--Barton
-----maxima-bounces at math.utexas.edu wrote: -----
On 12/17/11, Barton Willis <willisb at unk.edu> wrote:
>> (%i3) integrate (integrate (1+sin(5*x*y+y^2), y, -sqrt(1-x^2),
>> sqrt(1-x^2)), x, -1, 1);
>> defint: lower limit of integration must be real; found -sqrt(1-x^2)
>
> This is a bug. Try tracing sign--Maxima fails to recognize that 1-x^2 is pz.
I dunno. Given that the inner integral is evaluated before the outer one,
there's no way to know that x > -1 and x < 1.
Oh, I thought the calls to make-global-assumptions, assume, and with-new-context in $defint
did sometime useful--apparently not always:
(%i4) defint (defint (1+sin(5*x*y+y^2), y, -sqrt(1-x^2),sqrt(1-x^2)), x, -1, 1);
1> (MAKE-GLOBAL-ASSUMPTIONS)
2> (ASSUME ((MGREATERP) *Z* 0))
<2 (ASSUME ((MGREATERP) *Z* 0))
2> (ASSUME ((MGREATERP) EPSILON 0))
<2 (ASSUME ((MGREATERP) EPSILON 0))
2> (ASSUME ((MLESSP) EPSILON 1.0E-8))
<2 (ASSUME ((MLESSP) EPSILON 1.0E-8))
2> (ASSUME ((MGREATERP) PRIN-INF 1.0E8))
<2 (ASSUME ((MGREATERP) PRIN-INF 1.0E8))
<1 (MAKE-GLOBAL-ASSUMPTIONS
(((MGREATERP) PRIN-INF 1.0E8) ((MLESSP) EPSILON 1.0E-8)
((MGREATERP) EPSILON 0) ((MGREATERP) *Z* 0)))
1> (ASSUME (($NOTEQUAL)
((MPLUS SIMP) 1 ((MTIMES SIMP) -1 ((MEXPT SIMP) $X 2)))
0))
<1 (ASSUME ((MNOT) (($EQUAL) 1 ((MEXPT SIMP) $X 2))))
defint: lower limit of integration must be real; found -sqrt(1-x^2)
-- an error. To debug this try: debugmode(true);