cc'd to the maxima list.
This seems to be a bug in Maxima 5.13, not Sage.
(Maxima 5.16 is the current release, I think, and I don't know
if it is fixed there or not.)
sage: maxima_console()
Maxima 5.13.0 http://maxima.sourceforge.net
Using Lisp CLISP 2.46 (2008-07-02)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
This is a development version of Maxima. The function bug_report()
provides bug reporting information.
(%i1) t1 : (sqrt(3)-3)*(sqrt(3)+1)/6
;
(sqrt(3) - 3) (sqrt(3) + 1)
(%o1) ---------------------------
6
(%i2) t1 : (sqrt(3)-3)*(sqrt(3)+1)/6;
(sqrt(3) - 3) (sqrt(3) + 1)
(%o2) ---------------------------
6
(%i3) tt1 : -1/sqrt(3);
1
(%o3) - -------
sqrt(3)
(%i4) t2 : sqrt(3)/6;
- 1/2
3
(%o4) ------
2
(%i5) expand(t1+t2);
- 1/2
3 3
(%o5) - --------
2 2
(%i6) expand(tt1+t2);
1
(%o6) - ---------
2 sqrt(3)
++++++++++++++++++++++++++++++++++++++
On Mon, Aug 11, 2008 at 6:06 AM, Francis Colas <colas.francis at gmail.com> wrote:
> On 11 ao?t, 11:58, "William Stein" <wst... at gmail.com> wrote:
>> On Mon, Aug 11, 2008 at 2:42 AM, Francis Colas <colas.fran... at gmail.com> wrote:
>>
>> > Hello,
>>
>> > It seems there is an issue somewhere with the expand function with
>> > square roots and fractions. Here is an excerpt of a notebook (SAGE
>> > Version 3.0, Release Date: 2008-04-21, reproduced on the Sage online
>> > server):
>>
>> > sage: t1 = (sqrt(3)-3)*(sqrt(3)+1)/6
>> > sage: tt1 = -1/sqrt(3)
>> > sage: t2 = sqrt(3)/6
>> > sage: print t1+t2, tt1+t2
>> > (sqrt(3) - 3) (sqrt(3) + 1) 1
>> > --------------------------- + ---------
>> > 6 2 sqrt(3)
>> > 1
>> > - ---------
>> > 2 sqrt(3)
>> > sage: print expand(t1)
>> > sage: print expand(tt1)
>> > sage: print expand(t2)
>> > sage: print expand(t1+t2), expand(tt1+t2)
>> > 1
>> > - -------
>> > sqrt(3)
>>
>> > 1
>> > - -------
>> > sqrt(3)
>>
>> > 1
>> > ---------
>> > 2 sqrt(3)
>>
>> > 3
>> > - ---------
>> > 4 sqrt(3)
>> > 1
>> > - ---------
>> > 2 sqrt(3)
>
>> Please explain precisely why you think the expansion of t1 + t2 is wrong.
>
> Because t1+t2 = -1/(2*sqrt(3)) != -3/(4*sqrt(3))
>
> But I may have misunderstood your question.
>
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