Problem converting a Laurent Series from pari to Sage

[JohnCremona]

It seems that PARI laurent series can only be converted to Sage LaurentSeries if the valuation is >= 0.

Simple example:

sage: R = LaurentSeriesRing(QQ, 'q')
sage: R(pari('1/x'))
0                       # Very wrong
sage: R(pari('1/x + O(x^20)'))
Traceback (most recent call last)
[...]
PariError:  (5)

Example from John Cremona:

sage: E = EllipticCurve('11a1')
sage: R = LaurentSeriesRing(RationalField(),'q')
sage: XY = E.pari_mincurve().elltaniyama()
sage: [R(XY[0]),R(XY[1])]

CC: @jdemeyer

Component: interfaces

Keywords: Laurent series, pari

Author: Jeroen Demeyer

Reviewer: John Cremona

Merged: sage-4.5.3.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/2508

[aghitza]

comment:2

I cannot replicate John's example (maybe it has already been fixed?):

sage: X = E=EllipticCurve('389a1').modular_parametrization()[0]
sage: X
q^-2 + 2*q^-1 + 4 + 7*q + 13*q^2 + 18*q^3 + 31*q^4 + 49*q^5 + 74*q^6 + 111*q^7 + 173*q^8 + 251*q^9 + 379*q^10 + 560*q^11 + 824*q^12 + 1199*q^13 + 1773*q^14 + 2365*q^15 + 3463*q^16 + 4508*q^17 + O(q^18)
sage: type(X)
<type 'sage.rings.laurent_series_ring_element.LaurentSeries'>
sage: version()
'SAGE Version 2.10.4, Release Date: 2008-03-17'

Notice how modular_parametrization() now returns a Sage LaurentSeries instead of a pari object.

[JohnCremona]

comment:3

Alex,

That's right, I changed the code to return a proper Laurent series:

       R = LaurentSeriesRing(RationalField(),'q')
        XY = self.pari_mincurve().elltaniyama()
        return [1/R(1/XY[0]),1/R(1/XY[1])]

But look at what I had to do to coerce the pari Laurent series into the Sage ring R! X and Y have negative valuation; I could only get the coercions to work with things of positive valuation, so had to insert two spurious inversions (for each of X and Y)

The following shoud work but does not:

sage: E=EllipticCurve('11a1')
sage: R = LaurentSeriesRing(RationalField(),'q')
sage: XY = E.pari_mincurve().elltaniyama()
sage: [R(XY[0]),R(XY[1])]

[jdemeyer]

Description changed:

--- 
+++ 
@@ -1,47 +1,22 @@
-The elliptic curve function modular_parametrization() returns a list of two pari objects which are Laurent Series in x (of degrees -2, -3).  I wanted to convert these into proper Sage Laurent Series, but that does not work.  However if I invert these (so they have positive degree, i.e. are power series) then I can coerce them into the Laurent series ring, and then invert again!
+It seems that PARI laurent series can only be converted to Sage LaurentSeries if the valuation is >= 0.
+
+Simple example:
 
 ```
-sage: X = E=EllipticCurve('389a1').modular_parametrization()[0]
-sage: type(X)
-<type 'sage.libs.pari.gen.gen'>
-sage: X
-x^-2 + 2*x^-1 + 4 + 7*x + 13*x^2 + 18*x^3 + 31*x^4 + 49*x^5 + 74*x^6 + 111*x^7 + 173*x^8 + 251*x^9 + 379*x^10 + 560*x^11 + 824*x^12 + 1199*x^13 + 1773*x^14 + O(x^15)
-sage: R=LaurentSeriesRing(QQ,'q')
-sage: R(X)
----------------------------------------------------------------------------
-<class 'sage.libs.pari.gen.PariError'>    Traceback (most recent call last)
-
-/home/jec/<ipython console> in <module>()
-
-/home/jec/sage-2.10.3/local/lib/python2.5/site-packages/sage/rings/laurent_series_ring.py in __call__(self, x, n)
-    182             return self.gen()**n * x
-    183         else:
---> 184             return laurent_series_ring_element.LaurentSeries(self, x, n)
-    185
-    186     def _coerce_impl(self, x):
-
-/home/jec/laurent_series_ring_element.pyx in sage.rings.laurent_series_ring_element.LaurentSeries.__init__()
-
-/home/jec/sage-2.10.3/local/lib/python2.5/site-packages/sage/rings/power_series_ring.py in __call__(self, f, prec, check)
-    324             v = sage_eval(f.Eltseq())
-    325             return self(v) * (self.gen(0)**f.Valuation())
---> 326         return self.__power_series_class(self, f, prec, check=check)
-    327
-    328     def construction(self):
-
-/home/jec/power_series_poly.pyx in sage.rings.power_series_poly.PowerSeries_poly.__init__()
-
-/home/jec/sage-2.10.3/local/lib/python2.5/site-packages/sage/rings/polynomial/polynomial_ring.py in __call__(self, x, check, is_gen, construct, absprec)
-    237         elif isinstance(x, pari_gen):
-    238             if x.type() != 't_POL':
---> 239                 x = x.Polrev()
-    240
-    241         C = self.__polynomial_class
-
-/home/jec/gen.pyx in sage.libs.pari.gen._pari_trap()
-
-<class 'sage.libs.pari.gen.PariError'>:  (8)
-sage: 1/R(1/X)
-q^-2 + 2*q^-1 + 4 + 7*q + 13*q^2 + 18*q^3 + 31*q^4 + 49*q^5 + 74*q^6 + 111*q^7 + 173*q^8 + 251*q^9 + 379*q^10 + 560*q^11 + 824*q^12 + 1199*q^13 + 1773*q^14 + 2365*q^15 + 3463*q^16 + 4508*q^17 + O(q^18)
+sage: R = LaurentSeriesRing(QQ, 'q')
+sage: R(pari('1/x'))
+0                       # Very wrong
+sage: R(pari('1/x + O(x^20)'))
+Traceback (most recent call last)
+[...]
+PariError:  (5)
 ```
 
+Example from John Cremona:
+
+```
+sage: E = EllipticCurve('11a1')
+sage: R = LaurentSeriesRing(RationalField(),'q')
+sage: XY = E.pari_mincurve().elltaniyama()
+sage: [R(XY[0]),R(XY[1])]
+```