The only reason that monomial_divides is unimplemented there is that nobody
has done it yet. :-)
David
On Tue, Mar 1, 2016 at 12:20 PM, Ben Hutz <bn4...@gmail.com> wrote:
> ok, so that is what the logic is.
>
> Not begin familiar with the different polynomial ring classes: is there a
> reason not to implement the monomial_divides function in that class? I
> think the current function just checks the exponents and it's lack is
> preventing the groebner basis from running.
>
> On Monday, February 29, 2016 at 2:25:45 PM UTC-6, David Roe wrote:
>>
>>
>>
>> On Mon, Feb 29, 2016 at 9:19 AM, Ben Hutz <bn4...@gmail.com> wrote:
>>
>>> I was exploring some quotient ring operations and came across the
>>> following:
>>>
>>> {{{
>>> R.<y>=QQ[]
>>> K.<w>=NumberField(y^3 + 2*y - 2401)
>>> k.<v>=K.quo(K.prime_factors(7)[1])
>>> R.<x,y>=PolynomialRing(k)
>>> R.monomial_divides(y,x^3*y)
>>> Error
>>> }}}
>>>
>>> {{{
>>> R.<y>=QQ[]
>>> K.<w>=NumberField(y^3 + 2*y - 2401)
>>> k.<v>=K.residue_field(K.prime_factors(7)[1])
>>> R.<x,y>=PolynomialRing(k)
>>> R.monomial_divides(y,x^3*y)
>>> True
>>> }}}
>>>
>>> The second works, the first does not. I came across this since
>>> .monomial_divides is used is a groebner basis computation. So played around
>>> a little more and the following seems weirder
>>>
>>> {{{
>>> A.<x,y,z> = PolynomialRing(Zmod(42))
>>> A.monomial_divides(y,x^2*y)
>>> True
>>> }}}
>>>
>>> {{{
>>> A.<x,y,z> = PolynomialRing(Zmod(2521515232)) #but one less digit works
>>> A.monomial_divides(y,x^2*y)
>>> Error
>>> }}
>>>
>>> The first works, but the 2nd does not, even though neither is prime. It
>>> seems to have to do with what type of polynomial ring they are initialized
>>> as, but I had a hard time tracking down where that code lived and how it
>>> decided. Is there someone familiar with polynomial rings in Sage who could
>>> shed some light on whether this is expected behavior?
>>>
>>
>> The difference is that we use singular over Z/n for small enough n. You
>> can detect this in the types of the polynomial rings:
>>
>> sage: A.<x,y,z> = PolynomialRing(Zmod(42))
>> sage: type(A)
>> <type
>> 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular'>
>> sage: A.<x,y,z> = PolynomialRing(Zmod(2521515232))
>> sage: type(A)
>> <class
>> 'sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict_with_category'>
>>
>> The monomial_divides method just isn't implemented
>> for MPolynomialRing_polydict.
>> David
>>
>>>
>>> Thanks,
>>> Ben
>>>
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>>
>>
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