When integrating sin(x)*cos(2*n*x), n=1,10,20,30, there is a unusual growth
in run-time. I guess that the cause might be found in trigonometric
transformations. Is that so?
Of course we can integrate using the parameter "n" followed by evaluation,
however, I wonder whether this behavior is normal.
(1) -> )set mess time on
(1) -> integrate(sin(x)*cos(2*x),x=0..%pi)
2
(1) - -
3
Type: Union(f1:
OrderedCompletion(Expression(Integer)),...)
Time: 0.00 (IN) + 0.00 (EV) + 0.02 (OT) = 0.02
sec
(2) -> integrate(sin(x)*cos(2*10*x),x=0..%pi)
2
(2) - ---
399
Type: Union(f1:
OrderedCompletion(Expression(Integer)),...)
Time: 0.12 (EV) = 0.12
sec
(3) -> integrate(sin(x)*cos(2*20*x),x=0..%pi)
2
(3) - ----
1599
Type: Union(f1:
OrderedCompletion(Expression(Integer)),...)
Time: 2.90 (EV) = 2.90
sec
(4) -> integrate(sin(x)*cos(2*30*x),x=0..%pi)
2
(4) - ----
3599
Type: Union(f1:
OrderedCompletion(Expression(Integer)),...)
Time: 0.00 (IN) + 33.10 (EV) + 0.00 (OT) = 33.11
sec
...
(5) -> integrate(sin(x)*cos(2*m*x),x=0..%pi)
- cos(2m %pi) - 1
(5) -----------------
2
4m - 1
Type: Union(f1:
OrderedCompletion(Expression(Integer)),...)
Time: 0.00 (IN) + 0.01 (EV) + 0.01 (OT) = 0.03
sec
(8) -> eval(%,m=30)
2
(8) - ----
3599
Type:
Expression(Integer)
Time: 0.03 (IN) + 0.02 (OT) = 0.05
sec
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