Opened 13 years ago
Closed 13 years ago
#9217 closed defect (fixed)
Taylor expansion of gamma functions is broken
Reported by: | tomc | Owned by: | tomc |
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Priority: | minor | Milestone: | sage-4.4.4 |
Component: | calculus | Keywords: | symbolic calculus, gamma function, taylor expansion |
Cc: | Merged in: | sage-4.4.4.alpha1 | |
Authors: | Tom Coates | Reviewers: | Mike Hansen |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
Taylor expansion of the gamma function often causes an error. This example works:
sage: taylor(gamma(1/2+x),x,0,2) 1/4*(pi^2 + 2*euler_gamma^2 + 8*euler_gamma*log(2) + 8*log(2)^2)*sqrt(pi)*x^2 - (euler_gamma + 2*log(2))*sqrt(pi)*x + sqrt(pi)
but this doesn't:
sage: taylor(gamma(1/3+x),x,0,2) ERROR: An unexpected error occurred while tokenizing input The following traceback may be corrupted or invalid The error message is: ('EOF in multi-line statement', (1254, 0)) --------------------------------------------------------------------------- TypeError Traceback (most recent call last) /Users/tomc/sage-4.4.1/<ipython console> in <module>() /Users/tomc/sage-4.4.1/local/lib/python2.6/site-packages/sage/calculus/functional.pyc in taylor(f, *args) 369 if not isinstance(f, Expression): 370 f = SR(f) --> 371 return f.taylor(*args) 372 373 def expand(x, *args, **kwds): /Users/tomc/sage-4.4.1/local/lib/python2.6/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression.taylor (sage/symbolic/expression.cpp:13236)() /Users/tomc/sage-4.4.1/local/lib/python2.6/site-packages/sage/structure/parent.so in sage.structure.parent.Parent.__call__ (sage/structure/parent.c:6332)() /Users/tomc/sage-4.4.1/local/lib/python2.6/site-packages/sage/structure/coerce_maps.so in sage.structure.coerce_maps.NamedConvertMap._call_ (sage/structure/coerce_maps.c:4053)() /Users/tomc/sage-4.4.1/local/lib/python2.6/site-packages/sage/interfaces/maxima.pyc in _symbolic_(self, R) 1810 sqrt(2) 1811 """ -> 1812 return R(self._sage_()) 1813 1814 def __complex__(self): /Users/tomc/sage-4.4.1/local/lib/python2.6/site-packages/sage/interfaces/maxima.pyc in _sage_(self) 1791 import sage.calculus.calculus as calculus 1792 return calculus.symbolic_expression_from_maxima_string(self.name(), -> 1793 maxima=self.parent()) 1794 1795 def _symbolic_(self, R): /Users/tomc/sage-4.4.1/local/lib/python2.6/site-packages/sage/calculus/calculus.pyc in symbolic_expression_from_maxima_string(x, equals_sub, maxima) 1526 return symbolic_expression_from_string(s, syms, accept_sequence=True) 1527 except SyntaxError: -> 1528 raise TypeError, "unable to make sense of Maxima expression '%s' in Sage"%s 1529 finally: 1530 is_simplified = False TypeError: unable to make sense of Maxima expression 'gamma(1/3)-(6*euler_gamma+pi*sqrt(3)+9*log(3))*gamma(1/3)*x/6+(12*gamma(1/3)*psi[1](1/3)+(12*euler_gamma^2+(4*pi*sqrt(3)+36*log(3))*euler_gamma+6*log(3)*pi*sqrt(3)+pi^2+27*log(3)^2)*gamma(1/3))*x^2/24' in Sage
This occurs because when parsing the output from Maxima we should replace all occurrences of the polygamma function psi[n](foo) by psi(n,foo).
I am running Sage 4.4.1 on Mac OS X version 10.6 (Snow Leopard), built from source. But the second example also fails on Sage 4.3.5 on 64-bit Linux, built from source. Looking at the source code suggests that the second example will fail on all platforms.
Attachments (3)
Change History (8)
comment:1 Changed 13 years ago by
Status: | new → needs_review |
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Changed 13 years ago by
Attachment: | trac_9217_Taylor_gamma_fix.patch added |
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revised patch also changes the AUTHORS block to match the format suggested in the Developer's Guide
comment:2 follow-up: 3 Changed 13 years ago by
It looks like the patch just changes the AUTHORS block and doesn't have the actual fix for the problem in it.
comment:3 Changed 13 years ago by
Replying to mhansen:
It looks like the patch just changes the AUTHORS block and doesn't have the actual fix for the problem in it.
Argh! Will upload new patch.
Changed 13 years ago by
Attachment: | trac_9217-fix-1.patch added |
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Changed 13 years ago by
Attachment: | trac_9217-fix-2.patch added |
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comment:4 Changed 13 years ago by
OK, sorry about that. I uploaded 2 patches. The first one:
trac_9217-fix-1.patch
fixes the problem with Taylor expanding gamma functions. The second one:
trac_9217-fix-2.patch
should be applied after the first one, and fixes the AUTHOR block.
comment:5 Changed 13 years ago by
Authors: | → Tom Coates |
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Merged in: | → sage-4.4.4.alpha1 |
Resolution: | → fixed |
Reviewers: | → Mike Hansen |
Status: | needs_review → closed |
Looks good to me.
I uploaded a patch to fix this.