ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 28 Sep 2020 14:35:48 +0200Bug with newton polygons of Puiseux series in 9.1?https://ask.sagemath.org/question/53628/bug-with-newton-polygons-of-puiseux-series-in-91/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!Sun, 27 Sep 2020 23:32:57 +0200https://ask.sagemath.org/question/53628/bug-with-newton-polygons-of-puiseux-series-in-91/Answer by FrédéricC for <p>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.</p>
<pre><code>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)
</code></pre>
<p>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):</p>
<pre><code>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)
</code></pre>
<p>Similarly if you work over a p-adic field, there is no problem:</p>
<pre><code>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)
</code></pre>
<p>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!</p>
https://ask.sagemath.org/question/53628/bug-with-newton-polygons-of-puiseux-series-in-91/?answer=53634#post-id-53634Indeed
sage: R.<x> = PuiseuxSeriesRing(QQ)
sage: x.valuation()
1
sage: (x**(1/3)).valuation()
1/3
sage: R.zero().valuation()
0Mon, 28 Sep 2020 12:11:04 +0200https://ask.sagemath.org/question/53628/bug-with-newton-polygons-of-puiseux-series-in-91/?answer=53634#post-id-53634Comment by FrédéricC for <p>Indeed</p>
<pre><code>sage: R.<x> = PuiseuxSeriesRing(QQ)
sage: x.valuation()
1
sage: (x**(1/3)).valuation()
1/3
sage: R.zero().valuation()
0
</code></pre>
https://ask.sagemath.org/question/53628/bug-with-newton-polygons-of-puiseux-series-in-91/?comment=53638#post-id-53638I made a ticket ; https://trac.sagemath.org/ticket/30679Mon, 28 Sep 2020 14:35:48 +0200https://ask.sagemath.org/question/53628/bug-with-newton-polygons-of-puiseux-series-in-91/?comment=53638#post-id-53638