# [seqfan] Re: Cannonicalizing factorization matrices

Charles Greathouse charles.greathouse at case.edu
Tue Aug 2 20:50:42 CEST 2016

```PARI/GP. Sorry, I meant to send this there instead of here! Although we do
have a fair number of PARI users here.

> In Maple, ifactors(n)[2] will produce something like
[[2,1],[3,1],[5,2]].  There are never repeats of primes or exponents of 0.
The primes are not necessarily in order, but you can sort the result.

PARI/GP uses a similar format, and always gives the primes in order without
any 0 exponents. But you can modify the factorization matrix (like you
could for any other matrix) and denormalize it.

Charles Greathouse
Case Western Reserve University

On Mon, Aug 1, 2016 at 11:04 PM, <israel at math.ubc.ca> wrote:

> What software is this in?  It doesn't seem like a well-designed interface
> to the factoring algorithm.
>
> In Maple, ifactors(n)[2] will produce something like
> [[2,1],[3,1],[5,2]].  There are never repeats of primes or exponents of 0.
> The primes are not necessarily in order, but you can sort the result.
>
> Cheers,
> Robert
>
>
> On Aug 1 2016, Charles Greathouse wrote:
>
> It occasionally happens that I'm working with a number where it is
>> convenient to manipulate its factored form. Sometimes I will end up with a
>> matrix like
>>
>> [2, 1; 3, 0; 5, 2]
>>
>> (0 exponent) or
>>
>> [2, 2; 7, 1; 3, 1]
>>
>> (primes out of order). Conceivably it could even result in
>>
>> [2, 1; 3, 1; 2, 1]
>>
>> (primes appearing multiple times) although this has not happened to me
>> yet.
>> Is there a good/standard/recommended way to do this?
>>
>> Of course this can be achieved with factor(factorback(f)) but this throws
>> away the information I'm trying to preserve.
>>
>> Charles Greathouse
>> Case Western Reserve University
>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>>
>
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>
```