Done and thanks!
workaround before the ticket is merged:
sage: from sage.libs.pynac.pynac import register_symbol
sage: register_symbol(abs, {'fricas': 'abs'})
(would it be better not to create symbolic functions for functions returned
by fricas unknown to sage?)
Martin
Am Samstag, 30. März 2019 21:03:38 UTC+1 schrieb Frédéric Chapoton:
>
> I have made https://trac.sagemath.org/ticket/27577, which needs review
> (very simple ticket)
>
> Frederic
>
> Le samedi 30 mars 2019 10:56:59 UTC+1, Emmanuel Charpentier a écrit :
>>
>> *TL;DR :* Sage can produce a symbolic expression :
>>
>> - that it can't evaluate numerically when correcly substiuted, AND
>> - that can be evaluated when typed manually.
>>
>> The problem seems ti be bound to absolute values.
>>
>> That, IMHO, is a first-class bug...
>>
>> *Demonstation :* I think that some results produced by fricas'
>> integrator are wrong, and wanted to show it numerically.
>>
>> Problem setup :
>> x,y=var("x,y", domain="real")
>> assume(x>-1,x<1,y>-1,y<1,x^2+y^2<1)
>> eps1=var("eps1", latex_name="\\varepsilon_1", domain="positive")
>> eps2=var("eps2", latex_name="\\varepsilon_2", domain="positive")
>> assume(eps1<1,eps2<1, eps1^2+eps2^2<1)
>> f(x,y)=sqrt(1-x^2-y^2)
>>
>> Define the integral on a given rectangle as a function :
>>
>> foo(eps1,eps2)=f(x).integrate(x,0,eps1,
>> algorithm="fricas").integrate(y,0,eps2, algorithm="fricas")
>>
>> Use it :
>>
>> sage: bar=foo(1/10,1/10)
>> sage: bar
>> 299/12000*pi - 1/198*sqrt(11)*pi*abs(-3/2*sqrt(11)) + 7/1500*sqrt(1/2)
>> + 1/6*arctan(9799/140*sqrt(1/2)) - 299/6000*arctan(14*sqrt(1/2)) +
>> 299/6000*arctan(1/7*sqrt(1/2))
>>
>> So far so good. But when I want a numerical approximation :
>>
>> sage: bar.n()
>>
>> ---------------------------------------------------------------------------
>> TypeError Traceback (most recent call
>> last)
>> <ipython-input-104-425a0225c048> in <module>()
>> ----> 1 bar.n()
>>
>> /usr/local/sage-8/local/lib/python2.7/site-packages/sage/structure/element.pyx
>>
>> in sage.structure.element.Element.n
>> (build/cythonized/sage/structure/element.c:8020)()
>> 859 0.666666666666667
>> 860 """
>> --> 861 return self.numerical_approx(prec, digits, algorithm)
>> 862
>> 863 def _mpmath_(self, prec=53, rounding=None):
>>
>> /usr/local/sage-8/local/lib/python2.7/site-packages/sage/symbolic/expression.pyx
>>
>> in sage.symbolic.expression.Expression.numerical_approx
>> (build/cythonized/sage/symbolic/expression.cpp:33969)()
>> 5949 res = x.pyobject()
>> 5950 else:
>> -> 5951 raise TypeError("cannot evaluate symbolic expression
>> numerically")
>> 5952
>> 5953 # Important -- the we get might not be a valid output
>> for numerical_approx in
>>
>> TypeError: cannot evaluate symbolic expression numerically
>>
>> Let's debug it :
>>
>> def tryit(x):
>> try:
>> return x.n()
>> except:
>> return "Failed..."
>>
>> Let's see :
>>
>> sage: gee=[[u,tryit(u)] for u in bar.operands()]
>> sage: gee
>> [[299/12000*pi, 0.0782780169519457],
>> [-1/198*sqrt(11)*pi*abs(-3/2*sqrt(11)), 'Failed...'],
>> [7/1500*sqrt(1/2), 0.00329983164553722],
>> [1/6*arctan(9799/140*sqrt(1/2)), 0.258432327173397],
>> [-299/6000*arctan(14*sqrt(1/2)), -0.0732611082333419],
>> [299/6000*arctan(1/7*sqrt(1/2)), 0.00501690871860373]]
>>
>> However, when I copy and paste the very same expression (or type it
>> manually), it can be numerically approximated :
>>
>> sage: (-1/198*sqrt(11)*pi*abs(-3/2*sqrt(11))).n()
>> -0.261799387799149
>>
>> Diving recusively :
>>
>> sage: [[u,tryit(u)] for u in bar.operands()[1].operands()]
>> [[sqrt(11), 3.31662479035540],
>> [pi, 3.14159265358979],
>> [abs(-3/2*sqrt(11)), 'Failed...'],
>> [-1/198, -0.00505050505050505]]
>>
>> Again, the litigious expression can be evaluated by copy 'n paste :
>>
>> sage: abs(-3/2*sqrt(11)).n()
>> 4.97493718553310
>>
>> BUT the semi-obvious workaround fails :
>>
>> sage: SR(repr(bar.operands()[1])).n()
>>
>> ---------------------------------------------------------------------------
>> TypeError Traceback (most recent call
>> last)
>> <ipython-input-117-e426b18b4666> in <module>()
>> ----> 1 SR(repr(bar.operands()[Integer(1)])).n()
>>
>> /usr/local/sage-8/local/lib/python2.7/site-packages/sage/structure/element.pyx
>>
>> in sage.structure.element.Element.n
>> (build/cythonized/sage/structure/element.c:8020)()
>> 859 0.666666666666667
>> 860 """
>> --> 861 return self.numerical_approx(prec, digits, algorithm)
>> 862
>> 863 def _mpmath_(self, prec=53, rounding=None):
>>
>> /usr/local/sage-8/local/lib/python2.7/site-packages/sage/symbolic/expression.pyx
>>
>> in sage.symbolic.expression.Expression.numerical_approx
>> (build/cythonized/sage/symbolic/expression.cpp:33969)()
>> 5949 res = x.pyobject()
>> 5950 else:
>> -> 5951 raise TypeError("cannot evaluate symbolic expression
>> numerically")
>> 5952
>> 5953 # Important -- the we get might not be a valid output
>> for numerical_approx in
>>
>> TypeError: cannot evaluate symbolic expression numerically
>>
>> Recurse again :
>>
>> sage: [[u,tryit(u)] for u in bar.operands()[1].operands()[2].operands()]
>> [[-3/2*sqrt(11), -4.97493718553310]]
>>
>> Therefore, the problem seems to be with the numerical approximation of an
>> absolute value.
>>
>> I'm stuck.
>>
>> Two questions :
>>
>> - Ticket worthy (yes, IMHO)
>> - Workaround suggestions ?
>>
>>
>> HTH,
>>
>
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