#5993: rewrite numerical_approx (the n function) to use interval arithmetic
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Reporter: was | Owner: burcin
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.0
Component: calculus | Keywords:
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This email snippet pretty much describes the issue:
{{{
On Tue, May 5, 2009 at 11:16 PM, Henryk Trappmann
<[email protected]> wrote:
>
> Ah now I see, you mean though it displays 1/384 it is internally still
> the above sum, which is computed when evaluated with n.
True. In Sage right now the internal form of the expression (not the
simplified form) is used by the "n" command. This will change when Sage
switches from using maxima-based symbolics to Pynac.
By the way, you can use the real interval field to get a floating point
approximation to any symbolic expression to a given number of digits of
precision. Every digit is definitely right except the one right before
the question mark:
sage: a = 1/(48*sqrt(1)) - 7/(96*1**(3/2)) + 3/(32*1**(5/2)) - 5/
(128*1**(7/2))
sage: RealIntervalField(100)(a) # increase 100 for more digits
0.002604166666666666666666666667?
I think the n function (numerical_approx) for symbolics should be changed
to using interval arithmetic. This will be a huge improvement. Notice,
e.g., that interval arithmetic very nicely gives the right answer for the
infamous sin(10^50):
sage: a = sin(10^50)
sage: a.n(53)
-0.480500143493759
sage: a.n(100)
0.60974154556722786199645650055
sage: RealIntervalField(100)(a)
0.?
sage: RealIntervalField(1000)(a)
-0.7896724934293100827102895399174077539600834046214027191457808736221899969800609898633436757589688470442999273506152178357769064871103469499564331175635613221319397479785737324994506546860108913238488404198306006819757685879489185272089985858148036954222175628785469474395231359019098600625732453528693?
sage: RealIntervalField(2000)(a)
-0.78967249342931008271028953991740775396008340462140271914578087362218999698006098986334367575896884704429992735061521783577690648711034694995643311756356132213193974797857373249945065468601089132384884041983060068197576858794891852720899858581480369542221756287854694743952313590190986006257324535286926640214204183176856658976160340849634781130568053474154330242776565926107540133198976420887112928640131582614537425282391078909233424580311555104358881651194953182665408243214532152322603956371555619997139323527489307648072219268176687894373677502675114853503742816202001868587837402822439060931321957?
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5993>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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