This is related to a subtle, undocumented difference between these two
definitions of a symbolic expression:
var('v')
r(v)=v
print r
///
v |--> v
r=v
print r
///
v
so both are printed different, but they return the same value when
called with a question mark:
r?
///
*File:*
/opt/sage-4.1.1/local/lib/python2.6/site-packages/sage/symbolic/expression.so
*Type:* <type 'sage.symbolic.expression.Expression'>
*Definition:* r(*args, **kwds)
*Docstring:*
x.__init__(...) initializes x; see x.__class__.__doc__ for signature
Introducing F by hand pose no problem if the functions are introduced
using the second syntax, but gives the same problem if the first one is
used (only for F0(x)=x, not for F0(x)=2*x).
var('x')
F0(x)=x
print F0
F_bis=Piecewise([[(0, 1), F0], [(1,2), -1/2*x^2 + 4*x - 5/2], [(2, 3),
-1/10*e^2 +1/10*e^x + 7/2], [(3, 10), -1/10*e^2 + 1/10*e^3 -
1/2*cos(2*x)+ 1/2*cos(6) + 7/2]])
print F_bis
///
x |--> x
Piecewise defined function with 4 parts, [[(0, 1), x |--> x], [(1, 2),
-1/2*x^2 + 4*x - 5/2], [(2, 3), -1/10*e^2 + 1/10*e^x + 7/2], [(3, 10),
-1/10*e^2 + 1/10*e^3 - 1/2*cos(2*x) + 1/2*cos(6) + 7/2]]
plot(F_bis)
///
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "_sage_input_86.py", line 4, in <module>
exec compile(ur'plot(F_bis)' + '\n', '', 'single')
File "", line 1, in <module>
File
"/opt/sage-4.1.1/local/lib/python2.6/site-packages/sage/plot/misc.py",
line 243, in wrapper
return func(*args, **kwds)
File
"/opt/sage-4.1.1/local/lib/python2.6/site-packages/sage/plot/misc.py",
line 138, in wrapper
return func(*args, **options)
File
"/opt/sage-4.1.1/local/lib/python2.6/site-packages/sage/plot/plot.py",
line 2444, in plot
G = funcs.plot(*args, **original_opts)
File
"/opt/sage-4.1.1/local/lib/python2.6/site-packages/sage/functions/piecewise.py",
line 961, in plot
return sum([plot(f, a, b, *args, **kwds) for (a,b),f in self.list()])
File
"/opt/sage-4.1.1/local/lib/python2.6/site-packages/sage/plot/misc.py",
line 243, in wrapper
return func(*args, **kwds)
File
"/opt/sage-4.1.1/local/lib/python2.6/site-packages/sage/plot/misc.py",
line 138, in wrapper
return func(*args, **options)
File
"/opt/sage-4.1.1/local/lib/python2.6/site-packages/sage/plot/plot.py",
line 2444, in plot
G = funcs.plot(*args, **original_opts)
File "expression.pyx", line 6059, in
sage.symbolic.expression.Expression.plot
(sage/symbolic/expression.cpp:24894)
File "expression.pyx", line 5951, in
sage.symbolic.expression.Expression._fast_float_
(sage/symbolic/expression.cpp:24305)
File
"/opt/sage-4.1.1/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py",
line 1181, in fast_float
return FastFloatConverter(ex, *vars)()
File
"/opt/sage-4.1.1/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py",
line 208, in __call__
return self.symbol(ex)
File
"/opt/sage-4.1.1/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py",
line 1099, in symbol
raise ValueError, "free variable: %s" % repr(ex)
ValueError: free variable: x |--> x
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