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[MUG] Re: bug in invphi
| [MUG] Re: bug in invphi |
|
Author: Douglas B Meade
Posted: Tue, 25 Jun 2002 15:28:46 -0400
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>> From: "Douglas B. Meade" "meade"
Neil and MUG,
I have not worked with Maple's invphi function for several years
(Maple V, Release 2 in 1993) but remember that it was not very
efficient and was not perfect. At that time I wrote some general
pre-image routines for integer-valued functions. These have not been
updated to later versions of Maple but should not be difficult to
update. The PS and PDF versions of the technical report I wrote at
that time can be downloaded from the list of publication on my website
(http://www.math.sc.edu/~meade/publ.html).
I do not have time to update the code but will be happy to answer any
questions that you might have.
I hope this is of some assistance,
Doug
-----------------------------------------------------------------------
Prof. Douglas B. Meade Phone: (803) 777-6183 FAX: (803)
777-6527
Department of Mathematics URL: http://www.math.sc.edu/~meade/
USC, Columbia, SC 29208 E-mail: "mailto:meade"
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| [MUG] Re: bug in invphi |
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Author: Carl Devore
Posted: Thu, 27 Jun 2002 06:04:59 -0400
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>> From: Carl Devore "devore"
> >> From: "N. J. A. Sloane" "njas"
>
> Is this a known bug?
> > with(numtheory);
> > invphi(1610510);
> []
> > phi(1771561);
> 1610510
> In other words invphi(1610510); gave an incorrect answer.
My investigation so far shows that this bug will occur for
invphi((p-1)*p^n) for n>1 and p any of the primes
11, 23, 29, 31, 47, 53, 59, 67, 71, 79, 83, 89, 103, 107, 113, 131, ....
I can't see the pattern of the primes, except that it appears that if p is
such a prime, then so are all primes of the form (4*n+2)*p+1, n= 0, 1,
.... Tracking down the bug and verifying the above conjecture might lead
to an interesting result. Perhaps it is one of your Integer
Sequences. So the smallest example that I can find for this bug
is invphi(10*11^2).
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| [MUG] Re: bug in invphi |
|
Author: Aaron Meyerowitz
Posted: Thu, 27 Jun 2002 17:16:29 -0400
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>> From: Aaron Meyerowitz "meyerowi"
>>> From: Carl Devore "devore"
>
>> >> From: "N. J. A. Sloane" "njas"
>>
>> Is this a known bug?
>> > with(numtheory);
>> > invphi(1610510);
>> []
>> > phi(1771561);
>> 1610510
>> In other words invphi(1610510); gave an incorrect answer.
>
>My investigation so far shows that this bug will occur for
>invphi((p-1)*p^n) for n>1 and p any of the primes
>11, 23, 29, 31, 47, 53, 59, 67, 71, 79, 83, 89, 103, 107, 113, 131, ....
I.E. for phi(p^(n+1))
The code looks very "cute" but quite opaque. Other packages seem to find
invphi
correctly and MUCH more quickly. The problem goes back at least to Maple VR5.
Has it really never been noticed before?
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