Hi folks,
I noticed the following thread from the Maxima mailing list.
--
Regards
Minh Van Nguyen
---------- Forwarded message ----------
From: Richard Fateman <fate...@cs.berkeley.edu>
Date: Sun, Aug 16, 2009 at 12:35 AM
Subject: Re: [Maxima] mpmath + sage + hypergeometric numerics
To: Barton Willis <will...@unk.edu>
Cc: Maxima List <max...@math.utexas.edu>
I tried Mathematica 6.0 on
HypergeometricPFQ[{112, 51/10}, {-9/10}, -99999/100000]
and got the (presumably exact ??) result
-183933169187931829794351104521526197029774379000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000/
11324984934739307220163426028747102350310899924999124109622447068264\
2089509049347831693103349943262869210969949172830357221037131460936617\
2457317140303388728526568056839394088427274999192970896030049564669168\
5199955047630663915447045353398112210710118309005643847603222953120252\
7472676579674432971253271831088126529101868279771770153695910346445313\
9991441759761159325993368148026744708619920408656674968525340473179327\
4543394221143555750764130509074977665133986904900063950461891643545329\
6240971237497707332066495140483266031003755059081400674335749107079469\
7608945169169804679596517702998625671016983228364785324615691195240034\
1
which evaluates to the Mathematica result via N[%,100].
In the documentation for HypergeometricPFQ there are illustrations where the
internal $MaxExtraPrecision is insufficient to obtain the requested
precision for this function,
so apparently Mathematica fails to do adequate numerical evaluation
using N[] without resetting some global system parameter.
I don't know how to run your code or mpmath on exact inputs.
I have, in the past, used python-wrapped code from Allegro CL with
almost no effort.
This was for GMP.
I found, however, that the python wrappers were too unsophisticated for me, and
implemented only the "Functional" style in GMP. That is, A:=A*B+C could not
access the combined multiply-add-replace capability. I don't know if
that is still the case.
Barton Willis wrote:
For Maxima 5.19, I contributed code for numerical and symbolic
evaluation of the hypergeometric functions. The other day, I started
looking into how Sage evaluates these functions (but I haven't tried to
install Sage). One way seems to be mpmath
(http://code.google.com/p/mpmath/).
The NSF supported the development of mpmath:
http://groups.google.com/group/mpmath/browse_thread/thread/960b02f0a2ed5dfa
Let's try mpmath on a hypergeometric function; first let's try 50 digits
and
second 100 digits. The signs of the two values aren't the same:
mp.dps = 50
hyper(['112.0', '5.1'],['-0.9'],'-0.99999')
mpf('0.00000000000073150973254264463451967741826767251189694769140430165')
mp.dps = 100
hyper(['112.0', '5.1'],['-0.9'],'-0.99999')
mpf('-0.00000000000000000000000162413610479<junk>')
Wolfram Alpha (input: hypergeometricPQ[{112,5.1}, {-0.9}, -0.99999]) gives
-1.62413610479708629611767409391575176600337612526370... x 10^-24
And my (non-NSF) code gives
(%i4) hypergeometric([112.0b0, 5.1b0],[-0.9b0],-0.99999b0);
(%o4) - 1.6331655633849675761598634419620944688583571143885b-24
I'm not sure why my value differs from mma by about 9.0e-27, but
likely it is due to differences in the precisions of the inputs. At
least my code gets the sign correct. Grump^infinity.
Barton
_______________________________________________
Maxima mailing list
max...@math.utexas.edu
http://www.math.utexas.edu/mailman/listinfo/maxima
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send an email to sage-devel@googlegroups.com
To unsubscribe from this group, send an email to
sage-devel-unsubscr...@googlegroups.com
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://www.sagemath.org
-~----------~----~----~----~------~----~------~--~---
