Dr. Stein: The assume() command worked.
Thanks.
Tim: Thanks for your reply, too.
I noticed that I was integrating wrt y twice after
I sent off the email, but the result was still the same
if you change the outermost integration to be wrt x.
Thanks
On Dec 4, 3:07 pm, "William Stein" <[EMAIL PROTECTED]> wrote:
> On Thu, Dec 4, 2008 at 12:57 PM, Vijay <[EMAIL PROTECTED]> wrote:
>
> > Hi: I am trying to evaluate a double integral (since I cannot put
> > LaTeX, the 'S' below
> > stands for the integral sign:)
>
> > 1 sqrt(x)
> > S S 4xy - y^3 dy dx
> > 0 x^3
>
> > This is what I put into sage:
>
> > sage: var('x,y')
> > (x, y)
> > sage: f=4*x*y-y^3
> > sage: print f
> > 3
> > 4 x y - y
>
> > sage: print integrate(integrate(f,y,x^3,x^0.5),y,0,1)
> > ---------------------------------------------------------------------------
> > TypeError Traceback (most recent call
> > last)
>
> > /home/vkg/sage-3.1.1/<ipython console> in <module>()
>
> > /home/vkg/sage-3.1.1/local/lib/python2.5/site-packages/sage/calculus/
> > functional.
> > py in integral(f, *args, **kwds)
> > 252 """
> > 253 try:
> > --> 254 return f.integral(*args, **kwds)
> > 255 except ValueError, err:
> > 256 raise err
>
> > /home/vkg/sage-3.1.1/local/lib/python2.5/site-packages/sage/calculus/
> > calculus.py
> > in integral(self, v, a, b)
> > 2523 raise ValueError, "Integral is divergent."
> > 2524 else:
> > -> 2525 raise TypeError, error
> > 2526
> > 2527
>
> > TypeError: Computation failed since Maxima requested additional
> > constraints (use
> > assume):
> > Is x positive or negative?
>
> > Am I doing something wrong here?
>
> Use the assume command to get past this. Here's a complete session that shows
> what to do:
>
> sage: var('x,y')
> sage: f=4*x*y-y^3
> sage: print f
> 3
> 4 x y - y
> sage: print integrate(integrate(f,y,x^3,x^0.5),y,0,1)
> boom
> sage: forget(); assume(x>0)
> sage: print integrate(integrate(f,y,x^3,x^0.5),y,0,1)
> 12 7 2.0 2
> x - 8 x x - 8 x
> ---------- - -----------
> 4 4
> sage: forget(); assume(x<0)
> sage: print integrate(integrate(f,y,x^3,x^0.5),y,0,1)
> Traceback (most recent call last):
> ...
> TypeError: Error executing code in Maxima
>
> Do you think it would be better if instead of
>
> sage: print integrate(integrate(f,y,x^3,x^0.5),y,0,1)
> ... Is x positive or negative?
>
> one saw:
> ... Is x positive or negative? (Try using the assume command.)
>
> William
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