dlakelan wrote:
> Bob Baker wrote:
>
>> I too was impressed by what Mathematica could do and looked into getting
>> it. I gave up when I learned they will not sell the student version to
>> a retired electrical engineer pursuing math studies as a hobby. Next
>> year I could get the professional version with a senior discount, but
>> even 50% off is too steep for me.
>>
>
> You might look into taking a class at a local junior college. usually
> that will qualify you as a student. However, I'd prefer to sell you on
> maxima's ability to do a lot of useful stuff. so maybe we can figure out
> how to make maxima do this calculation by fixing some bugs.
>
> i dropped into the debugger when I got the "too many contexts" error,
> and got the following output:
>
>
> invalid array index 51 for #((*GC NIL DATA NIL CMARK 0 SUBC ($INITIAL))
> (*GC NIL SUBC
> ((*GC NIL DATA NIL CMARK 0 SUBC
> ($INITIAL))))
> (*GC NIL SUBC
> ((*GC NIL SUBC
> ((*GC NIL DATA NIL CMARK 0 SUBC
> ($INITIAL))))))
>
>
> ..... several pages
>
> ...
>
>
> ($INITIAL)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
> (should be nonnegative and <51)
>
>
> Perhaps from this error, someone who knows maxima internals can figure
> out what maxima has done wrong. clearly it's created some infinite loop
> or something...
>
> Also, by performing the transformations mentioned by others I found that
> the integrand is the same as:
>
> (cos(5 x) + sqrt(cos(2 x) - 8 cos(x) + 7)
> (sqrt(2) cos(4 x) - 4 sqrt(2) cos(3 x) + sqrt(2) cos(2 x) + 2 sqrt(2))
> - 8 cos(4 x) + 14 cos(3 x) - 8 cos(2 x) + cos(x))
> /(2 cos(2 x) - 16 cos(x) + 14)
>
> the procedure:
> ratsimp(trigreduce(subst(lambda([s], ''(exponentialize(sinh('s)))),
> sinh, integrand(1,3))));
>
> however, maxima still can't integrate this.
>
>
If that's the actual integrand, then perhaps trigexpand will express
cos(n*x) in terms of powers of cos(x) and sin(x). Maxima might be able
to integrate that.
Ray