Integrating a Taylor series?



The complicated casse does ok.
The f(x) case hangs.
See attachmrents.

-- 
Dennis J. Darland
student at dennisdarland.com
http://dennisdarland.com/
http://dennisdarland.com/philosophy/
http://sode.sourceforge.net/

On Sunday, May 12, 2013 11:15:30 AM Dennis J. Darland wrote:


You're right. This case isn't so bad.
See attachments

BTW: I wasn't saying what I was doing took a lot of time or memory.
-- 
Dennis J. Darland
student at dennisdarland.com
http://dennisdarland.com/
http://dennisdarland.com/philosophy/
http://sode.sourceforge.net/

On Saturday, May 11, 2013 03:12:39 PM you wrote:


Dennis,


Why did you think this should take a long time and lots of memory?


                  -s


On Thu, May 9, 2013 at 5:39 PM, Dennis J. Darland <student at dennisdarland.com[1]> 
wrote:


Dennis J. Darland
student at dennisdarland.com
http://dennisdarland.com/
http://dennisdarland.com/philosophy/
http://sode.sourceforge.net/
It might take a very long time, if you have enough memory!

--



amca01 at gmail.com[2]>writes:>     Alasdair> No, unfortunately - my system (Maxima 
5.24.0) just hangs>     Alasdair> on the "integrate" command and does nothing.>> 
Bummer.  I guess the obvious answer is to update your system to> something newer.  If 
you can.>> Ray>> _______________________________________________> Maxima mailing list> 
Maxima at math.utexas.edu[3]
http://www.math.utexas.edu/mailman/listinfo/maxima[4]
Maxima at math.utexas.edu[3]
http://www.math.utexas.edu/mailman/listinfo/maxima[4]








--------
[1] mailto:student at dennisdarland.com
[2] mailto:amca01 at gmail.com
[3] mailto:Maxima at math.utexas.edu
[4] http://www.math.utexas.edu/mailman/listinfo/maxima
-------------- next part --------------
load("stringproc");
block([fd,t_prev,t_prev,nn,x,a],
fd : openw("timelog_complex.txt"),
t_prev :  elapsed_real_time(),
nn : 1,
while (nn < 101) do  (
integrate(taylor(exp(x) * sin(x )+ cos(x) * x - x*x*x + x/exp(x),x,a,nn),x),
t : elapsed_real_time(),
t_new : t - t_prev,
printf(fd,"order = ~d time = ~g~%",nn,t_new),
t_prev : t,
nn : nn + 1),
close(fd)
);

-------------- next part --------------
load("stringproc");
block([fd,t_prev,t_prev,nn,x,a],
fd : openw("timelog_fx.txt"),
t_prev :  elapsed_real_time(),
nn : 1,
while (nn < 2) do  (
integrate(taylor(f(x),x,a,nn),x),
t : elapsed_real_time(),
t_new : t - t_prev,
printf(fd,"order = ~d time = ~g~%",nn,t_new),
t_prev : t,
nn : nn + 1),
close(fd)
);

-------------- next part --------------
order = 1 time = 1.430900000000001600E-2
order = 2 time = 2.00829999999999900E-2
order = 3 time = 2.690700000000001400E-2
order = 4 time = 3.331900000000001500E-2
order = 5 time = 4.116999999999998400E-2
order = 6 time = 4.631499999999999500E-2
order = 7 time = 6.35339999999999800E-2
order = 8 time = 5.55160000000000100E-2
order = 9 time = 6.26999999999999800E-2
order = 10 time = 7.882400E-2
order = 11 time = 7.33409999999999900E-2
order = 12 time = 7.69100000000000300E-2
order = 13 time = 9.33079999999999500E-2
order = 14 time = 8.88290000000000500E-2
order = 15 time = 0.10421799999999992    
order = 16 time = 0.10162500000000008    
order = 17 time = 0.11993000000000009    
order = 18 time = 0.11358899999999994    
order = 19 time = 0.12854300000000007    
order = 20 time = 0.12421099999999985    
order = 21 time = 0.14280899999999996    
order = 22 time = 0.1508100000000001    
order = 23 time = 0.15921700000000016    
order = 24 time = 0.16918199999999972    
order = 25 time = 0.16862000000000021    
order = 26 time = 0.18107099999999976    
order = 27 time = 0.17750500000000002    
order = 28 time = 0.19491499999999995    
order = 29 time = 0.19672400000000012    
order = 30 time = 0.20449099999999998    
order = 31 time = 0.20807900000000012    
order = 32 time = 0.22156299999999973    
order = 33 time = 0.22266200000000058    
order = 34 time = 0.22449799999999964    
order = 35 time = 0.22614    
order = 36 time = 0.23239199999999993    
order = 37 time = 0.24932900000000036    
order = 38 time = 0.2479969999999998    
order = 39 time = 0.262664    
order = 40 time = 0.26112800000000025    
order = 41 time = 0.2853829999999995    
order = 42 time = 0.28235399999999977    
order = 43 time = 0.2862810000000007    
order = 44 time = 0.30281499999999983    
order = 45 time = 0.30165299999999995    
order = 46 time = 0.3315520000000003    
order = 47 time = 0.3255669999999995    
order = 48 time = 0.3370380000000006    
order = 49 time = 0.34648199999999996    
order = 50 time = 0.3390109999999993    
order = 51 time = 0.35636000000000045    
order = 52 time = 0.36445600000000056    
order = 53 time = 0.3731479999999987    
order = 54 time = 0.3836530000000007    
order = 55 time = 0.39516799999999996    
order = 56 time = 0.41385000000000005    
order = 57 time = 0.41184900000000013    
order = 58 time = 0.4201560000000004    
order = 59 time = 0.43598999999999855    
order = 60 time = 0.4319450000000007    
order = 61 time = 0.43971299999999935    
order = 62 time = 0.4576070000000012    
order = 63 time = 0.4574090000000002    
order = 64 time = 0.46552099999999896    
order = 65 time = 0.4846459999999997    
order = 66 time = 0.48881700000000095    
order = 67 time = 0.506965000000001    
order = 68 time = 0.5147699999999986    
order = 69 time = 0.5133720000000004    
order = 70 time = 0.5327279999999988    
order = 71 time = 0.5438679999999998    
order = 72 time = 0.5508240000000022    
order = 73 time = 0.5501830000000005    
order = 74 time = 0.5690419999999996    
order = 75 time = 0.5836889999999997    
order = 76 time = 0.6231960000000001    
order = 77 time = 0.6425640000000001    
order = 78 time = 0.6376659999999994    
order = 79 time = 0.6517370000000007    
order = 80 time = 0.6626539999999999    
order = 81 time = 0.6816759999999995    
order = 82 time = 0.6808440000000004    
order = 83 time = 0.7072210000000005    
order = 84 time = 0.7064689999999985    
order = 85 time = 0.7286099999999998    
order = 86 time = 0.7458759999999991    
order = 87 time = 0.7646380000000015    
order = 88 time = 0.7762409999999988    
order = 89 time = 0.7730290000000011    
order = 90 time = 0.7949260000000002    
order = 91 time = 0.8067439999999984    
order = 92 time = 0.8109110000000008    
order = 93 time = 0.8427890000000033    
order = 94 time = 0.8444769999999977    
order = 95 time = 0.831040999999999    
order = 96 time = 0.8339500000000015    
order = 97 time = 0.8524949999999976    
order = 98 time = 0.8573730000000026    
order = 99 time = 0.8775459999999953    
order = 100 time = 0.8796540000000022