On 11/7/07, Martin Albrecht <[EMAIL PROTECTED]> wrote:
>
> Hi everybody,
>
> I've attached a 'random_monomial.py' to
>
>http://trac.sagemath.org/sage_trac/ticket/980
>
> which implements Steffen's and my proposal.
Hey guys,
I've attached a patch for this at
http://trac.sagemath.org/sage_trac/
Hi everybody,
I've attached a 'random_monomial.py' to
http://trac.sagemath.org/sage_trac/ticket/980
which implements Steffen's and my proposal.
Thoughts?
Martin
--
name: Martin Albrecht
_pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99
_www: http://www.informatik.uni-bre
On 26 Okt., 18:30, "didier deshommes" <[EMAIL PROTECTED]> wrote:
> 2007/10/26, Steffen <[EMAIL PROTECTED]>:
>
>
Ok, here an example. Lets take a polynomial over
F:=GF(nextprime(2**42)) in two variables x and y and a maximum total
degree of 3.
>
> > 1) Polynomial with max number of monomial. We
> Mike, your code had a subtle bug, where
> random_monomials(n,degree,terms) failed each time for degree =1 (but
> was fine for degree=0).
Yeah, I knew that when I wrote it -- it was just something quick that
I wrote up. The degree 1 case is trivial to handle though.
--Mike
--~--~-~--~
2007/10/26, Steffen <[EMAIL PROTECTED]>:
> 1) Polynomial with max number of monomial. We dont need to worry about
> that case, since here all the monomial are chosen, that means actually
> there is nothing to choose. So this will be efficient anyway.
> 2) A user wants an exact < totalmax number of
On 26 Okt., 00:48, Robert Bradshaw <[EMAIL PROTECTED]>
wrote:
> On Oct 25, 2007, at 4:23 PM, Martin Albrecht wrote:
>
> > On Friday 26 October 2007, Robert Bradshaw wrote:
> >> This is an interesting construction, but I am wondering if a uniform
> >> distribution for all polynomials of specified
No, it's not. I just wrote it up now as a proof-of-concept.
--Mike
On 10/25/07, didier deshommes <[EMAIL PROTECTED]> wrote:
>
> 2007/10/25, Mike Hansen <[EMAIL PROTECTED]>:
> >
> > > Is this function in sage? Where is it located?
> >
> > Which function?
>
> Sorry, the random_monomials() functio
2007/10/25, Mike Hansen <[EMAIL PROTECTED]>:
>
> > Is this function in sage? Where is it located?
>
> Which function?
Sorry, the random_monomials() function.
>
> --Mike
>
> >
>
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> Is this function in sage? Where is it located?
Which function?
--Mike
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2007/10/25, Mike Hansen <[EMAIL PROTECTED]>:
>
> > Since integers are chosen uniformly, this would guarantee (?) that the
> > polynomial is generated uniformly. Only hitch is that I don't know if
> > there is such inttovec is in in SAGE yet. mhansen, any idea?
>
> Yes, this is pretty much what I'm
On Oct 25, 2007, at 4:23 PM, Martin Albrecht wrote:
> On Friday 26 October 2007, Robert Bradshaw wrote:
>> This is an interesting construction, but I am wondering if a uniform
>> distribution for all polynomials of specified degree < d, with a
>> specified number of terms, is the most natural one
> Since integers are chosen uniformly, this would guarantee (?) that the
> polynomial is generated uniformly. Only hitch is that I don't know if
> there is such inttovec is in in SAGE yet. mhansen, any idea?
Yes, this is pretty much what I'm doing. While I don't have those
exact functions, they
2007/10/25, Martin Albrecht <[EMAIL PROTECTED]>:
> This construction is random if the random number generator ("randint") is
> random. Btw. how random is randint?
The core generator for all random functions in Python uses the
mersenne twister which is pretty strong.
