default precision for all series (symbolic, power, Laurent)

[rws]

Both Laurent and power series ring elements have a default precision of 20. OTOH, symbolic series expansions need the precision set:

sage: R.<t> = LaurentSeriesRing(QQ)
sage: 1/(1-t)
1 + t + t^2 + t^3 + t^4 + t^5 + t^6 + t^7 + t^8 + t^9 + t^10 + t^11 + t^12 + t^13 + t^14 + t^15 + t^16 + t^17 + t^18 + t^19 + O(t^20)
sage: var('x')
x
sage: ex=1/(1-x)
sage: ex.series(x)
...
TypeError: series() takes exactly 2 positional arguments (1 given)

This ticket proposes to unify the behaviour by allowing the following:

sage: ex.series(x)
1 + 1*x + 1*x^2 + 1*x^3 + 1*x^4 + 1*x^5 + 1*x^6 + 1*x^7 + 1*x^8 + 1*x^9 + 1*x^10 + 1*x^11 + 1*x^12 + 1*x^13 + 1*x^14 + 1*x^15 + 1*x^16 + 1*x^17 + 1*x^18 + 1*x^19 + Order(x^20)

As this is about reducing surprise for the user both algebra and symbolic series default precision should have the same value, so the ticket should also implement such a global value.

This ticket also deprecates the use of LaurentSeriesRing_generic.set_default_prec as it contradicts the immutability of parents and conflicts with the caching of LaurentSeriesRings?.

[rws]

New commits:

​5fc4999

16201: implement global default series precision, accessors

[cheuberg]

I do not think that order=-1 is a good default value, as it changes previous behaviour:

Prior to this patch:

sage: f = sin(x)^(-2)
....: f.series(x, -1)
1*x^(-2) + Order(1/x)

After this patch:

sage: f = sin(x)^(-2)
....: f.series(x, -1)
1*x^(-2) + 1/3 + 1/15*x^2 + 2/189*x^4 + 1/675*x^6 + 2/10395*x^8 + 1382/58046625*x^10 + 4/1403325*x^12 + 3617/10854718875*x^14 + 87734/2292899734125*x^16 + 349222/80596287646875*x^18 + Order(x^20)

Furthermore, I'd like to see doctests testing the new behaviour.

Finally, sage.misc.defaults could be added to the reference manual such that the documentation of all three modified methods (symbolic, power, Laurent) could link to that place for setting the default precision.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​b3cb457

16201: change keyword default; add doctests; add misc.defaults to doctree and point to it

[rws]

Done. Unfortunately this is Cython so I had to pick a value that signals default, changed to -65535 now.

Please add your realname to Reviewers.

[cheuberg]

Replying to rws:

Done. Unfortunately this is Cython so I had to pick a value that signals default, changed to -65535 now.

I think that replacing int order=-65535 by order=None would lead to clearer code at a negligible performance penalty.

Further comments:

• The docstrings of series_precision and set_series_precision should have EXAMPLE sections.
• The parameter default_prec of the Laurent series classes should be explained; the only explanation now is in def default_prec(self) which should be rephrased anyway ("Set ..." is not correct).
• I'd like to see doctests showing examples on how to construct series with different values for set_series_precision
• :meth:`set_series_precision` is a dead link.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​3b682e2

16201: misc.defauts doctests; deprecate LaurentSeriesRing.set_default_prec; cosmetics

[rws]

The default for order is now None. The misc functions now have examples. The description of def default_prec(self) was corrected. I think the LaurentSeriesRing method set_default_prec should be deprecated as is already hinted. Done.

The general improvement of Laurent series documentation is ticket #12259.

I don't think doctests showing examples on how to construct series with different values for set_series_precision should be added. I don't want to encourage frequent usage of the global setting to set single series precisions.

If the link is dead you should do make doc-clean; make doc. It will not suffice to sage -docbuild since a file was added.

[cheuberg]

For now, just three comments, I'll have a closer look later.

