[Maxima-bugs] [ maxima-Bugs-1468951 ] Error in "integrate" output (ver. 5.9.3)

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Bugs item #1468951, was opened at 2006-04-11 21:28
Message generated for change (Comment added) made by rtoy
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Category: Lisp Core - Integration
Group: None
>Status: Pending
Resolution: None
Priority: 5
Private: No
Submitted By: Nobody/Anonymous (nobody)
Assigned to: Nobody/Anonymous (nobody)
Summary: Error in "integrate" output (ver. 5.9.3)

Initial Comment:
Attempting to evaluate integral of a product of bessel
and trigonometric function.  Obtained following output
(error is given in %o5):


%i1) display2d:false;
(%o1) false
(%i2) w:bessel_j(0,2.4048*(r/R0))*cos(%pi*(z/H));
(%o2) bessel_j(0,2.4048*r/R0)*cos(%pi*z/H)
(%i3) phi1:c1*w;
(%o3) bessel_j(0,2.4048*r/R0)*c1*cos(%pi*z/H)
(%i4)
eq1:(1/r)*diff(r*diff(phi1,r,1))+diff(phi1,z,2)+Bsq*phi1=0;
(%o4) ((5.78306304*c1*r^2*cos(%pi*z/H)
		  *(bessel_j(0,2.4048*r/R0)
		   -.4158349966733201*bessel_j(1,2.4048*r/R0)*R0/r)
       /R0^3
      
+2.4048*bessel_j(1,2.4048*r/R0)*c1*r*cos(%pi*z/H)/R0^2)
       *del(R0)
      
-2.4048*%pi*bessel_j(1,2.4048*r/R0)*c1*r*z*sin(%pi*z/H)*del(H)/(H^2*R0)
      
+2.4048*%pi*bessel_j(1,2.4048*r/R0)*c1*r*sin(%pi*z/H)*del(z)/(H*R0)
       +(-5.78306304*c1*r*cos(%pi*z/H)
		    *(bessel_j(0,2.4048*r/R0)
		     -.4158349966733201*bessel_j(1,2.4048*r/R0)*R0/r)
	/R0^2
	-2.4048*bessel_j(1,2.4048*r/R0)*c1*cos(%pi*z/H)/R0)
	*del(r)-2.4048*bessel_j(1,2.4048*r/R0)*r*cos(%pi*z/H)*del(c1)/R0)
       /r
       -%pi^2*bessel_j(0,2.4048*r/R0)*c1*cos(%pi*z/H)/H^2
       +bessel_j(0,2.4048*r/R0)*Bsq*c1*cos(%pi*z/H)
        = 0
(%i5) int1:integrate(integrate(eq1*w*r,r,0,R0),z,0,H);
`rat' replaced 2.4048 by 1503//625 = 2.4048

`rat' replaced 2.4048 by 1503//625 = 2.4048

`rat' replaced -2.4048 by -1503//625 = -2.4048

`rat' replaced -2.4048 by -1503//625 = -2.4048

`rat' replaced 2.4048 by 1503//625 = 2.4048

`rat' replaced -2.4048 by -1503//625 = -2.4048

`rat' replaced 5.78306304 by 16048//2775 =
5.783063063063064

`rat' replaced .4158349966733201 by 625//1503 =
0.41583499667332

`rat' replaced -2.4048 by -1503//625 = -2.4048

`rat' replaced 2.4048 by 1503//625 = 2.4048

`rat' replaced -2.4048 by -1503//625 = -2.4048

`rat' replaced 5.78306304 by 16048//2775 =
5.783063063063064

`rat' replaced .4158349966733201 by 625//1503 =
0.41583499667332

`rat' replaced -2.4048 by -1503//625 = -2.4048

`rat' replaced -2.4048 by -1503//625 = -2.4048

`rat' replaced -5.78306304 by -16048//2775 =
-5.78306306306306

`rat' replaced -0.41583499667332 by -625//1503 =
-0.41583499667332

`rat' replaced 2.4048 by 1503//625 = 2.4048

`rat' replaced -2.4048 by -1503//625 = -2.4048

`rat' replaced 2.4048 by 1503//625 = 2.4048

`rat' replaced 5.78306304 by 16048//2775 =
5.783063063063064

`rat' replaced -0.41583499667332 by -625//1503 =
-0.41583499667332
Is  R0  positive, negative, or zero?

pos;
`rat' replaced 2.4048 by 1503//625 = 2.4048

`rat' replaced 2.4048 by 1503//625 = 2.4048

`rat' replaced -2.4048 by -1503//625 = -2.4048

`rat' replaced -2.4048 by -1503//625 = -2.4048

`rat' replaced -5.78306304 by -16048//2775 =
-5.78306306306306

`rat' replaced -0.41583499667332 by -625//1503 =
-0.41583499667332

`rat' replaced 2.4048 by 1503//625 = 2.4048

`rat' replaced -2.4048 by -1503//625 = -2.4048

`rat' replaced 2.4048 by 1503//625 = 2.4048

`rat' replaced 5.78306304 by 16048//2775 =
5.783063063063064

`rat' replaced -0.41583499667332 by -625//1503 =
-0.41583499667332

`rat' replaced 2.4048 by 1503//625 = 2.4048

`rat' replaced -2.4048 by -1503//625 = -2.4048

`rat' replaced 2.4048 by 1503//625 = 2.4048
(%o5) H*false = 0
(%i6) 

email address: eba...@in...

----------------------------------------------------------------------

>Comment By: Raymond Toy (rtoy)
Date: 2007-06-19 13:30

Message:
Logged In: YES 
user_id=28849
Originator: NO

I don't think this is an integration problem but really an ODE problem, as
Robert mentions.

Marking this as pending so it will be auto-closed in a couple of weeks.

----------------------------------------------------------------------

Comment By: Robert Dodier (robert_dodier)
Date: 2006-04-11 22:10

Message:
Logged In: YES 
user_id=501686

After trying this example a bit, I believe eq1 wants to be
solved with the function ode2 instead of integrate (because
integrate doesn't understand about stuff like dy/dx
appearing in integrands, and it doesn't like <expr> = 0, it
just wants <expr>).

Also to get the appropriate symbolic differentials like
dfoo/dr you *might* need to put depends (foo, r); before the
equation (to enable diff (foo, r); to come out as dfoo/dr).

A couple of ideas to help focus debugging in general. (1)
Replace the floats with equivalent rationals, or better
still replace them with 1's. (2) Try to find a simpler
version of the example.

Try posting a message to the mailing list
(http://maxima.sf.net/maximalist.html), preferably after
simplifying the example. Some people know a lot more about
Maxima's capabilities for diff eq's.


----------------------------------------------------------------------

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