#9240: applying full_simplify() to gamma functions causes an error
-------------------------+--------------------------------------------------
Reporter: tomc | Owner: tomc
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.7.1
Component: symbolics | Keywords: gamma function, full_simplify,
factorial
Work_issues: | Upstream: N/A
Reviewer: Dan Drake | Author: Tom Coates, Burcin Erocal
Merged: | Dependencies:
-------------------------+--------------------------------------------------
Changes (by newvalueoldvalue):
* author: Tom Coates => Tom Coates, Burcin Erocal
Old description:
> Applying full_simplify() to the gamma function sometimes causes an error.
> This example works:
>
> {{{
> sage: gamma(4/3).full_simplify()
> 1/3*gamma(1/3)
> }}}
>
> but this example does not:
>
> {{{
> sage: gamma(1/3).full_simplify()
> 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))
>
> ---------------------------------------------------------------------------
> ValueError 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/symbolic/expression.so in
> sage.symbolic.expression.Expression.simplify_full
> (sage/symbolic/expression.cpp:21549)()
>
> /Users/tomc/sage-4.4.1/local/lib/python2.6/site-
> packages/sage/symbolic/expression.so in
> sage.symbolic.expression.Expression.simplify_factorial
> (sage/symbolic/expression.cpp:22240)()
>
> /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)
> 1524 # evaluation of maxima code are assumed pre-simplified
> 1525 is_simplified = True
> -> 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
>
> /Users/tomc/sage-4.4.1/local/lib/python2.6/site-
> packages/sage/calculus/calculus.pyc in symbolic_expression_from_string(s,
> syms, accept_sequence)
> 1692 global _augmented_syms
> 1693 _augmented_syms = syms
> -> 1694 return parse_func(s)
> 1695 finally:
> 1696 _augmented_syms = {}
>
> /Users/tomc/sage-4.4.1/local/lib/python2.6/site-
> packages/sage/misc/parser.so in sage.misc.parser.Parser.parse_sequence
> (sage/misc/parser.c:3855)()
>
> /Users/tomc/sage-4.4.1/local/lib/python2.6/site-
> packages/sage/misc/parser.so in sage.misc.parser.Parser.parse_sequence
> (sage/misc/parser.c:3747)()
>
> /Users/tomc/sage-4.4.1/local/lib/python2.6/site-
> packages/sage/misc/parser.so in sage.misc.parser.Parser.p_sequence
> (sage/misc/parser.c:4376)()
>
> /Users/tomc/sage-4.4.1/local/lib/python2.6/site-
> packages/sage/misc/parser.so in sage.misc.parser.Parser.p_tuple
> (sage/misc/parser.c:5032)()
>
> /Users/tomc/sage-4.4.1/local/lib/python2.6/site-
> packages/sage/misc/parser.so in sage.misc.parser.Parser.p_eqn
> (sage/misc/parser.c:5145)()
>
> /Users/tomc/sage-4.4.1/local/lib/python2.6/site-
> packages/sage/misc/parser.so in sage.misc.parser.Parser.p_expr
> (sage/misc/parser.c:5465)()
>
> /Users/tomc/sage-4.4.1/local/lib/python2.6/site-
> packages/sage/misc/parser.so in sage.misc.parser.Parser.p_term
> (sage/misc/parser.c:5690)()
>
> /Users/tomc/sage-4.4.1/local/lib/python2.6/site-
> packages/sage/misc/parser.so in sage.misc.parser.Parser.p_factor
> (sage/misc/parser.c:6053)()
>
> /Users/tomc/sage-4.4.1/local/lib/python2.6/site-
> packages/sage/misc/parser.so in sage.misc.parser.Parser.p_power
> (sage/misc/parser.c:6264)()
>
> /Users/tomc/sage-4.4.1/local/lib/python2.6/site-
> packages/sage/symbolic/function.so in
> sage.symbolic.function.GinacFunction.__call__
> (sage/symbolic/function.cpp:6321)()
>
> /Users/tomc/sage-4.4.1/local/lib/python2.6/site-
> packages/sage/symbolic/expression.so in
> sage.symbolic.expression.Expression.factorial
> (sage/symbolic/expression.cpp:20595)()
>
> /Users/tomc/sage-4.4.1/local/lib/python2.6/site-
> packages/sage/symbolic/pynac.so in sage.symbolic.pynac.py_factorial
> (sage/symbolic/pynac.cpp:9156)()
>
> /Users/tomc/sage-4.4.1/local/lib/python2.6/site-
> packages/sage/rings/arith.pyc in factorial(n, algorithm)
> 403 """
> 404 if n < 0:
> --> 405 raise ValueError, "factorial -- must be nonnegative"
> 406 if algorithm == 'gmp':
> 407 return ZZ(n).factorial()
>
> ValueError: factorial -- must be nonnegative
> }}}
>
> 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.
