Dear All,
here is a brief status update on this issue. TL;DR: Laurent Polynomial Ring
does not provide a gcd implementation.
Recall that we are in this situation:
sage: L = LaurentPolynomialRing(LaurentPolynomialRing(ZZ,'t'),'x')
sage: R = L.fraction_field()
sage: R.inject_variables()
Defining x
sage: x.gcd(x)
1
This is the implementation of gcd called by x.gcd(x)
@coerce_binop
def gcd(self, other):
P = self.parent()
try:
selfN = self.numerator()
selfD = self.denominator()
selfGCD = selfN.gcd(selfD)
otherN = other.numerator()
otherD = other.denominator()
otherGCD = otherN.gcd(otherD)
selfN = selfN // selfGCD
selfD = selfD // selfGCD
otherN = otherN // otherGCD
otherD = otherD // otherGCD
tmp = P(selfN.gcd(otherN))/P(selfD.lcm(otherD))
return tmp
except (AttributeError, NotImplementedError, TypeError, ValueError):
zero = P.zero()
if self == zero and other == zero:
return zero
return P.one()
clearly selfN is x and selfD is 1 as elements of L but
sage: selfN.gcd(selfD)
...
NotImplementedError: Univariate Laurent Polynomial Ring in t over Integer Ring
does not provide a gcd implementation for univariate polynomials
S.
PS: of course this is not just a problem with units:
sage: (x+1).gcd(x+1)
1
sage: (x+1).numerator().gcd(1)
NotImplementedError: Univariate Laurent Polynomial Ring in t over Integer Ring
does not provide a gcd implementation for univariate polynomials
* Travis Scrimshaw <tsc...@ucdavis.edu> [2015-10-10 05:57:20]:
> I think I slightly misspoke about the gcd. See the details on
> [1]http://trac.sagemath.org/ticket/16993.
> Best,
> Travis
> On Friday, October 9, 2015 at 4:12:12 PM UTC-5, Travis Scrimshaw wrote:
>
> Hey Salvatore,
> Â Â I would say this is the same problem as simplifying scalars of
> fraction fields of polynomials over QQ, that gcd(x, x) = 1 rather than
> x because x is a unit. I don't think we have a way around this
> currently other than doing some kind of explicit coercion.
> Best,
> Travis
> On Friday, October 9, 2015 at 1:40:22 PM UTC-5, Salvatore Stella wrote:
>
> Dear all,
> I just noted the following odd behaviour:
> sage: L = LaurentPolynomialRing(ZZ, 'x').fraction_field()
> sage: L.inject_variables()
> Defining x
> sage: x/x
> 1
> As one should expect but if we change the base ring then things get
> messy:
> sage: L = LaurentPolynomialRing(LaurentPolynomialRing(ZZ,'t'),
> 'x').fraction_field()
> sage: L.inject_variables()
> Defining x
> sage: x/x
> x/x
> sage: _.denominator()
> x
> The fact that x/x is printed out as x/x is still ok if somewhat
> annoying. But
> the return value of denominator() is definitely not what I would
> expect.
> Is this intentional?
> Thanks
> Salvatore
>
> References
>
> 1. http://trac.sagemath.org/ticket/16993
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