Odd results when adding Laurent series

[sagetrac-ljpk]

The following code, which defines a Laurent series ring over a field extension of QQ, gives a weird error when one tries to add and subract Laurent series, all defined over the same ring.

Qx.<xxx>=PolynomialRing(QQ)

K.<w>=NumberField(xxx^2+xxx+1)

R.<y>=PolynomialRing(K)

L.<s>=K.extension(y^6+y^5+y^4+y^3+y^2+y+1)

S.<q>=LaurentSeriesRing(L,"q")

eta1=1 - q - q^2 + q^5 + q^7 - q^12 - q^15 + q^22 + q^26 - q^35 - q^40 + \
q^51+ q^57 - q^70 - q^77 + q^92 + q^100 - q^117 - q^126 + q^145 + q^155 -\
q^176 - q^187 + q^210 + q^222 - q^247 - q^260 + \
q^287 + q^301 - q^330 -q^345 + q^376 + q^392 - q^425 - q^442 + q^477 + q^495

eta7=eta1(q^7 )+O(q^500)

eta49=eta1(q^49)+O(q^500)

x=q^(-2)*eta1*eta49^-1
y=eta7^4*eta49^-4

x+y-x-y

The error is:

<type 'exceptions.TypeError'>             Traceback (most recent call last)

/home/ljpk/<ipython console> in <module>()

/home/ljpk/element.pyx in sage.structure.element.ModuleElement.__sub__()

/home/ljpk/coerce.pxi in sage.structure.element._sub_c()

/home/ljpk/laurent_series_ring_element.pyx in sage.rings.laurent_series_ring_element.LaurentSeries._sub_c_impl()

/home/ljpk/laurent_series_ring_element.pyx in sage.rings.laurent_series_ring_element.LaurentSeries.__init__()

/home/ljpk/power_series_poly.pyx in sage.rings.power_series_poly.PowerSeries_poly.valuation()

/home/ljpk/polynomial_element.pyx in sage.rings.polynomial.polynomial_element.Polynomial.valuation()

<type 'exceptions.TypeError'>: The polynomial, p, must have the same parent as self.

Component: algebra

Issue created by migration from https://trac.sagemath.org/ticket/2462

[sagetrac-dmharvey]

comment:2

I've been debugging this for a while. The problem is somehow connected to the following. After running the example given, then do:

sage: h = ((x + y) - x).valuation_zero_part()
sage: k = y.valuation_zero_part()
sage: type(h)
<type 'sage.rings.power_series_poly.PowerSeries_poly'>
sage: type(k)
<type 'sage.rings.power_series_poly.PowerSeries_poly'>
sage: parent(h) is parent(k)
True
sage: f = (h - k).polynomial()
sage: f
0
sage: len(f.coeffs())
498

So somehow a polynomial is being created whose value is zero, yet which has 498 zero coefficients, i.e. it's not being normalised properly. Then the valuation method blows up:

sage: f.valuation()
[boom]

[sagetrac-mabshoff]

comment:3

This is still a problem with 3.2.alpha2-ish:

----------------------------------------------------------------------
| Sage Version 3.2.alpha1, Release Date: 2008-10-26                  |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------

sage: Qx.<xxx>=PolynomialRing(QQ)
sage: 
sage: K.<w>=NumberField(xxx^2+xxx+1)
sage: 
sage: R.<y>=PolynomialRing(K)
sage: 
sage: L.<s>=K.extension(y^6+y^5+y^4+y^3+y^2+y+1)
sage: 
sage: S.<q>=LaurentSeriesRing(L,"q")
sage: 
sage: eta1=1 - q - q^2 + q^5 + q^7 - q^12 - q^15 + q^22 + q^26 - q^35 - q^40 + \
....: q^51+ q^57 - q^70 - q^77 + q^92 + q^100 - q^117 - q^126 + q^145 + q^155 -\
....: q^176 - q^187 + q^210 + q^222 - q^247 - q^260 + \
....: q^287 + q^301 - q^330 -q^345 + q^376 + q^392 - q^425 - q^442 + q^477 + q^495
sage: 
sage: eta7=eta1(q^7 )+O(q^500)
sage: 
sage: eta49=eta1(q^49)+O(q^500)
sage: 
sage: x=q^(-2)*eta1*eta49^-1
sage: y=eta7^4*eta49^-4
sage: 
sage: x+y-x-y
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/scratch/mabshoff/release-cycle/sage-3.2.alpha2/<ipython console> in <module>()

/scratch/mabshoff/release-cycle/sage-3.2.alpha2/local/lib/python2.5/site-packages/sage/structure/element.so in sage.structure.element.ModuleElement.__sub__ (sage/structure/element.c:5718)()

/scratch/mabshoff/release-cycle/sage-3.2.alpha2/local/lib/python2.5/site-packages/sage/rings/laurent_series_ring_element.so in sage.rings.laurent_series_ring_element.LaurentSeries._sub_ (sage/rings/laurent_series_ring_element.c:5543)()

/scratch/mabshoff/release-cycle/sage-3.2.alpha2/local/lib/python2.5/site-packages/sage/rings/laurent_series_ring_element.so in sage.rings.laurent_series_ring_element.LaurentSeries.__init__ (sage/rings/laurent_series_ring_element.c:1831)()

/scratch/mabshoff/release-cycle/sage-3.2.alpha2/local/lib/python2.5/site-packages/sage/rings/power_series_poly.so in sage.rings.power_series_poly.PowerSeries_poly.valuation (sage/rings/power_series_poly.c:2296)()

/scratch/mabshoff/release-cycle/sage-3.2.alpha2/local/lib/python2.5/site-packages/sage/rings/polynomial/polynomial_element.so in sage.rings.polynomial.polynomial_element.Polynomial.valuation (sage/rings/polynomial/polynomial_element.c:24197)()

TypeError: The polynomial, p, must have the same parent as self.

Robert: Any idea what is going on here?

Cheers,

Michael

[robertwb]

comment:4

I really don't think this is due to coercion, as no coercion is going on here (all parents are identical, arithmetic is dispatched immediately).

David Harvey is right, in polynomial_element.pyx:3672 we have

        if p is None:
            for k from 0 <= k <= self.degree():
                if self[k]:
                    return ZZ(k)

because self is not detected to be zero earlier (even though it really is) the loop exits without returning, hence the [boom]. The error, however, occurred earlier. Somewhere, something's not getting normalized like it should be. I think the error is in polynomials.

Continuing on David's session,

sage: f = h.polynomial() - k.polynomial()
sage: f
0
sage: sage: len(f.coeffs())
500
sage: k.degree()
499
sage: k[499]  # ?!!
0

[robertwb]

comment:5

More info

sage: x.valuation_zero_part().polynomial().degree()
499
sage: x.valuation_zero_part().polynomial()[499]
0

[robertwb]

comment:6

Here's the actual error:

sage: S.<q> = CC[] # generic poly implementation
sage: f = (1+q^10+q^100).truncate(50)
sage: f.degree()
49

I'm posting a patch to fix this.

[robertwb]

comment:7

Attachment: 2462-poly-truncate.patch.gz

[sagetrac-mabshoff]

comment:8

#4406 is a followup ticket to this.

Cheers,

Michael

[mwhansen]

comment:9

Looks good to me.

[sagetrac-mabshoff]

comment:10

Merged in Sage 3.2.alpha2