On Sunday, 5 April 2015 13:20:49 UTC+1, absinthe wrote:
>
> Justin thanks for your reply. When I realised that I have posted to dev I
> deleted the message and I posted to support. It looks like that you had
> already answered there. Since it might help others which will look at
> support and not dev, I copy and paste your dev reply here.
> 2. Yes no problem :)
> 1. The reason I resulted to Integers(p) was that I couldn't have the
> proper cooefficients when using GF.
> For the same "configuration" I tried the following
> Trying with the following
> p=32
> N=100
> FFQ.<t> = GF(q)#FiniteField(q)
> PR.<x> = PolynomialRing(K)
> Q.<xx> = PR.quotient(x^N - 1)
> pp=Q.random_element()
> while True:
> try:
> ppInv=pp.inverse_mod(xx^N-1)
> break
> except:
> pp=Q.random_element()
> print (pp*ppInv).mod(x^N-1)
>
> I get to a dead end as inverse_mod returns me a not implemented error
> (sage-6.3-x86_64-Linux)
>
What is K there? And what is q?
They are not defined in your code above.
As well,
it's not clear why you try to call inverse_mod(), as pp is already an
element
of the quotient ring modulo (x^N-1).
But pp^{-1} need not exist, still, as Q is not a field for each N>1.
On Sunday, April 5, 2015 at 3:59:42 AM UTC+3, Justin C. Walker wrote:
>
>
> On Apr 4, 2015, at 17:25 , absinthe wrote:
>
> > Dear all,
> >
> > I'm trying to work with polynomials modulo x^N-1 whose coefficients
> belong
> > to Z_p (If it helps p is a power of a prime). I know that I'm doing
> > something wrong, but I cannot figure out what so any help is welcome.
>
> I'm not sure how familiar you are with this stuff, so forgive me if this
> is already clear to you.
>
> 1. When "p" is a prime power, Z/pZ is not a field (it's a ring, but not a
> domain). If you want to deal with coefficients in a field, then you will
> want to use "GF(p)", not "Integers(p)". And a minor syntactic wrinkle to
> beware of is that when "p" (as above) is a prime power, and not a prime,
> you need a second argument, to be used as the name of the "generator" of
> F_p (as an extension of F_q, q being the prime in p).
>
> 2. Also, in computer algebra systems, you have to be careful about
> parentheses, to get what you want. In particular, "X^N-1" and X^(N-1)" are
> not the same.
>
> If this isn't helpful, we can look at this some more.
>
> HTH
>
> Justin
>
> --
> Justin C. Walker
> Curmudgeon at Large
> Director
> Institute for the Enhancement of the Director's Income
> --
> Build a man a fire and he'll be warm
> for a night.
> Set a man on fire and he'll be warm
> for the rest of his life.
>
>
>
> On Sunday, April 5, 2015 at 4:00:47 AM UTC+3, Justin C. Walker wrote:
>>
>>
>> On Apr 4, 2015, at 17:29 , absinthe wrote:
>>
>> > Dear all,
>> >
>> > I'm trying to work with polynomials modulo x^N-1 whose coefficients
>> belong
>> > to Z_p (If it helps p is a power of a prime). I know that I'm doing
>> > something wrong, but I cannot figure out what so any help is welcome.
>>
>> Answered, possibly, on sage-devel...
>>
>> --
>> Justin C. Walker, Curmudgeon at Large
>> Institute for the Absorption of Federal Funds
>> -----------
>> My wife 'n kids 'n dogs are gone,
>> I can't get Jesus on the phone,
>> But Ol' Milwaukee's Best is my best friend.
>> -----------
>>
>>
>>
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