Dear All,
I started this conversation back in sage-combinat-devel but then Nicolas
correctly pointed out that this is something that should be discussed here.
Sorry for the repetition if you read both lists.
Together with Dylan Rupel I am trying to implement cluster algebras as an
algebra and not as a collection of seeds at it is now. In order to do so I am
playing around with some "exotic" ways of using LaurentPolynomialRing and I
am getting a whole bunch of different issues. Here is an incomplete list of
them.
Eventually I will like to implement a TropicalSemifiled and be able to pass
it as argument to LaurentPolynomialRing as follows:
sage: P = TropicalSemifield('y', 3)
sage: P
Tropical semifield on the generators y0, y1, y2
sage: L = LaurentPolynomialRing(P,'x',3)
sage: L
Multivariate Laurent Polynomial Ring in x0, x1, x2 over Tropical Semifield on
the generators y0, y1, y2
I did not implement this yet so, at the moment, I would be happy to substitute
P with
sage: P = LaurentPolynomialRing(ZZ, 'y', 3)
Unfortunately, if one does that, there are few issues arising from how gcd
are computed; here is a small zoo of examples:
sage: P = LaurentPolynomialRing(ZZ, 'y', 3)
sage: P
Multivariate Laurent Polynomial Ring in y0, y1, y2 over Integer Ring
sage: L = LaurentPolynomialRing(P,'x',3)
sage: L
Multivariate Laurent Polynomial Ring in x0, x1, x2 over Multivariate Laurent
Polynomial Ring in y0, y1, y2 over Integer Ring
sage: L.inject_variables()
Defining x0, x1, x2
sage: x0/x0
1
sage: x0.gcd(x0)
...
AttributeError:
'sage.rings.polynomial.laurent_polynomial.LaurentPolynomial_mpair' object has
no attribute 'gcd'
sage: gcd(x0,x0)
...
TypeError: unable to find gcd
sage: R = L.fraction_field()
sage: R.inject_variables()
Defining x0, x1, x2
sage: x0.gcd(x0)
1
sage: x0/x0
x0/x0
sage: _.denominator()
x0
Ok, I figured this was not the way to go. The next best thing would be to have
sage: L = LaurentPolynomialRing(ZZ, 'x0,x1,x2,y0,y1,y2')
sage: P = LaurentPolynomialRing(ZZ, 'y0,y1,y2')
but then:
sage: P.inject_variables()
Defining y0, y1, y2
sage: y0 in P
True
sage: y0 in L
False
sage: y0.parent().fraction_field()(y0) in L
True
Note that this is an issue of the multivariate implementation since
sage: R = LaurentPolynomialRing(ZZ,'x,y')
sage: T = LaurentPolynomialRing(ZZ,'y')
sage: T.inject_variables()
Defining y
sage: y in T
True
sage: y in R
True
as expected.
It looks to me that the implementation of LaurentPolynomialRing is full of
such corner case bugs and, if I understand correctly, it is still based on
the old architecture not the new Category/Parent/Element framework. Is there
any plan to replace it in the near future with a more modern implementation?
Should I decide to invest time in improving it, would anyone here be
interested to help? Do you have any suggestion/reference on how this should
be done properly? I am relatively a newbie to all this so I might need as
many pointers as possible.
Thanks
S.
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