>
> The problem occurs because full_simplify() here runs the following
> commands in Maxima:
>
> {{{
> (%i1) minfactorial(factcomb(makefact(gamma(1/3))));
> 2
> (%o1) (- -)!
> 3
> }}}
>
> and then the Maxima interface converts this to Sage as factorial(-2/3).
> This causes an error. For Sage, factorial(x) is only defined if x is a
> non-negative integer, whereas for Maxima factorial(x) is equivalent to
> gamma(1+x) and so makes sense whenever x is not in {-1, -2, -3, ...}
New description:
Applying full_simplify() to the gamma function sometimes causes an error.
This example works:
{{{
sage: gamma(4/3).full_simplify()
1/3*gamma(1/3)
}}}
but this example does not:
{{{
sage: gamma(1/3).full_simplify()
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))
---------------------------------------------------------------------------
ValueError 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/symbolic/expression.so in
sage.symbolic.expression.Expression.simplify_full
(sage/symbolic/expression.cpp:21549)()
/Users/tomc/sage-4.4.1/local/lib/python2.6/site-
packages/sage/symbolic/expression.so in
sage.symbolic.expression.Expression.simplify_factorial
(sage/symbolic/expression.cpp:22240)()
/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)
1524 # evaluation of maxima code are assumed pre-simplified
1525 is_simplified = True
-> 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
/Users/tomc/sage-4.4.1/local/lib/python2.6/site-
packages/sage/calculus/calculus.pyc in symbolic_expression_from_string(s,
syms, accept_sequence)
1692 global _augmented_syms
1693 _augmented_syms = syms
-> 1694 return parse_func(s)
1695 finally:
1696 _augmented_syms = {}
/Users/tomc/sage-4.4.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.parse_sequence
(sage/misc/parser.c:3855)()
/Users/tomc/sage-4.4.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.parse_sequence
(sage/misc/parser.c:3747)()
/Users/tomc/sage-4.4.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.p_sequence
(sage/misc/parser.c:4376)()
/Users/tomc/sage-4.4.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.p_tuple
(sage/misc/parser.c:5032)()
/Users/tomc/sage-4.4.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.p_eqn
(sage/misc/parser.c:5145)()
/Users/tomc/sage-4.4.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.p_expr
(sage/misc/parser.c:5465)()
/Users/tomc/sage-4.4.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.p_term
(sage/misc/parser.c:5690)()
/Users/tomc/sage-4.4.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.p_factor
(sage/misc/parser.c:6053)()
/Users/tomc/sage-4.4.1/local/lib/python2.6/site-
packages/sage/misc/parser.so in sage.misc.parser.Parser.p_power
(sage/misc/parser.c:6264)()
/Users/tomc/sage-4.4.1/local/lib/python2.6/site-
packages/sage/symbolic/function.so in
sage.symbolic.function.GinacFunction.__call__
(sage/symbolic/function.cpp:6321)()
/Users/tomc/sage-4.4.1/local/lib/python2.6/site-
packages/sage/symbolic/expression.so in
sage.symbolic.expression.Expression.factorial
(sage/symbolic/expression.cpp:20595)()
/Users/tomc/sage-4.4.1/local/lib/python2.6/site-
packages/sage/symbolic/pynac.so in sage.symbolic.pynac.py_factorial
(sage/symbolic/pynac.cpp:9156)()
/Users/tomc/sage-4.4.1/local/lib/python2.6/site-
packages/sage/rings/arith.pyc in factorial(n, algorithm)
403 """
404 if n < 0:
--> 405 raise ValueError, "factorial -- must be nonnegative"
406 if algorithm == 'gmp':
407 return ZZ(n).factorial()
ValueError: factorial -- must be nonnegative
}}}
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.
The problem occurs because full_simplify() here runs the following
commands in Maxima:
{{{
(%i1) minfactorial(factcomb(makefact(gamma(1/3))));
2
(%o1) (- -)!
3
}}}
and then the Maxima interface converts this to Sage as factorial(-2/3).
This causes an error. For Sage, factorial(x) is only defined if x is a
non-negative integer, whereas for Maxima factorial(x) is equivalent to
gamma(1+x) and so makes sense whenever x is not in {-1, -2, -3, ...}
Apply: trac_9240_full_simplify_gamma.patch,
trac_9240-factorial_evaluation.patch
--
Comment:
attachment:trac_9240-factorial_evaluation.patch adds further doctests and
fixes for the evaluation of factorials. It should be applied after
attachment:trac_9240_full_simplify_gamma.patch.
My changes depend on a small patch to pynac, where I somehow used &&
instead of bitwise and. This patch can be obtained from:
https://bitbucket.org/burcin/pynac-patches/src/c3c5b3b8b1eb/bitwise.patch
This ticket now depends on a new pynac release, which should be coming
soon.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9240#comment:8>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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