Can someone explain the results here? http://www.wolframalpha.com/input/?i=n%5E4+%2B+n%281%2F3%29 I can come up with a hypothesis which explains some of the results, but can't think of anything at all which would explain the "alternate form." Any ideas? --Emma Cohen
Nothing said "alternate form" when I went to that page. But they did have an indefinite integral solved incorrectly, and a "global minimum" problem also solved incorrectly. I think it's buggy. --Dan Emma wrote: On 2012-09-17, at 5:26 PM, Emma Cohen wrote:
Can someone explain the results here? http://www.wolframalpha.com/input/?i=n%5E4+%2B+n%281%2F3%29 I can come up with a hypothesis which explains some of the results, but can't think of anything at all which would explain the "alternate form."
They're getting n as a variable and n as a function confused: n(1/3) is being read as an evaluation of the function n at the point 1/3 rather than n/3. Replacing the function name with f, the indefinite integral says int(n^4 + f(1/3)) dn = n^5 + n*f(1/3) + constant which is correct. On Mon, Sep 17, 2012 at 6:27 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Nothing said "alternate form" when I went to that page. But they did have an indefinite integral solved incorrectly, and a "global minimum" problem also solved incorrectly.
I think it's buggy.
--Dan
Emma wrote:
On 2012-09-17, at 5:26 PM, Emma Cohen wrote:
Can someone explain the results here? http://www.wolframalpha.com/input/?i=n%5E4+%2B+n%281%2F3%29 I can come up with a hypothesis which explains some of the results, but can't think of anything at all which would explain the "alternate form."
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You guys don't get an alternate form? I see Alternate form: n^4 + n^4(1/3) I, too, had come to the conclusion that it was thinking of the second "n" as a function (particularly since adding a space between it and the opening parenthesis fixes the problem), but I couldn't figure out how that might explain this particular result. Changing the exponent on the first "n" also changes it on the second, but changing it to a variable completely changes the sorts of results I get, so it's hard to compare. If I change the first "n" to an "m", this issue goes away (while the latter "n" is still clearly treated as a function). --Emma On Mon, Sep 17, 2012 at 9:56 PM, Mike Stay <metaweta@gmail.com> wrote:
They're getting n as a variable and n as a function confused: n(1/3) is being read as an evaluation of the function n at the point 1/3 rather than n/3. Replacing the function name with f, the indefinite integral says
int(n^4 + f(1/3)) dn = n^5 + n*f(1/3) + constant
which is correct.
On Mon, Sep 17, 2012 at 6:27 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Nothing said "alternate form" when I went to that page. But they did have an indefinite integral solved incorrectly, and a "global minimum" problem also solved incorrectly.
I think it's buggy.
--Dan
Emma wrote:
On 2012-09-17, at 5:26 PM, Emma Cohen wrote:
Can someone explain the results here? http://www.wolframalpha.com/input/?i=n%5E4+%2B+n%281%2F3%29 I can come up with a hypothesis which explains some of the results, but can't think of anything at all which would explain the "alternate form."
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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Yeah, I forgot about that (2nd line) because it wasn't clear to me what it was supposed to be the alternate form *of*. (Surely not the 1st line, I thought.) --Dan P.S. But you and Mike S. are brilliant to have figured out what mistake was being made. On 2012-09-17, at 7:52 PM, Emma Cohen wrote:
You guys don't get an alternate form? I see
Alternate form: n^4 + n^4(1/3)
I, too, had come to the conclusion that it was thinking of the second "n" as a function (particularly since adding a space between it and the opening parenthesis fixes the problem), but I couldn't figure out how that might explain this particular result. Changing the exponent on the first "n" also changes it on the second, but changing it to a variable completely changes the sorts of results I get, so it's hard to compare. If I change the first "n" to an "m", this issue goes away (while the latter "n" is still clearly treated as a function).
The expression parser is hard to understand --- x(y) can be multiplication or a function depending whether y is numeric and various other context attributes. The "alternate form" does not evaluate to the original form! In order to explain the bug, I think you'd have to imagine the expressions being represented in memory in a way that preserves the ambiguity of n*(1/3) and n(1/3). The system tries to factor out n^3, gets n + (n(1/3)/n^3, and then tries to undo the operation by multiplying through by n^3. In doing this, it multiplies the function symbol n as though it were a variable. This causes the function symbol to be replaced by n^4. Inexplicably, it also cancels the n^3 in the denominator. On the bug vs. feature scale, this pegs out on the bug side. Hilarie
From: Emma Cohen <emma@don-eve.dyndns.org> Date: Mon, 17 Sep 2012 20:26:13 -0400 To: math-fun <math-fun@mailman.xmission.com> Subject: [math-fun] Huh? Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit
Can someone explain the results here? http://www.wolframalpha.com/input/?i=n%5E4+%2B+n%281%2F3%29 I can come up with a hypothesis which explains some of the results, but can't think of anything at all which would explain the "alternate form."
Any ideas? --Emma Cohen _______________________________________________
participants (4)
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Dan Asimov -
Emma Cohen -
Hilarie Orman -
Mike Stay