On Tue, Mar 27, 2007 at 07:36:18AM -0700, William Stein wrote:
> 
> > On 3/27/07, Joel B. Mohler <[EMAIL PROTECTED]> wrote:
> > P.S.: Speed comparisons (all on sage.math).  I've included the basic integer
> 
> In all your timings below that involve a constant (e.g., 1 or 2), you
> should factor
> out the constant from the test.  E.g., do a = 1; b = 2; then do the
> test with a and b.
> Otherwise the Integer( ) function is being called every time on a Python int,
> and you're (1) testing the wrong thing, and (2) testing something that won't
> reflect how actual code will behave.

Good point!  Corrected timings are below.  That explains why the number field 
arithmetic was slower by a smaller multiplicative factor.

[EMAIL PROTECTED]:~$ magma
Magma V2.13-5     Tue Mar 27 2007 07:12:02 on sage     [Seed = 1950028839]
Type ? for help.  Type <Ctrl>-D to quit.
> C<I>:=QuadraticField(-1);
> time for x in [1..100000] do a:=I*I; end for;
Time: 0.260
> time for x in [1..100000] do a:=I/2; end for;
Time: 0.370
> time for x in [1..100000] do a:=1+1; end for;
Time: 0.020

[EMAIL PROTECTED]:~$ sage
----------------------------------------------------------------------
| SAGE Version 2.4, Release Date: 2007-03-25                         |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
Loading SAGE library. Current Mercurial branch is: nf
sage: C.<I>=QuadraticField(-1)
sage: time for i in xrange(100000): a=I*I
CPU times: user 1.80 s, sys: 0.02 s, total: 1.82 s
Wall time: 1.82
sage: two=2
sage: time for i in xrange(100000): a=I/two
CPU times: user 9.94 s, sys: 0.13 s, total: 10.07 s
Wall time: 10.07
sage: one=1
sage: time for i in xrange(100000): a=one+one
CPU times: user 0.10 s, sys: 0.01 s, total: 0.11 s
Wall time: 0.11

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