#13055: Better default precision for .n() method
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Reporter: dsm | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-6.4
Component: symbolics | Resolution:
Keywords: numerical_approx, sd40.5 | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by jdemeyer:
Old description:
> By going via SR we can lose precision when using numerical_approx:
>
> {{{
> sage: p
> 3.1415926535897932384626433832795028841971693993751058209749
> sage: parent(p)
> Real Field with 200 bits of precision
> sage: SR(p)
> 3.1415926535897932384626433832795028841971693993751058209749
> sage: SR(p).n()
> 3.14159265358979
> sage: parent(SR(p).n())
> Real Field with 53 bits of precision
> }}}
>
> The information is still there, though (as is obvious from the fact the
> string produced has all those extra digits):
>
> {{{
> sage: SR(p).pyobject()
> 3.1415926535897932384626433832795028841971693993751058209749
> sage: parent(SR(p).pyobject())
> Real Field with 200 bits of precision
> }}}
>
> This might not seem that significant -- we could interpret "n" as always
> defaulting to 53 bits unless specified otherwise -- but it can cause some
> headaches when trying to get hold=True to behave nicely. I'd prefer that
> `f(1.2345678901234567890)` give the same answer as
> `f(1.2345678901234567890, hold=True).n()`, especially now that we
> typically get the precision from the parent.
New description:
We can lose precision when using `numerical_approx`:
{{{
sage: p = pi.n(200)
sage: p
3.1415926535897932384626433832795028841971693993751058209749
sage: p.numerical_approx()
3.14159265358979
}}}
This might not seem that significant -- we could interpret `.n()` as
always defaulting to 53 bits unless specified otherwise -- but it can
cause some headaches when trying to get `hold=True` for symbolics to
behave nicely. I'd prefer that `f(1.2345678901234567890)` gives the same
answer as `f(1.2345678901234567890, hold=True).n()`, especially now that
we typically get the precision from the parent.
Related: #16025
--
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Ticket URL: <http://trac.sagemath.org/ticket/13055#comment:8>
Sage <http://www.sagemath.org>
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