2008/10/24 Stan Schymanski <[EMAIL PROTECTED]>:
>
> That's interesting. It seems that the bug lies in the use of floating
> point numbers? By the way, simplify_trig and simplify_rational create
> the same mistake. I agree that the use of simplify_radical() is not
> very useful here, but if it makes such an obvious mistake, how
> confident can we be that it doesn't make mistakes in more complicated
> cases where we don't actually notice the mistake straight away? I
> thought about using something like simplify_full() on any equation to
> see if it can be simplified before I carry on with calculations.
> Perhaps this is the wrong strategy, anyway. Any comments?
> How could I actually get Sage to cancel out the 'a' in the equation?
> None of the methods I tried do the job. I don't like doing things by
> hand, because then I have to redo everything if I change an equation
> somewhere at the top of the notebook.
>
Here's an approach which does not use maxima at all, but rather more
"pure" algebra:
sage: R.<a,b,c> = QQ[]
sage: (a*b - (1/2)*a*(b - c))//a
1/2*b + 1/2*c
Here, R is the set of all polynomials in a,b,c with rational
coefficients, and // does an exact division. (If you use / instead
the answer looks the same but lies in a different place:
sage: parent((a*b - (1/2)*a*(b - c))/a)
Fraction Field of Multivariate Polynomial Ring in a, b, c over Rational Field
sage: parent((a*b - (1/2)*a*(b - c))//a)
Multivariate Polynomial Ring in a, b, c over Rational Field
Now, whether or not you like this solution seems to depend on whether
or not you are a pure mathematician who is used to rings and fields,
as opposed so someone who just deals with symbolic expressions. The
former are much faster (and, as in this case, more accurate!) but are
conceptually harder -- and do not allow things like radicals and
exponentials.
John Cremona
> Thanks a lot for thinking about it!
>
> Stan
>
> On Oct 24, 3:04 pm, "John Cremona" <[EMAIL PROTECTED]> wrote:
>> A variation on your first try is:
>>
>> sage: ((a*b - (1/2)*a*(b - c))/a).simplify_radical()
>> (c + b)/2
>>
>> which works fine. Maybe it's a bug in maxima. I don't see why you
>> would need simplify_radical() at all here, since your expression
>> contains no radicals.
>>
>> John Cremona
>>
>> 2008/10/24 Stan Schymanski <[EMAIL PROTECTED]>:
>>
>>
>>
>> > Dear all,
>>
>> > I just noted some strange behaviour with simplify_radical():
>>
>> > ----------------------------------------------------------------------
>> > | SAGE Version 3.1.2, Release Date: 2008-09-19 |
>> > | Type notebook() for the GUI, and license() for information. |
>> > ----------------------------------------------------------------------
>>
>> > sage: sage: var('a b c')
>> > (a, b, c)
>> > sage: ((a*b - 0.5*a*(b - c))/a).simplify_radical()
>> > 0
>> > sage: ((b - 0.5*(b - c))).simplify_radical()
>> > 0.500000000000000*c + 0.500000000000000*b
>>
>> > Clearly, the second result should be the same as the first one, as 'a'
>> > cancels out. Does anyone know how to avoid such mistakes and whether
>> > it is advisable to use simplify_radical at all?
>>
>> > Cheers
>> > Stan
>>
>>
> >
>
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-support@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at
http://groups.google.com/group/sage-support
URLs: http://www.sagemath.org
-~----------~----~----~----~------~----~------~--~---
