NotImplementedError: can not rewrite Univariate Quotient Polynomial Ring ..

[swewers]

The following gives an error:

sage: F.<x> = FunctionField(QQ)
sage: R.<y> = F[]
sage: G = y^4 - 4*x^4 + 48*x^3 - 24*x^2 + 48*x - 132
sage: v_2 = QQ.valuation(2)
sage: v0 = GaussValuation(F._ring, v_2).augmentation(F._ring.gen()+1, 5/4)
sage: v = F.valuation(v0)
sage: v.mac_lane_approximants(G)

NotImplementedError: can not rewrite Univariate Quotient Polynomial Ring in u2 over Fraction Field of    
Univariate Polynomial Ring in x over Finite Field of size 2 (using GF2X) with modulus u2^2 + 1/x^3 as 
an isomorphic ring

TODO:

• Review #26123
• Review #16562
• Review #16564
• Fix #23174
• Fix #26128 once #23174 has been merged.
• Fix #26124 #16572 once #26128 has been merged.

[saraedum]

I see. The code only handles number fields and finite fields but no function fields yet. This should be fixed upstream and then monkey-patched here.

[swewers]

But it usually works! There must be something specific about this example which makes it fail.
Isn't the MacLane algorithm completely generic for discrete valuations (provided you have functions like reduce, lift or element_with_valuation)?

[saraedum]

True, but for some reason the code wants to replace the fraction field with a function field to improve performance. But that doesn't work yet.

[saraedum]

What happens is that a factorization needs to be computed and we don't know how to factor in a quotient so we try to rewrite it to a field with more features.

[saraedum]

Changing that does not solve the problem as the residue field is an extension of a rational function field and we don't know how to factor there…this is now: https://trac.sagemath.org/ticket/26123, https://trac.sagemath.org/ticket/26124.

[swewers]

#26123 has been fixed, but #26124 didn't make it into Sage-8.4, in spite of a positive review.

[saraedum]

#16564 is currently waiting to be reviewed :)

[JRSijsling]

To try to review that ticket, I checked it out and rebuilt, at first with sage -b and later using make. The doctests all fail and even defining a function field fails. This failure likely has nothing to do with your ticket, but I am at a loss what to do and whether this is a real bug that I should report (and if so, where) or just me being dense.

Gist here.

[saraedum]

Thanks for having a look. Seems like something broke when merging this with the latest beta.

Having to rebuild is quite annoying. I hope we could finally get https://trac.sagemath.org/ticket/24842 in so people would just have to click a button to be able to review a specific build of Sage…

[JRSijsling]

Either that, or there is a problem with the last beta itself. I do not have that built right now, but I would not exclude the possibility. The diff is very small.

[JRSijsling]

In fact no, the develop branch is all right. It seems that FunctionFieldVectorSpaceIsomorphism got replaced by a function with identical purposes named FunctionFieldIsomorphism. Will modify and rebuild to see what happens.