Maxima should never be asking questions involving variables that don't
appear in the input -- that is a bug.
On Mon, Nov 21, 2011 at 14:30, Edwin Woollett <woollett at charter.net> wrote:
> I'm not complaining, and I know Maxima needs user input
> to proceed, even though the answer does not depend on
> the user's input.
>
> I guess the user of integrate should use these
> questions from Maxima as an indication that the definite integral
> below should be checked using other means?
> ------------------------------**------------------------------**---------
> Maxima 5.25.1 http://maxima.sourceforge.net
> using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)
>
>
> (%i1) integrate(acos(%i*x),x,-2,3);
>
> Is W35620 positive or negative?
>
> pos;
> Is W37394 positive or negative?
>
> pos;
> (%o1) %i*(-3*log(sqrt(10)+3)-2*log(**sqrt(5)-2)+sqrt(10)-sqrt(5))+**
> 5*%pi/2
>
> (%i3) float(rectform(integrate(acos(**%i*x),x,-2,3)));
>
> Is W40485 positive or negative?
>
> pos;
> Is W42259 positive or negative?
>
> neg;
> (%o3) 7.853981633974483-1.**641858744669991*%i
> (%i4) float(rectform(integrate(acos(**%i*x),x,-2,3)));
>
> Is W44437 positive or negative?
>
> neg;
> Is W46056 positive or negative?
>
> pos;
> (%o4) 7.853981633974483-1.**641858744669991*%i
> (%i5) float(rectform(integrate(acos(**%i*x),x,-2,3)));
>
> Is W49147 positive or negative?
>
> neg;
> Is W50766 positive or negative?
>
> neg;
> (%o5) 7.853981633974483-1.**641858744669991*%i
> ------------------------------**------------------------------**--
> One way to check just the floating point answer is
> using quad_qag, for example, as in:
> ------------------------------**----------------
>
> (%i6) check(ex,var,v1,v2) :=
> (print(" integrate = ",
> float(rectform(integrate(ex,**var,v1,v2)))),
>
> print(" quad real = ",
> part(quad_qag(realpart(ex),**var,v1,v2,3),1)),
>
> print(" quad imag = ",
> part(quad_qag(imagpart(ex),**var,v1,v2,3),1)))$
>
> (%i7) check(acos(%i*x),x,-2,3)$
>
> Is W52944 positive or negative?
>
> pos;
> Is W54718 positive or negative?
>
> pos;
> integrate = 7.853981633974483-1.**641858744669991*%i
> quad real = 7.853981633974482
> quad imag = -1.64185874466999
> ------------------------------**-----------
>
>
> Ted Woollett
>
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