I am trying to define piecewise linear functions, and then integrate them.
But I get an error
AttributeError: 'sage.rings.integer.Integer' object has no attribute
'function'
when one of the pieces is a constant function. Strangely, the same code
works when
the function is non-constant.
Here is a printout of a session exhibiting both the error (for a constant
piece), and correct
behavior (for a non-constant piece).
----------------------------------------------------------------------------------------------------------------------------------
06:11:51 notes $ /Applications/sage/sage
Detected SAGE64 flag
Building Sage on OS X in 64-bit mode
----------------------------------------------------------------------
| Sage Version 4.6.1, Release Date: 2011-01-11 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: f0(x) = 0
sage: type(f0)
<type 'sage.symbolic.expression.Expression'>
sage: f = Piecewise([[(0,1),f0]])
sage: f
Piecewise defined function with 1 parts, [[(0, 1), x |--> 0]]
sage: f.integral(x,0,1)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
/Users/rivest/notes/<ipython console> in <module>()
/Applications/sage/local/lib/python2.6/site-packages/sage/functions/piecewise.pyc
in integral(self, x, a, b, definite)
789 """
790 if a != None and b != None:
--> 791 F = self.integral(x)
792 return F(b) - F(a)
793
/Applications/sage/local/lib/python2.6/site-packages/sage/functions/piecewise.pyc
in integral(self, x, a, b, definite)
831 if definite or end != infinity:
832 area += fun.integral(x, start, end)
--> 833 new_pieces.append([(start, end),
fun_integrated.function(x)])
834
835 if definite:
/Applications/sage/local/lib/python2.6/site-packages/sage/structure/element.so
in sage.structure.element.Element.__getattr__
(sage/structure/element.c:2666)()
/Applications/sage/local/lib/python2.6/site-packages/sage/structure/parent.so
in sage.structure.parent.getattr_from_other_class
(sage/structure/parent.c:2840)()
/Applications/sage/local/lib/python2.6/site-packages/sage/structure/parent.so
in sage.structure.parent.raise_attribute_error
(sage/structure/parent.c:2611)()
AttributeError: 'sage.rings.integer.Integer' object has no attribute
'function'
sage: f.integral()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
/Users/rivest/notes/<ipython console> in <module>()
/Applications/sage/local/lib/python2.6/site-packages/sage/functions/piecewise.pyc
in integral(self, x, a, b, definite)
831 if definite or end != infinity:
832 area += fun.integral(x, start, end)
--> 833 new_pieces.append([(start, end),
fun_integrated.function(x)])
834
835 if definite:
/Applications/sage/local/lib/python2.6/site-packages/sage/structure/element.so
in sage.structure.element.Element.__getattr__
(sage/structure/element.c:2666)()
/Applications/sage/local/lib/python2.6/site-packages/sage/structure/parent.so
in sage.structure.parent.getattr_from_other_class
(sage/structure/parent.c:2840)()
/Applications/sage/local/lib/python2.6/site-packages/sage/structure/parent.so
in sage.structure.parent.raise_attribute_error
(sage/structure/parent.c:2611)()
AttributeError: 'sage.rings.integer.Integer' object has no attribute
'function'
Sage: fx(x) = x
sage: type(fx)
<type 'sage.symbolic.expression.Expression'>
sage: g = Piecewise([[(0,1),fx]])
sage: g
Piecewise defined function with 1 parts, [[(0, 1), x |--> x]]
sage: g.integral()
Piecewise defined function with 1 parts, [[(0, 1), x |--> 1/2*x^2]]
sage:
This looks like a bug.
Is there a work-around??
Cheers,
Ron Rivest
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