#560 integrate((1/2)*u^2-1/u^5,u,1,sqrt(2)); is not correct...

[Luis Claudio]

Sorry, but in the integral
(1/2)*u^2-1/u^5 with u=1 to sqrt(2) them Maxima
program return

SQRT(2) 1
------- - -
3 6

Maxima comand: integrate((1/2)*u^2-1/u^5,u,1,sqrt
(2));

But the answer correct is:

sqrt(2) 17
------- - -----
3 48

See in MuPad, Maple or Mathematica.

sorry by english.
Luis Cláudio - Brasilia - Brazil.
luis_claudio2000@yahoo.com.br

[Barton Willis]

Logged In: YES
user_id=895922

Thank you for reporting this bug; I suspect that
the following bug is related to the one you found.

(C2) integrate(1/x^5,x,1,sqrt(2));
(D2) 0
(C3) build_info();

Maxima version: 5.9.0.1cvs
Maxima build date: 8:30 4/21/2004
host type: i686-pc-mingw32
lisp-implementation-type: Kyoto Common Lisp
lisp-implementation-version: GCL 2.7.0

If you find more Maxima bugs, please report them.

Regards,

Barton

[Barton Willis]

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user_id=895922

To integrate 1/x^5 from 1 to sqrt(s), Maxima makes a
change of variable and then it uses residues. But
when 'solvecase' fails to find the poles, it returns failure and
polelist returns nil. After that 'res' believes that there are no
poles so the sum of the residues vanishes.

I can put a trap in initial-analysis that catches more
easy cases and prevents Maxima from using the residue
method---I don't have a fix for the real problem.

(C4) integrate(1/x^5,x,1,sqrt(2));
1> (POLELIST
((MPLUS SIMP IRREDUCIBLE FACTORED) 1
((MTIMES SIMP RATSIMP) 5 ((MEXPT SIMP) 2 ((RAT
SIMP) 1 2))
|$x|)
((MTIMES SIMP) 20 ((MEXPT SIMP RATSIMP) |$x| 2))
((MTIMES SIMP) 20 ((MEXPT SIMP) 2 ((RAT SIMP) 1
2))
((MEXPT SIMP RATSIMP) |$x| 3))
((MTIMES SIMP) 20 ((MEXPT SIMP RATSIMP) |$x| 4))
((MTIMES SIMP) 4 ((MEXPT SIMP) 2 ((RAT SIMP) 1 2))
((MEXPT SIMP RATSIMP) |$x| 5)))
#<compiled-closure 108d7e8c> #<compiled-closure
108d7ea8>)
2> (SOLVECASE
((MPLUS SIMP IRREDUCIBLE FACTORED) 1
((MTIMES SIMP RATSIMP) 5 ((MEXPT SIMP) 2 ((RAT
SIMP) 1 2))
|$x|)
((MTIMES SIMP) 20 ((MEXPT SIMP RATSIMP) |$x|
2))
((MTIMES SIMP) 20 ((MEXPT SIMP) 2 ((RAT SIMP) 1
2))
((MEXPT SIMP RATSIMP) |$x| 3))
((MTIMES SIMP) 20 ((MEXPT SIMP RATSIMP) |$x|
4))
((MTIMES SIMP) 4 ((MEXPT SIMP) 2 ((RAT SIMP) 1
2))
((MEXPT SIMP RATSIMP) |$x| 5))))
<2 (SOLVECASE FAILURE)
<1 (POLELIST NIL)
(D4) 0
(C5)

Compare this to

(C5) integrate(1/x^5,x,1,2);
1> (POLELIST
((MEXPT SIMP FACTORED)
((MPLUS SIMP IRREDUCIBLE) 1 ((MTIMES SIMP
RATSIMP) 2 |$x|))
5)
#<compiled-closure 108d7e8c> #<compiled-closure
108d7ea8>)
2> (SOLVECASE
((MEXPT SIMP FACTORED)
((MPLUS SIMP IRREDUCIBLE) 1 ((MTIMES SIMP
RATSIMP) 2 |$x|))
5))
<2 (SOLVECASE (((MEQUAL SIMP) |$x| ((RAT SIMP) -1 2))
5))
<1 (POLELIST
((((RAT SIMP) -1 2)
((MEXPT SIMP) ((MPLUS SIMP) ((RAT SIMP) 1 2)
|$x|) 5))
((((RAT SIMP) -1 2) 5)) NIL NIL))

(c6) 15 / 64

(DEFUN POLELIST (D REGION REGION1)
(PROG (ROOTS $BREAKUP R RR SS R1 S POLE WFLAG CF)
(SETQ WFLAG T)
(SETQ LEADCOEF (POLYINX D VAR 'LEADCOEF))
(SETQ ROOTS (SOLVECASE D))
(if (eq roots 'failure) (return ())) ;; <-- this is a
trouble maker for res
LOOP1 (COND ((NULL ROOTS)
(COND ((AND SEMIRAT

Barton

[Barton Willis]

fix for residu.lisp

[Barton Willis]

Logged In: YES
user_id=895922

I thought of a fix that isn't terrible. I inserted a
call to gfactor in solvecases. I also put an
merror into polelist---this way a user will get
an error instead of a wrong value should
solvecases ever fail. The gfactor fix seems to
fix this problem.

Barton

[Raymond Toy]

Logged In: YES
user_id=28849

Maxima returns the correct answer now.