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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