File "src/sage/symbolic/expression.pyx", line 3542, in sage.symbolic.expression.Expression.series
Failed example:
    f.series(x)
Exception raised:
    Traceback (most recent call last):
      File "/local/sage/sage-6.5.beta4/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 488, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/local/sage/sage-6.5.beta4/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 850, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.symbolic.expression.Expression.series[9]>", line 1, in <module>
        f.series(x)
      File "sage/symbolic/expression.pyx", line 3584, in sage.symbolic.expression.Expression.series (build/cythonized/sage/symbolic/expression.cpp:20710)
        x = self._gobj.series(symbol0._gobj, order, 0)
    TypeError: an integer is required

The reason is that prec is set but never used.

Replying to rws:

I don't think doctests showing examples on how to construct series with different values for set_series_precision should be added. I don't want to encourage frequent usage of the global setting to set single series precisions.

I concur that we should not encourage the actual frequent usage of the global settings. However, I'd prefer it to be at least be covered by a test in a "TESTS" section, just to be sure to avoid small errors as the issue outlined above.

If the link is dead you should do make doc-clean; make doc. It will not suffice to sage -docbuild since a file was added.

I think that the problem is rather the meth instead of func.

[cheuberg]

The deprecation of set_series_precision leads to four failing doctests elsewhere:

sage -t src/sage/schemes/hyperelliptic_curves/hyperelliptic_padic_field.py
**********************************************************************
File "src/sage/schemes/hyperelliptic_curves/hyperelliptic_padic_field.py", line 74, in sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field.local_analytic_interpolation
Failed example:
    x,y,z = HK.local_analytic_interpolation(P,Q)
Expected nothing
Got:
    doctest:512: DeprecationWarning: This method is deprecated.
    See http://trac.sagemath.org/16201 for details.
**********************************************************************
sage -t src/sage/schemes/hyperelliptic_curves/hyperelliptic_generic.py
**********************************************************************
File "src/sage/schemes/hyperelliptic_curves/hyperelliptic_generic.py", line 490, in sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic.local_coordinates_at_infinity
Failed example:
    x,y = H.local_coordinates_at_infinity(10)
Expected nothing
Got:
    doctest:512: DeprecationWarning: This method is deprecated.
    See http://trac.sagemath.org/16201 for details.
**********************************************************************
sage -t src/sage/schemes/hyperelliptic_curves/monsky_washnitzer.py
**********************************************************************
File "src/sage/schemes/hyperelliptic_curves/monsky_washnitzer.py", line 3580, in sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferential.coleman_integral
Failed example:
    w.coleman_integral(P,2*P)
Expected:
    O(5^6)
Got:
    doctest:512: DeprecationWarning: This method is deprecated.
    See http://trac.sagemath.org/16201 for details.
    O(5^6)
**********************************************************************
sage -t src/sage/rings/morphism.pyx
**********************************************************************
File "src/sage/rings/morphism.pyx", line 249, in sage.rings.morphism
Failed example:
    R.set_default_prec(10)
Expected nothing
Got:
    doctest:1: DeprecationWarning: This method is deprecated.
    See http://trac.sagemath.org/16201 for details.
**********************************************************************

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​0fcce82

16201: more doctests, fixes; remove deprecated usage

[rws]

All done.

[cheuberg]

All Doctests (make ptestlong) pass; code looks ok; thanks.

The changes in hyperelliptic_generic.py demonstrate that there is a default precision of 20, too, which is not covered by this ticket. For the ReSt? formatting errors in that file, see #17599.

[rws]

Thanks for the review.

[rws]

Replying to cheuberg:

The changes in hyperelliptic_generic.py demonstrate that there is a default precision of 20, too, which is not covered by this ticket.

That is now #17613.

[jdemeyer]

This is wrongly indented:

TESTS:

    Check if changing global series precision does it right::

It should be

TESTS:

Check if changing global series precision does it right::

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​0d7da1b

16201: fix indentation

[rws]

Jeroen, can you please have a quick look again, so that we can finish it?

[cheuberg]

The wrong indentation has been fixed.