Re: [Maxima-discuss] Integration asksign bug

[Michel T. <ta...@lp...>]

Le 10/07/2023 à 09:02, Daniel Volinski via Maxima-discuss a écrit :
> limit(log(tan(x)^(2/3)-tan(x)^(1/3)+1)/18,x,0);
> atan2: atan2(0,0) is undefined.

As a matter of fact, this is also what appears in the backtrace of the 
original integral.

  maxima -g

(%i1) integrate(tan(x)^(1/3)/(cos(x)+sin(x))^2,x,0,%pi/2);

asksign: internal error.
  -- an error. To debug this try: debugmode(true);
(%i2) debugmode(true);
(%o2)                                true

(%i3) integrate(tan(x)^(1/3)/(cos(x)+sin(x))^2,x,0,%pi/2);
  -- an error.  Entering the Maxima debugger.
Enter ':h' for help.

(dbm:1) :break

..... in the lisp debugger

0] ba

.... Things related to the debugger

6: (MERROR "atan2: atan2(0,0) is undefined.")
7: (SUBST1 0 $X ((MTIMES SIMP) ((RAT SIMP) 1 3) (($ATAN2 SIMP) 0 ((%SIN 
SIMP) $X))))

....

9: (MAXIMA-SUBSTITUTE 0 $X ((%SIN SIMP IRREDUCIBLE) ((MTIMES SIMP) ((RAT 
SIMP) 1 3) (($ATAN2 SIMP) 0 ((%SIN SIMP) $X)))))

.....

18: (LIMIT1 ((MEXPT SIMP) ((%SIN SIMP IRREDUCIBLE) ((MTIMES SIMP) ((RAT 
SIMP) 1 3) (($ATAN2 SIMP) 0 (# $X)))) 2) $X $ZEROA)

....


I don't know if this is related to Barton's fix, but it seems there is a 
problem when introducing atan2, because

otherwise the limit seems simple at 0.


By the way, the integral in question reduces to a simpler form by 
setting y=tan(x).

(%i1) f: tan(x)^(1/3)/(sin(x)+cos(x))^2$

(%i2) changevar('integrate(f,x),y=tan(x),y,x);

yields the integral of  y^(1/3)/(y+1)^2

(%i3) ev(%,nouns);

yields a formula which is the same as the one returned by the original 
integral when substituting y=tan(x).

The integral of y^(1/3)/(y+1)^2 reduces to a rational one by setting 
y=z^3, which is then more or less

straightforward.



-- 
Michel Talon