Re: [sage-support] Re: Mathematically naive (and incorrect) output
Thanks a lot, John! (and sorry for the delay in answering)
I see the point: it is simply undefined.
But I do not quite agree with you in that [one] would not expect a
computer algebra system to give the same answers with simple
substitutions in the two orders: ideally, I would expect that the
answer to substituting x=1 is something like undefined, since it is
so. But I don't know if that is possible in Sage right now.
Cheers,
Jesús
2014-07-21 16:44 GMT+02:00 John Cremona john.crem...@gmail.com:
The expression y = (1-x)/(1-x*cos(t)) is, as given, undefined whenever
x*cos(t)=1, for example at (x,t)=(1,0).
When x=1 it simplifies to 0/(1-cos(t)), which equals 0 except where
cos(t)=1 where it is undefined but has a limiting value of 0.
When t=0 it simplfies to (1-x)/(1-x), which equals 1 except when x=1
where it is undefined, but has a limiting value of 1.
So you get different limits when first x - 1 and then t-0 compared
with first t-0 and then x-1. The function has no continuous
extension to (x,t)=(1,0). Hence I would not expect a computer algebra
system to give the same answers with simple substitutions in the two
orders.
On 21 July 2014 15:14, kcrisman kcris...@gmail.com wrote:
Hi guys,
This is so simple that probably someone else has already noticed it, but
just in case:
sage: x,t = var('x,t')
sage: f = (1-x)/(1-x*cos(t))
sage: f(x=1)
0
sage: f(t=0)(x=1)
1
My guess is that this is more of a convention than anything else.
sage: x/x
1
sage: 0/x
0
Maxima:
(%i1) x/x;
(%o1) 1
(%i2) 0/x;
(%o2) 0
If Mma and Maple do it too, that would be my guess. In any case, it is
'known' and I bet you'll find other examples with a search of the email
lists (though searching for x/x might be hard!). It's possible to not
immediately do such reductions
sage: x.mul(1/x,hold=True)
x/x
but I'm not sure how to combine that with the substitution that you are
doing.
- kcrisman
The second one is, of course, the correct answer. (FYI, Mathematica9
fails, too.)
Wouldn't the first one return some sort of conditional expression: if t=0
then 1, else 0
I would be happy to help in the debugging, if I can get some indication of
what is running in the background, i.e. what function is called when one
does the substitution f(x=1).
Cheers,
Jesús Torrado
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Re: [sage-support] Re: Mathematically naive (and incorrect) output
Thanks for the answer, kcrisman! My guess is that this is more of a convention than anything else. [...] sage: 0/x 0 If Mma and Maple do it too, that would be my guess. In any case, it is 'known' and I bet you'll find other examples with a search of the email lists (though searching for x/x might be hard!). Mathematica does indeed the same for 0/x. It may be a convention, so I guess there is no room to freak out because it's just wrong!. But it makes me sad, since I will not be able to avoid a feeling of insecurity when substituting variables that I didn't have before :( Isn't there a way to answer with an undetermined in those cases? Best, Jesús -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Re: Mathematically naive (and incorrect) output
The expression y = (1-x)/(1-x*cos(t)) is, as given, undefined whenever
x*cos(t)=1, for example at (x,t)=(1,0).
When x=1 it simplifies to 0/(1-cos(t)), which equals 0 except where
cos(t)=1 where it is undefined but has a limiting value of 0.
When t=0 it simplfies to (1-x)/(1-x), which equals 1 except when x=1
where it is undefined, but has a limiting value of 1.
So you get different limits when first x - 1 and then t-0 compared
with first t-0 and then x-1. The function has no continuous
extension to (x,t)=(1,0). Hence I would not expect a computer algebra
system to give the same answers with simple substitutions in the two
orders.
On 21 July 2014 15:14, kcrisman kcris...@gmail.com wrote:
Hi guys,
This is so simple that probably someone else has already noticed it, but
just in case:
sage: x,t = var('x,t')
sage: f = (1-x)/(1-x*cos(t))
sage: f(x=1)
0
sage: f(t=0)(x=1)
1
My guess is that this is more of a convention than anything else.
sage: x/x
1
sage: 0/x
0
Maxima:
(%i1) x/x;
(%o1) 1
(%i2) 0/x;
(%o2) 0
If Mma and Maple do it too, that would be my guess. In any case, it is
'known' and I bet you'll find other examples with a search of the email
lists (though searching for x/x might be hard!). It's possible to not
immediately do such reductions
sage: x.mul(1/x,hold=True)
x/x
but I'm not sure how to combine that with the substitution that you are
doing.
- kcrisman
The second one is, of course, the correct answer. (FYI, Mathematica9
fails, too.)
Wouldn't the first one return some sort of conditional expression: if t=0
then 1, else 0
I would be happy to help in the debugging, if I can get some indication of
what is running in the background, i.e. what function is called when one
does the substitution f(x=1).
Cheers,
Jesús Torrado
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