some theorems' > proofs.  Here's why. > > A program

[sage-devel] Re: Testing and Verification of Sage + Mathematica

2009-05-26 Thread rjf
Disregarding the obvious " marketing fluff" of Wolfram's statement, it seems to me plausible that some programs are more likely to be correct (at least in well-understood basic components) than some theorems' proofs. Here's why. A program can be run on test data. A program can sometimes be analy

[sage-devel] Re: Testing and Verification of Sage + Mathematica

2009-05-26 Thread William Stein
On Tue, May 26, 2009 at 10:48 AM, Dr. David Kirkby wrote: > > There was an discussion on sci.math.symbolic, which like many on > newsgroups, often go off the subject into something more intersting (or > more boring)! > > It was started by me under the title "Wolfram Alpha claims to be a > primary