I have another suggestion for
On Friday 26 October 2007, Robert Bradshaw wrote:
> This is an interesting construction, but I am wondering if a uniform
> distribution for all polynomials of specified degree < d, with a
> specified number of terms, is the most natural one to give, and how
> grave the impact is on efficiency. (De
This is an interesting construction, but I am wondering if a uniform
distribution for all polynomials of specified degree < d, with a
specified number of terms, is the most natural one to give, and how
grave the impact is on efficiency. (Depending on the coefficient
ring, this goal may not
Hi,
after realizing that Steffen and I share an office at RHUL I discussed this
thing with him today for some time.
The improved implementation (#980) still doesn't produce random polynomials
for two reasons: The code does not seem to produce monomials of degree up to
$d$ uniformly at random.
I've attached a patch that takes care of 1) only and updated
http://sagetrac.org/sage_trac/ticket/980 . The individual degree
distribution is a little better:
{{{
sage: GF(10007)['x,y,q'].random_element(6,10)
-2005*x^6 + 2400*x^4*y^2 - 3609*x^3*y^3 + 488*x*y^5 - 3093*x^4*y*q +
3482*x*y*q^3 - 989*x
On Oct 24, 5:45 am, "didier deshommes" <[EMAIL PROTECTED]> wrote:
> 2007/10/23, Steffen <[EMAIL PROTECTED]>:
>
> > Exactly, thats one of two points. The maximum degree in every variable
> > is (maximum total degree of resulting polynomial) / (number of
> > varialbes of the polynomial). Thus for
2007/10/23, Steffen <[EMAIL PROTECTED]>:
> Exactly, thats one of two points. The maximum degree in every variable
> is (maximum total degree of resulting polynomial) / (number of
> varialbes of the polynomial). Thus for example GF(10007)
> ['x,y,z'].random_element(5,9) will be limited in every var
On 10/23/07, Steffen <[EMAIL PROTECTED]> wrote:
> > Given this definition (which I agree is correct), I would expect that
> > if I ask for a total degree of 4, I would sometimes see monomials like
> > x^4 or x*y^3. I think the lack of these monomials is what surprises
> > (and, coincidentally, pl
On 17 Okt., 06:20, cwitty <[EMAIL PROTECTED]> wrote:
> On Oct 16, 8:32 pm, "didier deshommes" <[EMAIL PROTECTED]> wrote:
>
> > 2007/10/16, Steffen <[EMAIL PROTECTED]>:
>
> > > Hi didier,
>
> > > the implementation does not return a polynomial of a total degree of
> > > at most 4, but a polynomia
On Oct 16, 8:32 pm, "didier deshommes" <[EMAIL PROTECTED]> wrote:
> 2007/10/16, Steffen <[EMAIL PROTECTED]>:
>
> > Hi didier,
>
> > the implementation does not return a polynomial of a total degree of
> > at most 4, but a polynomial of total degree of at most 4/2 = 2 in x
> > and in y. If I change
2007/10/16, Steffen <[EMAIL PROTECTED]>:
> Hi didier,
>
> the implementation does not return a polynomial of a total degree of
> at most 4, but a polynomial of total degree of at most 4/2 = 2 in x
> and in y. If I change the total degree to 5, nothing happens, since
> 5/2 = 2. This might be a bug
Hi and thanks for your quick answers!
> Hi Stephen,
> This is not an "exact" function. The only guarantee we have is that we
> will get a polynomial with total degree of *at most* 4 and total
> number of terms is *at most* 9.
>
> You're right, in such a big field the coefficient is almost alwa
> "??" will give you this together with the corresponding code.
>
> There are some glitches in the system, but it works pretty well.
Glitches that I would love to hear about, and hopefully fix.
Nick
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2007/10/15, Steffen <[EMAIL PROTECTED]>:
>
> Hi,
>
> I need to create a random multivariate polynomial. I do it as follows:
>
> F = GF(10007)['x,y'].random_element(4,9)
Hi Stephen,
This is not an "exact" function. The only guarantee we have is that we
will get a polynomial with total degree of
On Oct 15, 2007, at 4:47 PM, Steffen wrote:
>
> Hi,
>
> I need to create a random multivariate polynomial. I do it as follows:
>
> F = GF(10007)['x,y'].random_element(4,9)
>
> Now, sage creates a polynomial in x and y of degree 2 in every
> variable, since 4 = 2+2. Furthermore 9 restricts the po
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