integrate hangs with acos(1+%i*x)
- Subject: integrate hangs with acos(1+%i*x)
- From: Michel Talon
- Date: Tue, 22 Nov 2011 15:03:58 +0000 (UTC)
Robert Dodier wrote:
> integrate(acos(1+%i*x),x,-1,2);
hangs.
Indeed i see the same here under sbcl and maxima 5.25.1.
I have a backtrace which supports looping always on the same computation:
0: (SB-KERNEL:TWO-ARG-+ -4199579596574115072 -317738973225728000)
1: (CPLUS -4199579596574115072 -317738973225728000)
2: (PCPLUS -317738973225728000 -4199579596574115072)
3: (PPLUS -317738973225728000 -4199579596574115072)
4: (PPLUS1
(14 -317738973225728000 10 1470207527488473600 6 -197927315224332800)
(14 -4199579596574115072 10 10377946040669729152 6 -940439922132963072 2
2014186520221184))
5: (PPLUS1
(18 -4497499316480000 14 -317738973225728000 10 1470207527488473600 6
-197927315224332800)
(18 -111090916028310400 14 -4199579596574115072 10 10377946040669729152 6
-940439922132963072 2 2014186520221184))
6: (PPLUS
(#:|cos(atan(2/(?g3298-1))/2)3381| 18 -111090916028310400 14
-4199579596574115072 10 10377946040669729152 6 -940439922132963072 2
2014186520221184)
(#:|cos(atan(2/(?g3298-1))/2)3381| 18 -4497499316480000 14
-317738973225728000 10 1470207527488473600 6 -197927315224332800))
7: (PTIMES1
(44 (#:|cos(atan(2/(?g3298-1))/2)3381| 1 3548232542740416) 43
(#:|cos(atan(2/(?g3298-1))/2)3381| 2 6479997022956096) 42
(#:|cos(atan(2/(?g3298-1))/2)3381| 3 -3222785130866112) 41
(#:|cos(atan(2/(?g3298-1))/2)3381| 4 -12202858201253952 0
321141710217408)
40
(#:|cos(atan(2/(?g3298-1))/2)3381| 5 -50326150422114432 1
1581529052717568)
39
(#:|cos(atan(2/(?g3298-1))/2)3381| 6 -79274235964789632 2
1223110823844288)
...)
(28 -1150000 27 (#:|cos(atan(2/(?g3298-1))/2)3381| 1 -4350000) 26
(#:|cos(atan(2/(?g3298-1))/2)3381| 2 -4350000) 25
(#:|cos(atan(2/(?g3298-1))/2)3381| 3 -4850000) 24
(#:|cos(atan(2/(?g3298-1))/2)3381| 4 -7150000 0 -50000) 23
(#:|cos(atan(2/(?g3298-1))/2)3381| 5 -14050000 1 -400000) ...))
8: (PTIMES
(#:|sin(atan(2/(?g3298-1))/2)3382| 44
(#:|cos(atan(2/(?g3298-1))/2)3381| 1 3548232542740416) 43
(#:|cos(atan(2/(?g3298-1))/2)3381| 2 6479997022956096) 42
(#:|cos(atan(2/(?g3298-1))/2)3381| 3 -3222785130866112) 41
(#:|cos(atan(2/(?g3298-1))/2)3381| 4 -12202858201253952 0
321141710217408)
40
(#:|cos(atan(2/(?g3298-1))/2)3381| 5 -50326150422114432 1
1581529052717568)
39 ...)
(#:|sin(atan(2/(?g3298-1))/2)3382| 28 -1150000 27
(#:|cos(atan(2/(?g3298-1))/2)3381| 1 -4350000) 26
(#:|cos(atan(2/(?g3298-1))/2)3381| 2 -4350000) 25
(#:|cos(atan(2/(?g3298-1))/2)3381| 3 -4850000) 24
(#:|cos(atan(2/(?g3298-1))/2)3381| 4 -7150000 0 -50000) 23 ...))
9: (PTIMES1
(28
(#:|sin(atan(2/(?g3298-1))/2)3382| 28 4 26
(#:|cos(atan(2/(?g3298-1))/2)3381| 2 8) 24
(#:|cos(atan(2/(?g3298-1))/2)3381| 4 20))
27
(#:|sin(atan(2/(?g3298-1))/2)3382| 28 -112 27
(#:|cos(atan(2/(?g3298-1))/2)3381| 1 -16) 26
(#:|cos(atan(2/(?g3298-1))/2)3381| 2 -224) 25
(#:|cos(atan(2/(?g3298-1))/2)3381| 3 -32) 24
(#:|cos(atan(2/(?g3298-1))/2)3381| 4 -560) 23 ...)
26
(#:|sin(atan(2/(?g3298-1))/2)3382| 28 1608 27
(#:|cos(atan(2/(?g3298-1))/2)3381| 1 432) 26
(#:|cos(atan(2/(?g3298-1))/2)3381| 2 3224) 25
(#:|cos(atan(2/(?g3298-1))/2)3381| 3 864) 24
(#:|cos(atan(2/(?g3298-1))/2)3381| 4 8056 0 8) 23 ...)
25
(#:|sin(atan(2/(?g3298-1))/2)3382| 28 -15600 27
(#:|cos(atan(2/(?g3298-1))/2)3381| 1 -6000) 26
??.
--
Michel Talon