#20062: Make _floordiv_() for power series a deprecated alias for _div_()
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Reporter: pbruin | Owner:
Type: task | Status: needs_work
Priority: minor | Milestone: sage-7.1
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: Peter Bruin | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/pbruin/20062-PowerSeries_floordiv| e9719f7399ffab100407a360c16fe0596e7f2689
Dependencies: | Stopgaps:
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Comment (by bruno):
Replying to [comment:3 pbruin]:
> Why would this be necessary? If the user calls `__floordiv__`, he
presumably does this for a reason, i.e. expects that it behaves
differently from `__div__`...
One case I very often encounter is the need of an "exact division", that
is a division when you know in advance that the result is exact.
>
> > That's why (I guess) there is a `__floordiv__` in the class
`FieldElement`.
>
> Well, power series rings are not fields. There is also an
implementation of `_floordiv_` in `RingElement`, which explicitly raises
an error saying `unsupported operand parent(s) for '//'`. In fact, this
error is even raised when applying `__floordiv__` to elements of `RR`:
> {{{
> sage: RR(1.2) // RR(2.3)
> ...
> TypeError: unsupported operand parent(s) for '//': 'Real Field with 53
bits of precision' and 'Real Field with 53 bits of precision'
> }}}
Right. But this behavior for `RR` is currently being discussed in #15260.
>
> > So I would not deprecate it, but rather simply make it an (non-
deprecated) alias of `__div__`.
>
> Then we should do this in general for ring elements; I don't really see
the advantage of this...
That's right, it is probably a bad idea to make `__floordiv__` an alias of
`__div__` in this case.
>
> In my opinion, it would make more sense to make sure that power series
rings `R` over a field, or more generally all discrete valuation rings
`(R, v)`, are put into the category of Euclidean domains. Then floor
division in `R` can be implemented using Euclidean division, so `f // g =
f / g` if `v(g) <= v(f)` and `f // g = 0` if `v(g) > v(f)`. However, this
has the disadvantage that it is not the same as the current
`__floordiv__`, which (as far as I can see) is the same as `__div__`.
You're perfectly right. My two-cent on this would be as follows:
* `__div__` should return an element of the fraction field, as it is the
case for elements of `ZZ` or polynomials for instance; I find the current
situation weird:
{{{#!python
sage: R.<x> = QQ[[]]
sage: (1/(1+x)).parent()
Power Series Ring in x over Rational Field
sage: (1/x).parent()
Laurent Series Ring in x over Rational Field
}}}
while for instance for `ZZ`:
{{{#!python
sage: (1/1).parent() is (1/2).parent()
True
}}}
* `__floordiv__` in power series rings over a field should return the
quotient in the euclidean division, since these rings are euclidean.
* `__floordiv__` in power series rings over `ZZ` (say) should behave the
same way as it behaves for polynomials over `ZZ`, that is return the
quotient in the euclidean division (as over `QQ`) but reducing each
coefficient modulo the leading coefficient of the divisor. For instance,
`2-3*x-x^2+O(x^3)//(2+x)` should equal `1-2*x+0*x^2+O(x^3)`.
--
Ticket URL: <http://trac.sagemath.org/ticket/20062#comment:4>
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