On Tuesday, August 15, 2017 at 7:21:03 AM UTC-7, chandra chowdhury wrote:
>
> Is it possible to factor polynomials completely over modular ring?
>
> Like
> x = var('x')
> factor(x^5-x, IntegerModRing(25)['x'])
> gives
>
> (x-1)*(x+1)*(x^2+1)*x
>
The second argument is simply ignored here, by the looks of it
sage: factor(x^5-x,"moo")
(x^2 + 1)*(x + 1)*(x - 1)*x
You could file that as a (mild) bug.
Factorization of Z/25 directly isn't implemented:
sage: R=IntegerModRing(25)
sage: Rx.<x>=R[]
sage: factor(x^5-x)
NotImplementedError: factorization of polynomials over rings with composite
characteristic is not implemented
Root finding is apparently implemented:
sage: (x^5-x).roots(multiplicities=False)
[0, 1, 7, 18, 24]
Alternatively, (beccause you're working mod a prime power) you could look
at p-adic rings:
sage: R=Zp(5,2,"fixed-mod",print_mode="terse")
sage: Rx.<x>=R[]
sage: (x^5-x).factor()
((1 + O(5^2))*x + (1 + O(5^2))) * ((1 + O(5^2))*x + (7 + O(5^2))) * ((1 +
O(5^2))*x + (18 + O(5^2))) * ((1 + O(5^2))*x + (24 + O(5^2))) * ((1 +
O(5^2))*x + (0 + O(5^2)))
The "+O(5^2)" is a p-adic thing that would be nice to suppress here.
--
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 https://groups.google.com/group/sage-support.
For more options, visit https://groups.google.com/d/optout.
