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Bug with newton polygons of Puiseux series in 9.1?

asked 2020-09-27 16:32:57 -0500

cfranc gravatar image

updated 2020-09-28 08:17:57 -0500

slelievre gravatar image

I've been playing with Puiseux series and noticed that zero coefficients are not being assigned the correct valuation of infinity, so that the Newton polygon is not always correct. A minimal example follows: the two newton polygons should be the same, but they are not. The polygon for f2 is correct, while that of f1 is in error.

R.<x> = PuiseuxSeriesRing(QQ)
S.<y> = PolynomialRing(R)
f1 = y^2+x
f2 = y^2+x*y+x
X1=f1.newton_polygon().plot()
X2=f2.newton_polygon().plot()
show(X1)
show(X2)

If you do the same thing with Laurent series as opposed to Puiseux series, there is no problem and the polygons are equal (as expected):

R.<x> = LaurentSeriesRing(QQ)
S.<y> = PolynomialRing(R)
f1 = y^2+x
f2 = y^2+x*y+x
X1=f1.newton_polygon().plot()
X2=f2.newton_polygon().plot()
show(X1)
show(X2)

Similarly if you work over a p-adic field, there is no problem:

K=pAdicField(2)
S.<y> = PolynomialRing(K)
f1 = y^2+2
f2 = y^2+2*y+2
X1=f1.newton_polygon().plot()
X2=f2.newton_polygon().plot()
show(X1)
show(X2)

So this does seem to be a problem specific to Puiseux series. I'm not sure how to post a bug report, so I'm documenting this here in the hope that someone can help. Thanks!

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answered 2020-09-28 05:11:04 -0500

FrédéricC gravatar image

Indeed

sage: R.<x> = PuiseuxSeriesRing(QQ)                                             
sage: x.valuation()                                                             
1
sage: (x**(1/3)).valuation()                                                    
1/3
sage: R.zero().valuation()                                                      
0
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FrédéricC gravatar imageFrédéricC ( 2020-09-28 07:35:48 -0500 )edit

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Asked: 2020-09-27 16:32:57 -0500

Seen: 34 times

Last updated: Sep 27